Investigation of β^--decay half-life and delayed neutron emission with uncertainty analysis

Investigation of β - -decay half-life and delayed neutron emission with uncertainty analysis 1 2 3 first-author 3 3 corresp † yuancx@mail.sysu.edu.cn † yuancx@mail.sysu.edu.cn yuancx@mail.sysu.edu.cn https://orcid.org/0000-0002-3495-3614 Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China School of Nuclear Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China Sino-French Institute of Nuclear Engineering and Technology, Sun Yat-Sen University, Zhuhai 519082, China β -decay half-life and β -delayed neutron emission ( βn ) are of great importance in the development of basic science and industrial applications, such as nuclear physics and nuclear energy, where β - -decay plays an important role. Many theoretical models have been proposed to describe β -decay half-lives, whereas the systematic study of βn is still rare. This study aimed to investigate β - -decay half-lives and βn probabilities through analytical formulas and by comparing them with experimental data. Analytical formulas for β - -decay properties have been proposed by considering prominent factors, that is, decay energy, odevity, and the shell effect. The bootstrap method was used to simultaneously evaluate the total uncertainty on calculations, which was composed of statistic and systematic uncertainties. β - -decay half-lives, βn probabilities, and the corresponding uncertainties were evaluated for the neutron-rich region. The experimental half-lives were well reproduced. Additional predictions are also presented with theoretical uncertainties, which helps to better understand the disparity between the experimental and theoretical results. Neutron-rich nucleus β -delayed neutron emissions Bootstrap method Introduction 1 The β -decay of exotic nuclei, especially approaching the proton dripline [ 1 1 - 3 3 1-3 ] and neutron dripline [ 4 4 - 6 6 4-6 ], has been focused on in recent decades. The development of experimental setups and techniques [ 7 7 - 9 9 7-9 ] provides more experimental data for theoretical investigations and enables more theoretical research tools [ 10 10 - 12 12 10-12 ]. However, estimating the related p roperties with satisfactory accuracy remains a challenge owing to the complexity of the nuclear structure and interactions between nucleons [ 5 5 ]. The study of β - -decay and β - -delayed neutron emission ( βn ) is of great importance in the development of both basic nuclear physics [ 13 13 - 15 15 13-15 ] and applied nuclear physics [ 16 16 , 17 17 ]. In parameterizing the observed properties of atomic nuclei, some studies used quasiparticle random phase approximation based on energy density functionals [ 18 18 - 20 20 18-20 ] or semi-empirical models [ 21 21 - 23 23 21-23 ], while others have proceeded from a microscopic perspective, such as interacting bosons models [ 24 24 - 26 26 24-26 ] and the Hartree-Fock-Bogoliubov framework [ 27 27 - 30 30 27-30 ]. Such microscopic calculations, even with certain approximations on interactions and/or wavefunctions, are still time-consuming. Neat and reliable formulas are beneficial for the study of β -decay. Phenomenological models have been successively proposed for β - -decay [ 31 31 - 33 33 31-33 ]. Along with the development of high-precision experimental techniques, we are gradually compensating for the deficiency in experimental data on β - -decay [ 34 34 - 36 36 34-36 ], especially for nuclei near the neutron shell closures of 50 and 82 [ 37 37 - 39 39 37-39 ]. Therefore, a new systematic study is of interest and helps to understand β - -delayed neutron emission more comprehensively with reliable calculations. This study focused on the β - -decay half-life T 1/2 and βn probability P βn of neutron-rich nuclei. Analytical formulas for the β - -decay strength are proposed based on standard β -decay theory with further physics considerations on decay energy, odevity, and the shell effect. Moreover, the bootstrap method was used to evaluate the uncertainties on calculations. According to previous studies on β - -decay, the contribution of the first-forbidden (FF) transition to the total decay rate has been found as not negligible for nuclei far from the β -stable valley [ 40 40 , 23 23 , 41 41 ]. Note that we equated FF branches and other forbidden transitions to one or two effective Gamow-Teller (GT) branches in this study. For a better evaluation of β - -delayed neutrons, this study was only concerned with neutron-rich nuclei with Z = 29 ∼ 57, which included important fission products and the precursors of the delayed neutron in the nuclear reactor [ 42 42 ]. The experimental data used for this study was taken from the newest compilation and evaluation of β -delayed neutron emission probabilities and half-lives for Z > 28 precursors provided by the AME-2020 [ 36 36 , 43 43 ]. The main purposes of this study were to determine the parameters of the analytical formulas to describe T 1/2 and P βn , to estimate the uncertainties on corresponding formulas using the bootstrap method, and to make predictions for nuclei without experimental data on T 1/2 and P βn . Methods 1 Theoretical derivation and formulas 2 In this study, we investigated the half-lives of the β - -decay and βn probabilities of neutron-rich nuclei. According to Fermi’s β -decay theory, the standard formula of the β - -decay half-life T 1/2 through the Fermi and GT transitions is as follows [ 44 44 ]: <math display="block" id="M1"><mrow><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo>=</mo><mfrac><mi>κ</mi><mrow><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><msub><mi>B</mi><mtext>F</mtext></msub><mo>+</mo><msub><mi>B</mi><mrow><mtext>GT</mtext></mrow></msub><mo stretchy="false">)</mo></mrow></mfrac><mn>,</mn></mrow></math> where <math id="M2"><mrow><mi>κ</mi><mo>≡</mo><mfrac><mrow><mn>2</mn><msup><mi>π</mi><mn>3</mn></msup><msup><mi>ℏ</mi><mn>7</mn></msup><mi>ln</mi><mn>2</mn></mrow><mrow><msubsup><mi>m</mi><mtext>e</mtext><mn>5</mn></msubsup><msup><mi>c</mi><mn>4</mn></msup><msubsup><mi>G</mi><mtext>F</mtext><mn>2</mn></msubsup></mrow></mfrac><mo>=</mo><mn>6147</mn></mrow></math> s, B F and B GT are the reduced transition probability term for the Fermi and GT transitions, respectively, and f 0 is the phase-space factor, also known as the Fermi integral. With the Primakoff–Rosen approximation [ 45 45 ] applied to f 0 , Eq. (1) was simplified to a manipulable form, which also imposed a relatively high value of the β -decay energy Q β for the constraint on the selection of experimental data. All nuclei in this study were selected with Q β greater than 3 MeV, taken from a new compilation [ 43 43 , 36 36 ]. All other branches were equated to one or two effective GT branches, and a logarithmic formula was derived from Eq. (1) with the same notations as in Eq. (2) in removing the term B F . <math display="block" id="M3"><mtable columnalign="left"><mtr><mtd><mo>−</mo><mi>ln</mi><mo stretchy="false">(</mo><msub><mi>B</mi><mrow><mtext>GT</mtext></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mi>ln</mi><mo stretchy="false">(</mo><mi>κ</mi><mo stretchy="false">)</mo><mo>+</mo><mi>ln</mi><mrow><mo>[</mo><mrow><mfrac><mrow><mn>2</mn><mi>π</mi><mi>α</mi><msub><mi>Z</mi><mtext>f</mtext></msub></mrow><mrow><mn>1</mn><mo>−</mo><mi>exp</mi><mo stretchy="false">(</mo><mo>−</mo><mn>2</mn><mi>π</mi><mi>α</mi><msub><mi>Z</mi><mtext>f</mtext></msub><mo stretchy="false">)</mo></mrow></mfrac></mrow><mo>]</mo></mrow><mn>,</mn></mtd></mtr><mtr><mtd><mo>+</mo><mi>ln</mi><mo stretchy="false">(</mo><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub><mo stretchy="false">)</mo><mo>+</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mrow><mn>30</mn></mrow></mfrac><mrow><mo>(</mo><mrow><msubsup><mi>E</mi><mn>0</mn><mn>5</mn></msubsup><mo>−</mo><mn>10</mn><msubsup><mi>E</mi><mn>0</mn><mn>2</mn></msubsup><mo>+</mo><mn>15</mn><msub><mi>E</mi><mn>0</mn></msub><mo>−</mo><mn>6</mn></mrow><mo>)</mo></mrow></mrow><mo>)</mo></mrow><mn>,</mn></mtd></mtr></mtable></math> where <math id="M4"><mrow><msub><mi>E</mi><mn>0</mn></msub><mo>≡</mo><mfrac><mrow><msub><mi>E</mi><mtext>i</mtext></msub><mo>−</mo><msub><mi>E</mi><mtext>f</mtext></msub></mrow><mrow><msub><mi>m</mi><mtext>e</mtext></msub><msup><mi>c</mi><mn>2</mn></msup></mrow></mfrac></mrow></math> , E i and E f are the energy levels of the initial and final states, respectively, whose difference ( E i - E f ) is consequently the decay energy Q β , and Z f is the number of protons of the daughter nucleus. Subsequently, a linear formula describing -ln( B GT ) was established based on physical meanings. After β -decay, an odd-odd (oo) nucleus decays into an even-even (ee) nucleus, whereas an odd-A (oA) nucleus decays into another oA nucleus. Q β , calculated from ground state to ground state, does not necessarily reflect the actuality of E 0 of the effective branch. Thus, multiplicative factors were introduced to include the odevity in E 0 . Moreover, the oo nucleus more likely decays into the excited state of the ee nucleus for small effective decay energies because the angular momentum of the ground state of the oo parent nucleus tends to differ significantly from that of the ground state of the ee daughter nucleus. With a similar analysis for the case of oA and ee nuclei, there is a pronounced stratification of reduced transition intensities of the three types owing to the different magnitudes of the multiplicative factors. Considering Eq. (2) and the differences in effective decay energy owing to different odevities, a new formula was accordingly constructed for -ln( B GT ) with the Dirac function, <math display="block" id="M5"><mrow><mo>−</mo><mi>ln</mi><mo stretchy="false">(</mo><msub><mi>B</mi><mrow><mtext>GT</mtext></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>δ</mi><mrow><mtext>oA</mtext></mrow></msub><mo>+</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>δ</mi><mrow><mtext>oo</mtext></mrow></msub><mn>.</mn></mrow></math> The Dirac functions δ oo and δ oA can discern the odevity. The corresponding term for ee nuclei was set as a constant, a 0 . Furthermore, the pronounced peaks of the -ln( B GT ) values observed in the distribution of experimental data are bound up with the periodic arrangement of the nuclei, namely, the shell effect of the nucleus. Therefore, a correction term, a 3 x 3 , for the shell effect was added, <math display="block" id="M6"><mrow><mo>−</mo><mi>ln</mi><mo stretchy="false">(</mo><msub><mi>B</mi><mrow><mtext>GT</mtext></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>δ</mi><mrow><mtext>oA</mtext></mrow></msub><mo>+</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>δ</mi><mrow><mtext>oo</mtext></mrow></msub><mo>+</mo><msub><mi>a</mi><mn>3</mn></msub><msub><mi>x</mi><mn>3</mn></msub><mn>,</mn></mrow></math> where a 0 , a 1 , a 2 , and a 3 are fitting parameters, <math id="M7"><mrow><msub><mi>x</mi><mn>3</mn></msub><mo>=</mo><mstyle displaystyle="true"><msub><mo>∑</mo><mrow><msub><mi>N</mi><mi>k</mi></msub><mn>,</mn><msub><mi>Z</mi><mi>k</mi></msub></mrow></msub></mstyle><mi>exp</mi><mrow><mo>[</mo><mrow><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>N</mi><mo>−</mo><msub><mi>N</mi><mi>k</mi></msub></mrow><mn>5</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup><mo>−</mo><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mi>Z</mi><mo>−</mo><msub><mi>Z</mi><mi>k</mi></msub></mrow><mn>5</mn></mfrac></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow><mo>]</mo></mrow></mrow></math> , and N k and Z k describe the shell and sub-shell structures and were chosen to be (50, 32) and (82, 50) according to the locations of distinct peak points. Eqs. (3) and (4) can only describe a single decay branch without considering the βn branch. In the below content, β o denotes the branch that is not βn . The relations between β -decay half-life and βn probability are as follows: <math display="block" id="M8"><mrow><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub><mo>+</mo><msub><mi>P</mi><mrow><mi>β</mi><mtext>o</mtext></mrow></msub><mo>=</mo><mn>1,</mn></mrow></math> <math display="block" id="M9"><mrow><mfrac><mn>1</mn><mrow><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><msub><mi>T</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><msub><mi>T</mi><mrow><mi>β</mi><mtext>o</mtext></mrow></msub></mrow></mfrac><mn>,</mn></mrow></math> <math display="block" id="M10"><mrow><mo>−</mo><mi>ln</mi><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub><mo>=</mo><mo>−</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>T</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msub></mrow><mrow><msub><mi>T</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mn>,</mn></mrow></math> <math display="block" id="M11"><mrow><mo>−</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow><mrow><mn>1</mn><mo>−</mo><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mo>=</mo><mo>−</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>T</mi><mrow><mi>β</mi><mtext>o</mtext></mrow></msub></mrow><mrow><msub><mi>T</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mn>,</mn></mrow></math> where T βn ( T βo ) and P βn ( P βo ) denote the partial half-life and probability of the βn ( β o ) branch. Thus, an analogical formula could be proposed for -ln( P βn ) with a new optimizing term for the effect of the difference between Q βn and Q β on the βn probability, <math display="block" id="M12"><mrow><mo>−</mo><mi>ln</mi><mo stretchy="false">(</mo><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>δ</mi><mrow><mtext>oA</mtext></mrow></msub><mo>+</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>δ</mi><mrow><mtext>oo</mtext></mrow></msub><mo>+</mo><msub><mi>a</mi><mn>3</mn></msub><msub><mi>x</mi><mn>3</mn></msub><mo>+</mo><msub><mi>a</mi><mn>4</mn></msub><msub><mi>x</mi><mn>4</mn></msub><mn>,</mn></mrow></math> where <math id="M13"><mrow><msub><mi>x</mi><mn>4</mn></msub><mo>=</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>Q</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow><mrow><msub><mi>m</mi><mtext>e</mtext></msub><msup><mi>c</mi><mn>2</mn></msup></mrow></mfrac></mrow><mo>)</mo></mrow><mo>−</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>Q</mi><mrow><mi>β</mi><mtext>o</mtext></mrow></msub></mrow><mrow><msub><mi>m</mi><mtext>e</mtext></msub><msup><mi>c</mi><mn>2</mn></msup></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> , and Q βn ( Q βo ) denotes the decay energy of the βn ( β o ) branch from ground state to ground state. This makes use of a direct logarithmization of P βn , yet it may obtain nonphysical results during fitting, that is, P βn > 1. P βn was replaced by <math id="M14"><mrow><mfrac><mrow><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow><mrow><mn>1</mn><mo>−</mo><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow></math> to avoid such results, and the derived formula is expressed as <math display="block" id="M15"><mrow><mo>−</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow><mrow><mn>1</mn><mo>−</mo><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow><mo>=</mo><msub><mi>a</mi><mn>0</mn></msub><mo>+</mo><msub><mi>a</mi><mn>1</mn></msub><msub><mi>δ</mi><mrow><mtext>oA</mtext></mrow></msub><mo>+</mo><msub><mi>a</mi><mn>2</mn></msub><msub><mi>δ</mi><mrow><mtext>oo</mtext></mrow></msub><mo>+</mo><msub><mi>a</mi><mn>3</mn></msub><msub><mi>x</mi><mn>3</mn></msub><mo>+</mo><msub><mi>a</mi><mn>4</mn></msub><msub><mi>x</mi><mn>4</mn></msub><mn>.</mn></mrow></math> Bootstrap method 2 This study evaluated the fitting parameters and uncertainties of β - -decay half-lives and βn probabilities by applying the bootstrap method. In applied statistics, the bootstrap method was proposed by Efron Bradley in 1985 [ 46 46 ] and used to determine the accuracy of estimating the unknown parameters of a chosen estimator through the basic idea of resampling [ 47 47 ]. After the first proposal of its application on alpha decay laws [ 47 47 ], it was successfully applied to the uncertainty determination of nuclear mass models [ 48 48 , 49 49 ], proton decay stability [ 49 49 ], and the binary cluster model [ 50 50 ]. Similar to Monte Carlo events, a new dataset was obtained by resampling with replacements from a given experimental dataset. A group of parameters in the model was obtained by minimizing the root-mean-square of the residuals. Repeating this process M times, the total uncertainty was thus <math display="block" id="M16"><mrow><msub><mi>σ</mi><mrow><mtext>tot</mtext></mrow></msub><mo>=</mo><msqrt><mrow><mfrac><mn>1</mn><mrow><mi>M</mi><mi>K</mi></mrow></mfrac><mstyle displaystyle="true"><munder><mo>∑</mo><mrow><mi>m</mi><mn>,</mn><mi>k</mi></mrow></munder></mstyle><msup><mrow><mo stretchy="false">(</mo><msub><mi>r</mi><mrow><mi>m</mi><mn>,</mn><mi>k</mi></mrow></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></mrow></msqrt><mn>,</mn></mrow></math> where m denotes the m th resampling of the dataset, k denotes the k th nucleus in the original dataset among the K nuclei, and r m, k is the residual between the observed value and its estimated value from the m th replication of bootstrap for the k th nucleus. The total uncertainty was then decomposed into the statistical uncertainty σ sys and systematic uncertainty σ sys , which can be written as <math display="block" id="M17"><mrow><msub><mi>σ</mi><mrow><mtext>stat</mtext></mrow></msub><mo>=</mo><msqrt><mrow><mfrac><mn>1</mn><mrow><mo stretchy="false">(</mo><mi>M</mi><mo>−</mo><mn>1</mn><mo stretchy="false">)</mo><mi>K</mi></mrow></mfrac><mstyle displaystyle="true"><munder><mo>∑</mo><mrow><mi>m</mi><mn>,</mn><mi>k</mi></mrow></munder></mstyle><msup><mrow><mo stretchy="false">(</mo><msub><mi>r</mi><mrow><mi>m</mi><mn>,</mn><mi>k</mi></mrow></msub><mo>−</mo><msub><mrow><mover accent="true"><mi>r</mi><mo stretchy="true">¯</mo></mover></mrow><mi>k</mi></msub><mo stretchy="false">)</mo></mrow><mn>2</mn></msup></mrow></msqrt><mn>,</mn></mrow></math> <math display="block" id="M18"><mrow><msub><mi>σ</mi><mrow><mtext>sys</mtext></mrow></msub><mo>=</mo><msqrt><mrow><mfrac><mn>1</mn><mi>K</mi></mfrac><mstyle displaystyle="true"><munder><mo>∑</mo><mi>k</mi></munder></mstyle><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mn>1</mn><mi>M</mi></mfrac><mstyle displaystyle="true"><munder><mo>∑</mo><mi>m</mi></munder></mstyle><msub><mi>r</mi><mrow><mi>m</mi><mn>,</mn><mi>k</mi></mrow></msub></mrow><mo>)</mo></mrow></mrow><mn>2</mn></msup></mrow></msqrt><mn>.</mn></mrow></math> In this study, this method was used to assess the uncertainty on Eqs. (3), (4), (9), and (10). The global systematic uncertainty of model deficiency, σ sys , and the statistical uncertainty appropriate to the specific nucleus were combined to evaluate the confidence interval. <math display="block" id="M19"><mrow><msub><mi>σ</mi><mrow><mtext>pred</mtext><mn>,</mn><mi>k</mi></mrow></msub><mo>=</mo><msqrt><mrow><msubsup><mi>σ</mi><mrow><mtext>stat</mtext><mn>,</mn><mi>k</mi></mrow><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>σ</mi><mrow><mtext>sys</mtext></mrow><mn>2</mn></msubsup></mrow></msqrt><mn>.</mn></mrow></math> Because the reduced transition probability term and the probabilities of the βn and β o branches were in the logarithmic form, the uncertainties obtained were propagated to be different positive and negative deviations when the half-lives and probabilities were further calculated. Results and discussions 1 Next, the half-life of β - decay and the probability of occurrence of βn decay were investigated using two experimental datasets and several previously proposed formulas. The bootstrap method was used to deal with the uncertainty analysis. One effective decay branch 2 Nuclei were carefully selected from the newest compilation and evaluation with experimental half-lives smaller than 2 s and Q greater than 3 MeV because forbidden transitions may dominate long-lived transitions and are not suitable for study as effective GT branches. Nuclei with βn basically meet these two conditions. Among 256 selected nuclei, two datasets were taken: one containing all 256, which have half-life measurements, and the other containing 133, which have βn probability measurements. Based on the assumption of one effective decay, the bootstrap method was used to investigate the first dataset, as listed in Table1 Table1 . The shell effect did contribute to the description of half-lives, as indicated by the decreasing systematic uncertainty. Fig. 1 Fig. 1 shows the results of the difference between the observed data and calculation corresponding to Eqs. (3) and (4). In general, the latter with the shell effect reproduced better than the former, especially where the major shell and sub-shell closures were located. 1 1   4 1 Fitting parameters 3 1 Uncertainties 1 1   1 1 a 0 1 1 a 1 1 1 a 2 1 1 a 3 1 1 <math id="M23"><mrow><msubsup><mi>σ</mi><mrow><mtext>stat</mtext></mrow><mn>2</mn></msubsup></mrow></math> 1 1 <math id="M24"><mrow><msubsup><mi>σ</mi><mrow><mtext>sys</mtext></mrow><mn>2</mn></msubsup></mrow></math> 1 1 <math id="M25"><mrow><msubsup><mi>σ</mi><mrow><mtext>tot</mtext></mrow><mn>2</mn></msubsup></mrow></math> 1 1 Equation (3) 1 1 0.8938 1 1 1.0489 1 1 1.9296 1 1 - 1 1 0.0059 1 1 0.4887 1 1 0.4946 1 1 Equation (4) 1 1 0.5053 1 1 1.0450 1 1 1.9081 1 1 0.9459 1 1 0.0053 1 1 0.3226 1 1 0.3278 Two effective decay branches 2 Then, we considered the case in which there are neutron emissions after β decay, that is, two decay branches with βn emitting neutrons and β o without emitting. It should be noted that there is no distinction between the number of neutrons emitted. Eq. (4) was applied to each branch with the second dataset. The corresponding results are listed in the last two lines of Table2 Table2 with the notations Eq. (4) βn and Eq. (4) βo . 1 1   4 1 Fitting parameters 3 1 Uncertainties 1 1   1 1 a 0 1 1 a 1 1 1 a 2 1 1 a 3 1 1 <math id="M26"><mrow><msubsup><mi>σ</mi><mrow><mtext>stat</mtext></mrow><mtext>2</mtext></msubsup></mrow></math> 1 1 <math id="M27"><mrow><msubsup><mi>σ</mi><mrow><mtext>sys</mtext></mrow><mtext>2</mtext></msubsup></mrow></math> 1 1 <math id="M28"><mrow><msubsup><mi>σ</mi><mrow><mtext>tot</mtext></mrow><mtext>2</mtext></msubsup></mrow></math> 1 1 Equation (4) 1 1 0.3649 1 1 1.0179 1 1 2.0070 1 1 1.0725 1 1 0.0079 1 1 0.2565 1 1 0.2644 1 1 EqEquation (4) βn 1 1 0.4384 1 1 0.6672 1 1 0.9952 1 1 0.3666 1 1 0.0255 1 1 0.8433 1 1 0.8687 1 1 EqEquation (4) βo 1 1 0.6838 1 1 1.1007 1 1 1.9844 1 1 1.4825 1 1 0.0131 1 1 0.4428 1 1 0.4559 Moreover, the one-branch result was re-fitted to compare the adaptability of Eq. (4) with the changed dataset. The values of βn probability largely varied from nuclide to nuclide, resulting in larger uncertainties in Eq. (4) βn and Eq. (4) βo compared with 1 b 4 p . The values of -ln( B GT ) were calculated to deduce the partial half-life of the two branches, T βn and T β o , then the T 1/2 appearing in Eqs. (6) and (7), and the branching ratios. The experimental half-lives were generally well reproduced. In particular, the shorter the half-life, the better the consistency. The root-mean-square deviation (RMS), which characterizes the goodness-of-fit of one dataset, is defined as <math display="block" id="M29"><mrow><mtext>RMS</mtext><mo>=</mo><mfrac><mn>1</mn><mi>K</mi></mfrac><mstyle displaystyle="true"><munderover><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>1</mn></mrow><mi>K</mi></munderover></mstyle><msup><mrow><mo stretchy="false">[</mo><msub><mi>Y</mi><mrow><mi>k</mi><mn>,</mn><mtext>cal</mtext></mrow></msub><mo>−</mo><msub><mi>Y</mi><mrow><mi>k</mi><mn>,</mn><mtext>exp</mtext></mrow></msub><mo stretchy="false">]</mo></mrow><mn>2</mn></msup><mn>.</mn></mrow></math> The results obtained by direct fitting to the βn probability are listed in Table3 Table3 . The three results and experimental values were generally consistent within approximately 10% RMS (10.389%, 10.002%, and 10.231%, respectively). 1 1   5 1 Fitting parameters 3 1 Uncertainties 1 1   1 1 a 0 1 1 a 1 1 1 a 2 1 1 a 3 1 1 a 4 1 1 <math id="M33"><mrow><msubsup><mi>σ</mi><mrow><mtext>stat</mtext></mrow><mn>2</mn></msubsup></mrow></math> 1 1 <math id="M34"><mrow><msubsup><mi>σ</mi><mrow><mtext>sys</mtext></mrow><mn>2</mn></msubsup></mrow></math> 1 1 <math id="M35"><mrow><msubsup><mi>σ</mi><mrow><mtext>tot</mtext></mrow><mn>2</mn></msubsup></mrow></math> 1 1 Equation (9) 1 1 0.1956 1 1 -0.2570 1 1 -0.7434 1 1 -0.7137 1 1 -3.9323 1 1 0.0287 1 1 0.6966 1 1 0.7253 1 1 Equation (10) 1 1 -0.2697 1 1 -0.3780 1 1 -0.8663 1 1 -1.0562 1 1 -4.4410 1 1 0.0307 1 1 0.7492 1 1 0.7800 The value given by -ln( P βn ) was close to the experimental value in general. However, the <math id="M36"><mrow><mo>−</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow><mrow><mn>1</mn><mo>−</mo><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> results were closer to the experimental data in several cases with great undulations, such as in the regions of shell closure. The form of <math id="M37"><mrow><mo>−</mo><mi>ln</mi><mrow><mo>(</mo><mrow><mfrac><mrow><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow><mrow><mn>1</mn><mo>−</mo><msub><mi>P</mi><mrow><mi>β</mi><mi>n</mi></mrow></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> was determined in a more physical transformation, guaranteeing that the calculated probabilities always lay between 0 and 1. The experimental and calculated values of the half-life and probability are shown in Table4 Table4 for the two-branch case. The calculated values of the half-life were obtained from the fitting results of Eq. (4) βn and Eq. (4) βo listed in Table2 Table2 , whereas the probability corresponds to Eq. (9) listed in Table3 Table3 . 1 1 Nucl. 1 1 Q β 1 1 Q βn 1 1 ln T exp 1 1 ln T cal 1 1 <math id="M38"><mrow><msub><mi>σ</mi><mrow><mi>ln</mi><msub><mi>T</mi><mrow><mtext>cal</mtext></mrow></msub></mrow></msub></mrow></math> 1 1 P exp (%) 1 1 P cal (%) 1 1 <math id="M39"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>74</mn></mrow></msubsup></mrow></math> Cu 1 1 9750.5 1 1 1515.9 1 1 0.469 1 1 0.254 1 1 0.573 1 1 0.075 1 1 0.17 <math id="M40"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.24</mn></mrow><mrow><mo>−</mo><mn>0.10</mn></mrow></msubsup></mrow></math> 1 1 <math id="M41"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>75</mn></mrow></msubsup></mrow></math> Cu 1 1 8087.6 1 1 3214.1 1 1 0.202 1 1 0.33 1 1 0.575 1 1 2.7 1 1 6.84 <math id="M42"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>8.19</mn></mrow><mrow><mo>−</mo><mn>3.88</mn></mrow></msubsup></mrow></math> 1 1 <math id="M43"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>76</mn></mrow></msubsup></mrow></math> Cu 1 1 11327 1 1 3511.6 1 1 -0.451 1 1 -0.232 1 1 0.575 1 1 7.2 1 1 4.16 <math id="M44"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.29</mn></mrow><mrow><mo>−</mo><mn>2.39</mn></mrow></msubsup></mrow></math> 1 1 <math id="M45"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>77</mn></mrow></msubsup></mrow></math> Cu 1 1 10170 1 1 5610 1 1 -0.755 1 1 -0.766 1 1 0.574 1 1 30.1 1 1 26.95 <math id="M46"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.98</mn></mrow><mrow><mo>−</mo><mn>13.61</mn></mrow></msubsup></mrow></math> 1 1 <math id="M47"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>78</mn></mrow></msubsup></mrow></math> Cu 1 1 12990 1 1 6220 1 1 -1.104 1 1 -0.969 1 1 0.573 1 1 51 1 1 25.10 <math id="M48"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.46</mn></mrow><mrow><mo>−</mo><mn>12.84</mn></mrow></msubsup></mrow></math> 1 1 <math id="M49"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>79</mn></mrow></msubsup></mrow></math> Cu 1 1 11690 1 1 7670 1 1 -1.422 1 1 -1.647 1 1 0.573 1 1 66 1 1 45.82 <math id="M50"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.08</mn></mrow><mrow><mo>−</mo><mn>19.68</mn></mrow></msubsup></mrow></math> 1 1 <math id="M51"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>80</mn></mrow></msubsup></mrow></math> Cu 1 1 15450 1 1 9160 1 1 -2.178 1 1 -2.143 1 1 0.572 1 1 58 1 1 46.40 <math id="M52"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.02</mn></mrow><mrow><mo>−</mo><mn>19.82</mn></mrow></msubsup></mrow></math> 1 1 <math id="M53"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>81</mn></mrow></msubsup></mrow></math> Cu 1 1 14780 1 1 12160 1 1 -2.615 1 1 -3.428 1 1 0.574 1 1 81 1 1 68.53 <math id="M54"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.30</mn></mrow><mrow><mo>−</mo><mn>20.77</mn></mrow></msubsup></mrow></math> 1 1 <math id="M55"><mrow><msubsup><mrow/><mrow><mn>30</mn></mrow><mrow><mn>79</mn></mrow></msubsup></mrow></math> Zn 1 1 9115.4 1 1 2202.3 1 1 -0.293 1 1 0.102 1 1 0.58 1 1 1.75 1 1 0.98 <math id="M56"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.41</mn></mrow><mrow><mo>−</mo><mn>0.58</mn></mrow></msubsup></mrow></math> 1 1 <math id="M57"><mrow><msubsup><mrow/><mrow><mn>30</mn></mrow><mrow><mn>80</mn></mrow></msubsup></mrow></math> Zn 1 1 7575.1 1 1 2827.8 1 1 -0.576 1 1 -0.153 1 1 0.584 1 1 1.36 1 1 4.52 <math id="M58"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.77</mn></mrow><mrow><mo>−</mo><mn>2.60</mn></mrow></msubsup></mrow></math> 1 1 <math id="M59"><mrow><msubsup><mrow/><mrow><mn>30</mn></mrow><mrow><mn>81</mn></mrow></msubsup></mrow></math> Zn 1 1 11428.3 1 1 4952.7 1 1 -1.205 1 1 -1.08 1 1 0.578 1 1 18 1 1 11.75 <math id="M60"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.56</mn></mrow><mrow><mo>−</mo><mn>6.52</mn></mrow></msubsup></mrow></math> 1 1 <math id="M61"><mrow><msubsup><mrow/><mrow><mn>30</mn></mrow><mrow><mn>82</mn></mrow></msubsup></mrow></math> Zn 1 1 10616.8 1 1 7242.7 1 1 -1.727 1 1 -2.234 1 1 0.579 1 1 69 1 1 40.15 <math id="M62"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.53</mn></mrow><mrow><mo>−</mo><mn>18.30</mn></mrow></msubsup></mrow></math> 1 1 <math id="M63"><mrow><msubsup><mrow/><mrow><mn>30</mn></mrow><mrow><mn>84</mn></mrow></msubsup></mrow></math> Zn 1 1 12160 1 1 9260 1 1 -2.926 1 1 -3.177 1 1 0.579 1 1 73 1 1 50.33 <math id="M64"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.47</mn></mrow><mrow><mo>−</mo><mn>20.59</mn></mrow></msubsup></mrow></math> 1 1 <math id="M65"><mrow><msubsup><mrow/><mrow><mn>31</mn></mrow><mrow><mn>80</mn></mrow></msubsup></mrow></math> Ga 1 1 10311.6 1 1 2232 1 1 0.642 1 1 0.388 1 1 0.578 1 1 0.9 1 1 0.99 <math id="M66"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.38</mn></mrow><mrow><mo>−</mo><mn>0.58</mn></mrow></msubsup></mrow></math> 1 1 <math id="M67"><mrow><msubsup><mrow/><mrow><mn>31</mn></mrow><mrow><mn>81</mn></mrow></msubsup></mrow></math> Ga 1 1 8663.7 1 1 3836 1 1 0.196 1 1 0.209 1 1 0.577 1 1 12.5 1 1 12.85 <math id="M68"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>13.37</mn></mrow><mrow><mo>−</mo><mn>7.09</mn></mrow></msubsup></mrow></math> 1 1 <math id="M69"><mrow><msubsup><mrow/><mrow><mn>31</mn></mrow><mrow><mn>82</mn></mrow></msubsup></mrow></math> Ga 1 1 12484.3 1 1 5289.6 1 1 -0.509 1 1 -0.688 1 1 0.575 1 1 22.7 1 1 16.48 <math id="M70"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.67</mn></mrow><mrow><mo>−</mo><mn>8.89</mn></mrow></msubsup></mrow></math> 1 1 <math id="M71"><mrow><msubsup><mrow/><mrow><mn>31</mn></mrow><mrow><mn>83</mn></mrow></msubsup></mrow></math> Ga 1 1 11719.3 1 1 8086.6 1 1 -1.171 1 1 -1.814 1 1 0.573 1 1 67 1 1 51.24 <math id="M72"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.26</mn></mrow><mrow><mo>−</mo><mn>20.68</mn></mrow></msubsup></mrow></math> 1 1 <math id="M73"><mrow><msubsup><mrow/><mrow><mn>31</mn></mrow><mrow><mn>84</mn></mrow></msubsup></mrow></math> Ga 1 1 14060 1 1 8820 1 1 -2.352 1 1 -1.859 1 1 0.572 1 1 47.6 1 1 52.66 <math id="M74"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.00</mn></mrow><mrow><mo>−</mo><mn>20.89</mn></mrow></msubsup></mrow></math> 1 1 <math id="M75"><mrow><msubsup><mrow/><mrow><mn>31</mn></mrow><mrow><mn>85</mn></mrow></msubsup></mrow></math> Ga 1 1 13270 1 1 10230 1 1 -2.387 1 1 -2.72 1 1 0.574 1 1 81.3 1 1 62.76 <math id="M76"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.31</mn></mrow><mrow><mo>−</mo><mn>21.34</mn></mrow></msubsup></mrow></math> 1 1 <math id="M77"><mrow><msubsup><mrow/><mrow><mn>31</mn></mrow><mrow><mn>86</mn></mrow></msubsup></mrow></math> Ga 1 1 15320 1 1 10970 1 1 -3.012 1 1 -2.666 1 1 0.573 1 1 85.2 1 1 66.10 <math id="M78"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>16.20</mn></mrow><mrow><mo>−</mo><mn>21.11</mn></mrow></msubsup></mrow></math> 1 1 <math id="M79"><mrow><msubsup><mrow/><mrow><mn>31</mn></mrow><mrow><mn>87</mn></mrow></msubsup></mrow></math> Ga 1 1 14830 1 1 12080 1 1 -3.54 1 1 -3.448 1 1 0.574 1 1 91.2 1 1 67.57 <math id="M80"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.66</mn></mrow><mrow><mo>−</mo><mn>20.91</mn></mrow></msubsup></mrow></math> 1 1 <math id="M81"><mrow><msubsup><mrow/><mrow><mn>32</mn></mrow><mrow><mn>84</mn></mrow></msubsup></mrow></math> Ge 1 1 7705.1 1 1 3449.6 1 1 -0.049 1 1 -0.32 1 1 0.582 1 1 10.6 1 1 9.60 <math id="M82"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>10.82</mn></mrow><mrow><mo>−</mo><mn>5.39</mn></mrow></msubsup></mrow></math> 1 1 <math id="M83"><mrow><msubsup><mrow/><mrow><mn>32</mn></mrow><mrow><mn>85</mn></mrow></msubsup></mrow></math> Ge 1 1 10065.7 1 1 4658.8 1 1 -0.699 1 1 -0.542 1 1 0.577 1 1 16.2 1 1 15.22 <math id="M84"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>14.96</mn></mrow><mrow><mo>−</mo><mn>8.28</mn></mrow></msubsup></mrow></math> 1 1 <math id="M85"><mrow><msubsup><mrow/><mrow><mn>32</mn></mrow><mrow><mn>86</mn></mrow></msubsup></mrow></math> Ge 1 1 9560 1 1 5720 1 1 -1.505 1 1 -1.55 1 1 0.579 1 1 45 1 1 27.79 <math id="M86"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.29</mn></mrow><mrow><mo>−</mo><mn>14.00</mn></mrow></msubsup></mrow></math> 1 1 <math id="M87"><mrow><msubsup><mrow/><mrow><mn>33</mn></mrow><mrow><mn>86</mn></mrow></msubsup></mrow></math> As 1 1 11541 1 1 5380.2 1 1 -0.058 1 1 -0.449 1 1 0.573 1 1 34.5 1 1 22.93 <math id="M88"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.72</mn></mrow><mrow><mo>−</mo><mn>11.90</mn></mrow></msubsup></mrow></math> 1 1 <math id="M89"><mrow><msubsup><mrow/><mrow><mn>33</mn></mrow><mrow><mn>87</mn></mrow></msubsup></mrow></math> As 1 1 10808.2 1 1 6813.9 1 1 -0.726 1 1 -1.293 1 1 0.573 1 1 15.4 1 1 40.82 <math id="M90"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.43</mn></mrow><mrow><mo>−</mo><mn>18.43</mn></mrow></msubsup></mrow></math> 1 1 <math id="M91"><mrow><msubsup><mrow/><mrow><mn>34</mn></mrow><mrow><mn>88</mn></mrow></msubsup></mrow></math> Se 1 1 6831.8 1 1 1936.2 1 1 0.412 1 1 0.148 1 1 0.583 1 1 0.99 1 1 1.24 <math id="M92"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.73</mn></mrow><mrow><mo>−</mo><mn>0.73</mn></mrow></msubsup></mrow></math> 1 1 <math id="M93"><mrow><msubsup><mrow/><mrow><mn>34</mn></mrow><mrow><mn>89</mn></mrow></msubsup></mrow></math> Se 1 1 9281.9 1 1 3652.3 1 1 -0.821 1 1 -0.323 1 1 0.576 1 1 7.8 1 1 6.95 <math id="M94"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>8.32</mn></mrow><mrow><mo>−</mo><mn>3.95</mn></mrow></msubsup></mrow></math> 1 1 <math id="M95"><mrow><msubsup><mrow/><mrow><mn>34</mn></mrow><mrow><mn>91</mn></mrow></msubsup></mrow></math> Se 1 1 10530 1 1 5350 1 1 -1.309 1 1 -1.207 1 1 0.572 1 1 21 1 1 16.97 <math id="M96"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.91</mn></mrow><mrow><mo>−</mo><mn>9.11</mn></mrow></msubsup></mrow></math> 1 1 <math id="M97"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>90</mn></mrow></msubsup></mrow></math> Br 1 1 10959 1 1 4464.2 1 1 0.648 1 1 -0.517 1 1 0.571 1 1 25.6 1 1 10.76 <math id="M98"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>11.66</mn></mrow><mrow><mo>−</mo><mn>5.97</mn></mrow></msubsup></mrow></math> 1 1 <math id="M99"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>91</mn></mrow></msubsup></mrow></math> Br 1 1 9866.7 1 1 5780.6 1 1 -0.609 1 1 -1.216 1 1 0.57 1 1 30.4 1 1 25.02 <math id="M100"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.35</mn></mrow><mrow><mo>−</mo><mn>12.77</mn></mrow></msubsup></mrow></math> 1 1 <math id="M101"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>92</mn></mrow></msubsup></mrow></math> Br 1 1 12536.5 1 1 6669.8 1 1 -1.097 1 1 -1.619 1 1 0.569 1 1 33.1 1 1 24.14 <math id="M102"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.11</mn></mrow><mrow><mo>−</mo><mn>12.41</mn></mrow></msubsup></mrow></math> 1 1 <math id="M103"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>93</mn></mrow></msubsup></mrow></math> Br 1 1 11250 1 1 7810 1 1 -1.884 1 1 -2.298 1 1 0.568 1 1 64 1 1 36.52 <math id="M104"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.34</mn></mrow><mrow><mo>−</mo><mn>17.10</mn></mrow></msubsup></mrow></math> 1 1 <math id="M105"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>94</mn></mrow></msubsup></mrow></math> Br 1 1 13950 1 1 8670 1 1 -2.659 1 1 -2.548 1 1 0.568 1 1 30 1 1 34.36 <math id="M106"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.27</mn></mrow><mrow><mo>−</mo><mn>16.43</mn></mrow></msubsup></mrow></math> 1 1 <math id="M107"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>92</mn></mrow></msubsup></mrow></math> Kr 1 1 6003.1 1 1 904.4 1 1 0.61 1 1 -0.022 1 1 0.578 1 1 0.0332 1 1 0.04 <math id="M108"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.07</mn></mrow><mrow><mo>−</mo><mn>0.03</mn></mrow></msubsup></mrow></math> 1 1 <math id="M109"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>93</mn></mrow></msubsup></mrow></math> Kr 1 1 8483.9 1 1 2565.1 1 1 0.25 1 1 -0.716 1 1 0.569 1 1 1.99 1 1 1.26 <math id="M110"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.74</mn></mrow><mrow><mo>−</mo><mn>0.74</mn></mrow></msubsup></mrow></math> 1 1 <math id="M111"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>94</mn></mrow></msubsup></mrow></math> Kr 1 1 7215 1 1 3201 1 1 -1.556 1 1 -1.218 1 1 0.577 1 1 1.11 1 1 4.17 <math id="M112"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.37</mn></mrow><mrow><mo>−</mo><mn>2.41</mn></mrow></msubsup></mrow></math> 1 1 <math id="M113"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>95</mn></mrow></msubsup></mrow></math> Kr 1 1 9733 1 1 4333 1 1 -2.172 1 1 -1.643 1 1 0.569 1 1 2.87 1 1 5.66 <math id="M114"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>6.94</mn></mrow><mrow><mo>−</mo><mn>3.22</mn></mrow></msubsup></mrow></math> 1 1 <math id="M115"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>96</mn></mrow></msubsup></mrow></math> Kr 1 1 8275 1 1 4741 1 1 -2.526 1 1 -2.098 1 1 0.576 1 1 3.7 1 1 10.70 <math id="M116"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>11.82</mn></mrow><mrow><mo>−</mo><mn>5.99</mn></mrow></msubsup></mrow></math> 1 1 <math id="M117"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>97</mn></mrow></msubsup></mrow></math> Kr 1 1 11100 1 1 5860 1 1 -2.779 1 1 -2.436 1 1 0.568 1 1 6.7 1 1 10.51 <math id="M118"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>11.47</mn></mrow><mrow><mo>−</mo><mn>5.84</mn></mrow></msubsup></mrow></math> 1 1 <math id="M119"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>98</mn></mrow></msubsup></mrow></math> Kr 1 1 10060 1 1 6140 1 1 -3.147 1 1 -3.123 1 1 0.576 1 1 7 1 1 13.05 <math id="M120"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>13.65</mn></mrow><mrow><mo>−</mo><mn>7.23</mn></mrow></msubsup></mrow></math> 1 1 <math id="M121"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>99</mn></mrow></msubsup></mrow></math> Kr 1 1 12360 1 1 7540 1 1 -3.297 1 1 -3.076 1 1 0.568 1 1 11 1 1 17.75 <math id="M122"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>16.34</mn></mrow><mrow><mo>−</mo><mn>9.49</mn></mrow></msubsup></mrow></math> 1 1 <math id="M123"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>95</mn></mrow></msubsup></mrow></math> Rb 1 1 9228 1 1 4883 1 1 -0.973 1 1 -1.533 1 1 0.568 1 1 8.8 1 1 10.94 <math id="M124"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>11.81</mn></mrow><mrow><mo>−</mo><mn>6.07</mn></mrow></msubsup></mrow></math> 1 1 <math id="M125"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>96</mn></mrow></msubsup></mrow></math> Rb 1 1 11569.8 1 1 5693.9 1 1 -1.601 1 1 -1.799 1 1 0.569 1 1 14.1 1 1 12.23 <math id="M126"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.89</mn></mrow><mrow><mo>−</mo><mn>6.76</mn></mrow></msubsup></mrow></math> 1 1 <math id="M127"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>97</mn></mrow></msubsup></mrow></math> Rb 1 1 10062.3 1 1 6333.7 1 1 -1.778 1 1 -2.133 1 1 0.568 1 1 24.9 1 1 19.96 <math id="M128"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.44</mn></mrow><mrow><mo>−</mo><mn>10.53</mn></mrow></msubsup></mrow></math> 1 1 <math id="M129"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>98</mn></mrow></msubsup></mrow></math> Rb 1 1 12054 1 1 6141 1 1 -2.163 1 1 -2.056 1 1 0.57 1 1 14.354 1 1 13.58 <math id="M130"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>13.88</mn></mrow><mrow><mo>−</mo><mn>7.46</mn></mrow></msubsup></mrow></math> 1 1 <math id="M131"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>99</mn></mrow></msubsup></mrow></math> Rb 1 1 11400.3 1 1 7230.6 1 1 -2.851 1 1 -2.752 1 1 0.568 1 1 19.1 1 1 20.25 <math id="M132"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.58</mn></mrow><mrow><mo>−</mo><mn>10.67</mn></mrow></msubsup></mrow></math> 1 1 <math id="M133"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>100</mn></mrow></msubsup></mrow></math> Rb 1 1 13574 1 1 8203 1 1 -2.976 1 1 -2.775 1 1 0.569 1 1 5.75 1 1 24.98 <math id="M134"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.51</mn></mrow><mrow><mo>−</mo><mn>12.83</mn></mrow></msubsup></mrow></math> 1 1 <math id="M135"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>101</mn></mrow></msubsup></mrow></math> Rb 1 1 12480 1 1 8910 1 1 -3.474 1 1 -3.318 1 1 0.568 1 1 28 1 1 29.98 <math id="M136"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.63</mn></mrow><mrow><mo>−</mo><mn>14.81</mn></mrow></msubsup></mrow></math> 1 1 <math id="M137"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>102</mn></mrow></msubsup></mrow></math> Rb 1 1 14450 1 1 9550 1 1 -3.297 1 1 -3.195 1 1 0.569 1 1 18 1 1 33.11 <math id="M138"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.23</mn></mrow><mrow><mo>−</mo><mn>16.04</mn></mrow></msubsup></mrow></math> 1 1 <math id="M139"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>97</mn></mrow></msubsup></mrow></math> Sr 1 1 7540 1 1 1683.1 1 1 -0.846 1 1 -0.594 1 1 0.569 1 1 0.03 1 1 0.25 <math id="M140"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.36</mn></mrow><mrow><mo>−</mo><mn>0.15</mn></mrow></msubsup></mrow></math> 1 1 <math id="M141"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>98</mn></mrow></msubsup></mrow></math> Sr 1 1 5871.7 1 1 1627 1 1 -0.426 1 1 -0.543 1 1 0.579 1 1 0.23 1 1 0.44 <math id="M142"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.63</mn></mrow><mrow><mo>−</mo><mn>0.26</mn></mrow></msubsup></mrow></math> 1 1 <math id="M143"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>99</mn></mrow></msubsup></mrow></math> Sr 1 1 8128.4 1 1 1702.1 1 1 -1.313 1 1 -0.959 1 1 0.569 1 1 0.096 1 1 0.18 <math id="M144"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.27</mn></mrow><mrow><mo>−</mo><mn>0.11</mn></mrow></msubsup></mrow></math> 1 1 <math id="M145"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>100</mn></mrow></msubsup></mrow></math> Sr 1 1 7506 1 1 2757.6 1 1 -1.606 1 1 -1.699 1 1 0.578 1 1 1.11 1 1 1.51 <math id="M146"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>2.10</mn></mrow><mrow><mo>−</mo><mn>0.89</mn></mrow></msubsup></mrow></math> 1 1 <math id="M147"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>101</mn></mrow></msubsup></mrow></math> Sr 1 1 9736 1 1 3931 1 1 -2.163 1 1 -1.842 1 1 0.569 1 1 2.52 1 1 3.29 <math id="M148"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>4.29</mn></mrow><mrow><mo>−</mo><mn>1.90</mn></mrow></msubsup></mrow></math> 1 1 <math id="M149"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>102</mn></mrow></msubsup></mrow></math> Sr 1 1 9014 1 1 4830 1 1 -2.631 1 1 -2.618 1 1 0.577 1 1 5.5 1 1 7.58 <math id="M150"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>9.04</mn></mrow><mrow><mo>−</mo><mn>4.32</mn></mrow></msubsup></mrow></math> 1 1 <math id="M151"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>98</mn></mrow></msubsup></mrow></math> Y 1 1 8992 1 1 2576.6 1 1 -0.601 1 1 -0.578 1 1 0.571 1 1 0.33 1 1 1.20 <math id="M152"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.65</mn></mrow><mrow><mo>−</mo><mn>0.70</mn></mrow></msubsup></mrow></math> 1 1 <math id="M153"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>99</mn></mrow></msubsup></mrow></math> Y 1 1 6971 1 1 2566 1 1 0.391 1 1 -0.277 1 1 0.569 1 1 1.97 1 1 2.21 <math id="M154"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>2.97</mn></mrow><mrow><mo>−</mo><mn>1.28</mn></mrow></msubsup></mrow></math> 1 1 <math id="M155"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>100</mn></mrow></msubsup></mrow></math> Y 1 1 9050 1 1 2222 1 1 -0.312 1 1 -0.605 1 1 0.571 1 1 1.02 1 1 0.61 <math id="M156"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.85</mn></mrow><mrow><mo>−</mo><mn>0.36</mn></mrow></msubsup></mrow></math> 1 1 <math id="M157"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>101</mn></mrow></msubsup></mrow></math> Y 1 1 8105 1 1 3245 1 1 -0.839 1 1 -0.992 1 1 0.569 1 1 1.98 1 1 3.18 <math id="M158"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>4.15</mn></mrow><mrow><mo>−</mo><mn>1.83</mn></mrow></msubsup></mrow></math> 1 1 <math id="M159"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>102</mn></mrow></msubsup></mrow></math> Y 1 1 10414.5 1 1 3921.5 1 1 -1.204 1 1 -1.303 1 1 0.571 1 1 4 1 1 3.91 <math id="M160"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.03</mn></mrow><mrow><mo>−</mo><mn>2.25</mn></mrow></msubsup></mrow></math> 1 1 <math id="M161"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>103</mn></mrow></msubsup></mrow></math> Y 1 1 9358 1 1 5059 1 1 -1.444 1 1 -1.749 1 1 0.568 1 1 8.1 1 1 11.07 <math id="M162"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>11.93</mn></mrow><mrow><mo>−</mo><mn>6.14</mn></mrow></msubsup></mrow></math> 1 1 <math id="M163"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>104</mn></mrow></msubsup></mrow></math> Y 1 1 11660 1 1 5680 1 1 -1.551 1 1 -1.918 1 1 0.57 1 1 34 1 1 11.32 <math id="M164"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.21</mn></mrow><mrow><mo>−</mo><mn>6.29</mn></mrow></msubsup></mrow></math> 1 1 <math id="M165"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>106</mn></mrow></msubsup></mrow></math> Nb 1 1 9931 1 1 3062.5 1 1 0.013 1 1 -1.088 1 1 0.571 1 1 4.5 1 1 1.65 <math id="M166"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>2.24</mn></mrow><mrow><mo>−</mo><mn>0.96</mn></mrow></msubsup></mrow></math> 1 1 <math id="M167"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>107</mn></mrow></msubsup></mrow></math> Nb 1 1 8828 1 1 4339 1 1 -1.248 1 1 -1.47 1 1 0.569 1 1 7.4 1 1 7.54 <math id="M168"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>8.84</mn></mrow><mrow><mo>−</mo><mn>4.26</mn></mrow></msubsup></mrow></math> 1 1 <math id="M169"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>108</mn></mrow></msubsup></mrow></math> Nb 1 1 11210 1 1 4934 1 1 -1.65 1 1 -1.723 1 1 0.57 1 1 6.3 1 1 7.53 <math id="M170"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>8.87</mn></mrow><mrow><mo>−</mo><mn>4.26</mn></mrow></msubsup></mrow></math> 1 1 <math id="M171"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>109</mn></mrow></msubsup></mrow></math> Nb 1 1 9980 1 1 5990 1 1 -2.18 1 1 -2.147 1 1 0.568 1 1 31 1 1 16.53 <math id="M172"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.66</mn></mrow><mrow><mo>−</mo><mn>8.90</mn></mrow></msubsup></mrow></math> 1 1 <math id="M173"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>110</mn></mrow></msubsup></mrow></math> Nb 1 1 12230 1 1 6280 1 1 -2.59 1 1 -2.207 1 1 0.57 1 1 40 1 1 13.90 <math id="M174"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>14.11</mn></mrow><mrow><mo>−</mo><mn>7.62</mn></mrow></msubsup></mrow></math> 1 1 <math id="M175"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>109</mn></mrow></msubsup></mrow></math> Mo 1 1 7617 1 1 1185 1 1 -0.368 1 1 -0.719 1 1 0.569 1 1 1.3 1 1 0.05 <math id="M176"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.07</mn></mrow><mrow><mo>−</mo><mn>0.03</mn></mrow></msubsup></mrow></math> 1 1 <math id="M177"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>110</mn></mrow></msubsup></mrow></math> Mo 1 1 6492 1 1 1669 1 1 -1.248 1 1 -1.077 1 1 0.579 1 1 2 1 1 0.31 <math id="M178"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.45</mn></mrow><mrow><mo>−</mo><mn>0.19</mn></mrow></msubsup></mrow></math> 1 1 <math id="M179"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>109</mn></mrow></msubsup></mrow></math> Tc 1 1 6456 1 1 1307 1 1 -0.117 1 1 0.035 1 1 0.569 1 1 0.08 1 1 0.16 <math id="M180"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.23</mn></mrow><mrow><mo>−</mo><mn>0.09</mn></mrow></msubsup></mrow></math> 1 1 <math id="M181"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>110</mn></mrow></msubsup></mrow></math> Tc 1 1 9038 1 1 1633 1 1 -0.093 1 1 -0.659 1 1 0.571 1 1 0.04 1 1 0.16 <math id="M182"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.23</mn></mrow><mrow><mo>−</mo><mn>0.09</mn></mrow></msubsup></mrow></math> 1 1 <math id="M183"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>111</mn></mrow></msubsup></mrow></math> Tc 1 1 7761 1 1 2977 1 1 -1.224 1 1 -0.848 1 1 0.569 1 1 0.85 1 1 2.64 <math id="M184"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>3.50</mn></mrow><mrow><mo>−</mo><mn>1.53</mn></mrow></msubsup></mrow></math> 1 1 <math id="M185"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>112</mn></mrow></msubsup></mrow></math> Tc 1 1 10372 1 1 3455 1 1 -1.187 1 1 -1.333 1 1 0.571 1 1 1.7 1 1 2.31 <math id="M186"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>3.08</mn></mrow><mrow><mo>−</mo><mn>1.34</mn></mrow></msubsup></mrow></math> 1 1 <math id="M187"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>113</mn></mrow></msubsup></mrow></math> Tc 1 1 9057 1 1 4748 1 1 -1.884 1 1 -1.646 1 1 0.568 1 1 2.1 1 1 9.79 <math id="M188"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>10.88</mn></mrow><mrow><mo>−</mo><mn>5.47</mn></mrow></msubsup></mrow></math> 1 1 <math id="M189"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>114</mn></mrow></msubsup></mrow></math> Tc 1 1 11620 1 1 5200 1 1 -2.408 1 1 -1.932 1 1 0.57 1 1 1.3 1 1 8.06 <math id="M190"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>9.38</mn></mrow><mrow><mo>−</mo><mn>4.55</mn></mrow></msubsup></mrow></math> 1 1 <math id="M191"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>118</mn></mrow></msubsup></mrow></math> Rh 1 1 10501 1 1 3466 1 1 -1.255 1 1 -1.366 1 1 0.57 1 1 3.1 1 1 2.31 <math id="M192"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>3.08</mn></mrow><mrow><mo>−</mo><mn>1.34</mn></mrow></msubsup></mrow></math> 1 1 <math id="M193"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>119</mn></mrow></msubsup></mrow></math> Rh 1 1 8585 1 1 4494.6 1 1 -1.661 1 1 -1.318 1 1 0.568 1 1 6.4 1 1 10.48 <math id="M194"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>11.44</mn></mrow><mrow><mo>−</mo><mn>5.83</mn></mrow></msubsup></mrow></math> 1 1 <math id="M195"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>123</mn></mrow></msubsup></mrow></math> Pd 1 1 9120 1 1 2610 1 1 -2.226 1 1 -0.862 1 1 0.571 1 1 10 1 1 1.27 <math id="M196"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.76</mn></mrow><mrow><mo>−</mo><mn>0.74</mn></mrow></msubsup></mrow></math> 1 1 <math id="M197"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>124</mn></mrow></msubsup></mrow></math> Pd 1 1 7810 1 1 3090 1 1 -2.513 1 1 -1.056 1 1 0.579 1 1 17 1 1 4.12 <math id="M198"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.29</mn></mrow><mrow><mo>−</mo><mn>2.37</mn></mrow></msubsup></mrow></math> 1 1 <math id="M199"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>125</mn></mrow></msubsup></mrow></math> Pd 1 1 10400 1 1 4010 1 1 -2.813 1 1 -1.135 1 1 0.575 1 1 12 1 1 6.03 <math id="M200"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>7.37</mn></mrow><mrow><mo>−</mo><mn>3.44</mn></mrow></msubsup></mrow></math> 1 1 <math id="M201"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>126</mn></mrow></msubsup></mrow></math> Pd 1 1 8820 1 1 4590 1 1 -3.024 1 1 -1.396 1 1 0.579 1 1 22 1 1 15.74 <math id="M202"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.31</mn></mrow><mrow><mo>−</mo><mn>8.55</mn></mrow></msubsup></mrow></math> 1 1 <math id="M203"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>121</mn></mrow></msubsup></mrow></math> Ag 1 1 6671 1 1 1483 1 1 -0.252 1 1 0.408 1 1 0.57 1 1 0.08 1 1 0.36 <math id="M204"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.53</mn></mrow><mrow><mo>−</mo><mn>0.22</mn></mrow></msubsup></mrow></math> 1 1 <math id="M205"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>122</mn></mrow></msubsup></mrow></math> Ag 1 1 9506 1 1 1896 1 1 -0.637 1 1 -0.232 1 1 0.571 1 1 0.186 1 1 0.41 <math id="M206"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.57</mn></mrow><mrow><mo>−</mo><mn>0.24</mn></mrow></msubsup></mrow></math> 1 1 <math id="M207"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>123</mn></mrow></msubsup></mrow></math> Ag 1 1 7866 1 1 2993 1 1 -1.217 1 1 -0.113 1 1 0.572 1 1 0.56 1 1 4.68 <math id="M208"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.89</mn></mrow><mrow><mo>−</mo><mn>2.68</mn></mrow></msubsup></mrow></math> 1 1 <math id="M209"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>124</mn></mrow></msubsup></mrow></math> Ag 1 1 10500 1 1 3140 1 1 -1.655 1 1 -0.428 1 1 0.573 1 1 1.3 1 1 2.97 <math id="M210"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>3.87</mn></mrow><mrow><mo>−</mo><mn>1.71</mn></mrow></msubsup></mrow></math> 1 1 <math id="M211"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>125</mn></mrow></msubsup></mrow></math> Ag 1 1 8830 1 1 4110 1 1 -1.833 1 1 -0.449 1 1 0.573 1 1 11.8 1 1 12.9 <math id="M212"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>13.33</mn></mrow><mrow><mo>−</mo><mn>7.09</mn></mrow></msubsup></mrow></math> 1 1 <math id="M213"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>127</mn></mrow></msubsup></mrow></math> Ag 1 1 10310 1 1 5750 1 1 -2.477 1 1 -1.145 1 1 0.574 1 1 14.6 1 1 27.92 <math id="M214"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.22</mn></mrow><mrow><mo>−</mo><mn>14.01</mn></mrow></msubsup></mrow></math> 1 1 <math id="M215"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>128</mn></mrow></msubsup></mrow></math> Ag 1 1 12620 1 1 6060 1 1 -2.813 1 1 -1.136 1 1 0.573 1 1 20 1 1 25.34 <math id="M216"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.53</mn></mrow><mrow><mo>−</mo><mn>12.94</mn></mrow></msubsup></mrow></math> 1 1 <math id="M217"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>130</mn></mrow></msubsup></mrow></math> Cd 1 1 8766 1 1 3649 1 1 -2.064 1 1 -1.163 1 1 0.583 1 1 3.5 1 1 7.13 <math id="M218"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>8.54</mn></mrow><mrow><mo>−</mo><mn>4.06</mn></mrow></msubsup></mrow></math> 1 1 <math id="M219"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>131</mn></mrow></msubsup></mrow></math> Cd 1 1 12810 1 1 6590 1 1 -2.489 1 1 -2.043 1 1 0.575 1 1 3.5 1 1 22.19 <math id="M220"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.46</mn></mrow><mrow><mo>−</mo><mn>11.58</mn></mrow></msubsup></mrow></math> 1 1 <math id="M221"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>132</mn></mrow></msubsup></mrow></math> Cd 1 1 12150 1 1 9690 1 1 -2.477 1 1 -3.522 1 1 0.582 1 1 60 1 1 57.31 <math id="M222"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.93</mn></mrow><mrow><mo>−</mo><mn>21.35</mn></mrow></msubsup></mrow></math> 1 1 <math id="M223"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>128</mn></mrow></msubsup></mrow></math> In 1 1 9220 1 1 1250 1 1 -0.174 1 1 0.614 1 1 0.578 1 1 0.0384 1 1 0.12 <math id="M224"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.18</mn></mrow><mrow><mo>−</mo><mn>0.07</mn></mrow></msubsup></mrow></math> 1 1 <math id="M225"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>129</mn></mrow></msubsup></mrow></math> In 1 1 7753 1 1 2453 1 1 -0.496 1 1 0.528 1 1 0.58 1 1 0.23 1 1 3.19 <math id="M226"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>4.24</mn></mrow><mrow><mo>−</mo><mn>1.85</mn></mrow></msubsup></mrow></math> 1 1 <math id="M227"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>130</mn></mrow></msubsup></mrow></math> In 1 1 10249 1 1 2636 1 1 -1.291 1 1 0.11 1 1 0.578 1 1 1.2 1 1 2.1 <math id="M228"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>2.84</mn></mrow><mrow><mo>−</mo><mn>1.22</mn></mrow></msubsup></mrow></math> 1 1 <math id="M229"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>131</mn></mrow></msubsup></mrow></math> In 1 1 9239.5 1 1 4035.9 1 1 -1.324 1 1 -0.382 1 1 0.577 1 1 2.21 1 1 12.19 <math id="M230"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.89</mn></mrow><mrow><mo>−</mo><mn>6.75</mn></mrow></msubsup></mrow></math> 1 1 <math id="M231"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>132</mn></mrow></msubsup></mrow></math> In 1 1 14135 1 1 6782 1 1 -1.603 1 1 -1.691 1 1 0.573 1 1 12.3 1 1 25.53 <math id="M232"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.59</mn></mrow><mrow><mo>−</mo><mn>13.02</mn></mrow></msubsup></mrow></math> 1 1 <math id="M233"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>133</mn></mrow></msubsup></mrow></math> In 1 1 13410 1 1 11010 1 1 -1.82 1 1 -3.251 1 1 0.575 1 1 90 1 1 69.46 <math id="M234"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>14.96</mn></mrow><mrow><mo>−</mo><mn>20.61</mn></mrow></msubsup></mrow></math> 1 1 <math id="M235"><mrow><msubsup><mrow/><mrow><mn>50</mn></mrow><mrow><mn>133</mn></mrow></msubsup></mrow></math> Sn 1 1 8049.6 1 1 690.1 1 1 0.351 1 1 0.38 1 1 0.581 1 1 0.0294 1 1 0.01 <math id="M236"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.02</mn></mrow><mrow><mo>−</mo><mn>0.01</mn></mrow></msubsup></mrow></math> 1 1 <math id="M237"><mrow><msubsup><mrow/><mrow><mn>50</mn></mrow><mrow><mn>134</mn></mrow></msubsup></mrow></math> Sn 1 1 7586.8 1 1 4418.4 1 1 -0.103 1 1 -0.73 1 1 0.579 1 1 17 1 1 25.45 <math id="M238"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.66</mn></mrow><mrow><mo>−</mo><mn>13.03</mn></mrow></msubsup></mrow></math> 1 1 <math id="M239"><mrow><msubsup><mrow/><mrow><mn>50</mn></mrow><mrow><mn>135</mn></mrow></msubsup></mrow></math> Sn 1 1 9058.1 1 1 5317 1 1 -0.662 1 1 -0.589 1 1 0.574 1 1 21 1 1 34.03 <math id="M240"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.23</mn></mrow><mrow><mo>−</mo><mn>16.31</mn></mrow></msubsup></mrow></math> 1 1 <math id="M241"><mrow><msubsup><mrow/><mrow><mn>50</mn></mrow><mrow><mn>136</mn></mrow></msubsup></mrow></math> Sn 1 1 8610 1 1 5720 1 1 -1.064 1 1 -1.503 1 1 0.579 1 1 27 1 1 37.98 <math id="M242"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.53</mn></mrow><mrow><mo>−</mo><mn>17.66</mn></mrow></msubsup></mrow></math> 1 1 <math id="M243"><mrow><msubsup><mrow/><mrow><mn>50</mn></mrow><mrow><mn>137</mn></mrow></msubsup></mrow></math> Sn 1 1 10270 1 1 6650 1 1 -1.444 1 1 -1.354 1 1 0.573 1 1 50 1 1 44.37 <math id="M244"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.22</mn></mrow><mrow><mo>−</mo><mn>19.35</mn></mrow></msubsup></mrow></math> 1 1 <math id="M245"><mrow><msubsup><mrow/><mrow><mn>51</mn></mrow><mrow><mn>135</mn></mrow></msubsup></mrow></math> Sb 1 1 8038.5 1 1 4772.1 1 1 0.512 1 1 -0.071 1 1 0.573 1 1 20 1 1 35.01 <math id="M246"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.32</mn></mrow><mrow><mo>−</mo><mn>16.64</mn></mrow></msubsup></mrow></math> 1 1 <math id="M247"><mrow><msubsup><mrow/><mrow><mn>51</mn></mrow><mrow><mn>136</mn></mrow></msubsup></mrow></math> Sb 1 1 9918.4 1 1 5150.6 1 1 -0.079 1 1 -0.159 1 1 0.572 1 1 25.14 1 1 32.46 <math id="M248"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.06</mn></mrow><mrow><mo>−</mo><mn>15.75</mn></mrow></msubsup></mrow></math> 1 1 <math id="M249"><mrow><msubsup><mrow/><mrow><mn>51</mn></mrow><mrow><mn>137</mn></mrow></msubsup></mrow></math> Sb 1 1 9243 1 1 6294 1 1 -0.681 1 1 -1.006 1 1 0.573 1 1 49 1 1 49.27 <math id="M250"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.60</mn></mrow><mrow><mo>−</mo><mn>20.36</mn></mrow></msubsup></mrow></math> 1 1 <math id="M251"><mrow><msubsup><mrow/><mrow><mn>51</mn></mrow><mrow><mn>138</mn></mrow></msubsup></mrow></math> Sb 1 1 11500 1 1 7000 1 1 -1.1 1 1 -1.18 1 1 0.571 1 1 72 1 1 48.66 <math id="M252"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.71</mn></mrow><mrow><mo>−</mo><mn>20.26</mn></mrow></msubsup></mrow></math> 1 1 <math id="M253"><mrow><msubsup><mrow/><mrow><mn>51</mn></mrow><mrow><mn>139</mn></mrow></msubsup></mrow></math> Sb 1 1 10420 1 1 7840 1 1 -1.704 1 1 -1.85 1 1 0.573 1 1 90 1 1 59.42 <math id="M254"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.31</mn></mrow><mrow><mo>−</mo><mn>21.37</mn></mrow></msubsup></mrow></math> 1 1 <math id="M255"><mrow><msubsup><mrow/><mrow><mn>51</mn></mrow><mrow><mn>140</mn></mrow></msubsup></mrow></math> Sb 1 1 12640 1 1 8200 1 1 -1.772 1 1 -1.816 1 1 0.571 1 1 30.6 1 1 54.76 <math id="M256"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.53</mn></mrow><mrow><mo>−</mo><mn>21.12</mn></mrow></msubsup></mrow></math> 1 1 <math id="M257"><mrow><msubsup><mrow/><mrow><mn>52</mn></mrow><mrow><mn>138</mn></mrow></msubsup></mrow></math> Te 1 1 6283.9 1 1 2589 1 1 0.378 1 1 0.195 1 1 0.581 1 1 4.82 1 1 6.21 <math id="M258"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>7.59</mn></mrow><mrow><mo>−</mo><mn>3.54</mn></mrow></msubsup></mrow></math> 1 1 <math id="M259"><mrow><msubsup><mrow/><mrow><mn>53</mn></mrow><mrow><mn>140</mn></mrow></msubsup></mrow></math> I 1 1 9380 1 1 3967 1 1 -0.528 1 1 -0.085 1 1 0.571 1 1 7.88 1 1 12.47 <math id="M260"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.98</mn></mrow><mrow><mo>−</mo><mn>6.86</mn></mrow></msubsup></mrow></math> 1 1 <math id="M261"><mrow><msubsup><mrow/><mrow><mn>53</mn></mrow><mrow><mn>141</mn></mrow></msubsup></mrow></math> I 1 1 8271 1 1 4988 1 1 -0.868 1 1 -0.707 1 1 0.569 1 1 21.2 1 1 27.50 <math id="M262"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.05</mn></mrow><mrow><mo>−</mo><mn>13.80</mn></mrow></msubsup></mrow></math> 1 1 <math id="M263"><mrow><msubsup><mrow/><mrow><mn>54</mn></mrow><mrow><mn>141</mn></mrow></msubsup></mrow></math> Xe 1 1 6280.2 1 1 781.5 1 1 0.547 1 1 0.779 1 1 0.572 1 1 0.0433 1 1 0.03 <math id="M264"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.05</mn></mrow><mrow><mo>−</mo><mn>0.02</mn></mrow></msubsup></mrow></math> 1 1 <math id="M265"><mrow><msubsup><mrow/><mrow><mn>54</mn></mrow><mrow><mn>142</mn></mrow></msubsup></mrow></math> Xe 1 1 5284.9 1 1 1176.6 1 1 0.2 1 1 0.278 1 1 0.578 1 1 0.36 1 1 0.25 <math id="M266"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.36</mn></mrow><mrow><mo>−</mo><mn>0.15</mn></mrow></msubsup></mrow></math> 1 1 <math id="M267"><mrow><msubsup><mrow/><mrow><mn>54</mn></mrow><mrow><mn>143</mn></mrow></msubsup></mrow></math> Xe 1 1 7472.6 1 1 2240.4 1 1 -0.671 1 1 -0.402 1 1 0.569 1 1 1 1 1 1.21 <math id="M268"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.68</mn></mrow><mrow><mo>−</mo><mn>0.71</mn></mrow></msubsup></mrow></math> 1 1 <math id="M269"><mrow><msubsup><mrow/><mrow><mn>54</mn></mrow><mrow><mn>144</mn></mrow></msubsup></mrow></math> Xe 1 1 6399 1 1 2731.9 1 1 -0.947 1 1 -0.937 1 1 0.577 1 1 3 1 1 3.54 <math id="M270"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>4.63</mn></mrow><mrow><mo>−</mo><mn>2.05</mn></mrow></msubsup></mrow></math> 1 1 <math id="M271"><mrow><msubsup><mrow/><mrow><mn>54</mn></mrow><mrow><mn>145</mn></mrow></msubsup></mrow></math> Xe 1 1 8561 1 1 3707 1 1 -1.671 1 1 -1.314 1 1 0.569 1 1 5 1 1 5.04 <math id="M272"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>6.27</mn></mrow><mrow><mo>−</mo><mn>2.88</mn></mrow></msubsup></mrow></math> 1 1 <math id="M273"><mrow><msubsup><mrow/><mrow><mn>54</mn></mrow><mrow><mn>146</mn></mrow></msubsup></mrow></math> Xe 1 1 7355 1 1 4028 1 1 -1.924 1 1 -1.811 1 1 0.576 1 1 6.9 1 1 8.93 <math id="M274"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>10.29</mn></mrow><mrow><mo>−</mo><mn>5.04</mn></mrow></msubsup></mrow></math> 1 1 <math id="M275"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>142</mn></mrow></msubsup></mrow></math> Cs 1 1 7327.7 1 1 1146.8 1 1 0.523 1 1 0.692 1 1 0.57 1 1 0.0916 1 1 0.12 <math id="M276"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.18</mn></mrow><mrow><mo>−</mo><mn>0.07</mn></mrow></msubsup></mrow></math> 1 1 <math id="M277"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>143</mn></mrow></msubsup></mrow></math> Cs 1 1 6261.7 1 1 2095.4 1 1 0.585 1 1 0.328 1 1 0.569 1 1 1.582 1 1 1.86 <math id="M278"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>2.52</mn></mrow><mrow><mo>−</mo><mn>1.08</mn></mrow></msubsup></mrow></math> 1 1 <math id="M279"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>144</mn></mrow></msubsup></mrow></math> Cs 1 1 8496 1 1 2595 1 1 -0.011 1 1 -0.357 1 1 0.57 1 1 2.98 1 1 1.83 <math id="M280"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>2.47</mn></mrow><mrow><mo>−</mo><mn>1.06</mn></mrow></msubsup></mrow></math> 1 1 <math id="M281"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>145</mn></mrow></msubsup></mrow></math> Cs 1 1 7462 1 1 3641 1 1 -0.541 1 1 -0.784 1 1 0.568 1 1 13.5 1 1 7.89 <math id="M282"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>9.16</mn></mrow><mrow><mo>−</mo><mn>4.44</mn></mrow></msubsup></mrow></math> 1 1 <math id="M283"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>146</mn></mrow></msubsup></mrow></math> Cs 1 1 9637 1 1 4134.5 1 1 -1.134 1 1 -1.155 1 1 0.57 1 1 14.3 1 1 7.04 <math id="M284"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>8.38</mn></mrow><mrow><mo>−</mo><mn>3.99</mn></mrow></msubsup></mrow></math> 1 1 <math id="M285"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>147</mn></mrow></msubsup></mrow></math> Cs 1 1 8344 1 1 4956 1 1 -1.472 1 1 -1.485 1 1 0.568 1 1 28.5 1 1 16.16 <math id="M286"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.44</mn></mrow><mrow><mo>−</mo><mn>8.72</mn></mrow></msubsup></mrow></math> 1 1 <math id="M287"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>148</mn></mrow></msubsup></mrow></math> Cs 1 1 10683 1 1 5282 1 1 -1.89 1 1 -1.744 1 1 0.57 1 1 29 1 1 12.09 <math id="M288"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.80</mn></mrow><mrow><mo>−</mo><mn>6.69</mn></mrow></msubsup></mrow></math> 1 1 <math id="M289"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>149</mn></mrow></msubsup></mrow></math> Cs 1 1 9870 1 1 6270 1 1 -2.235 1 1 -2.349 1 1 0.568 1 1 25 1 1 20.36 <math id="M290"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.63</mn></mrow><mrow><mo>−</mo><mn>10.72</mn></mrow></msubsup></mrow></math> 1 1 <math id="M291"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>150</mn></mrow></msubsup></mrow></math> Cs 1 1 11730 1 1 6880 1 1 -2.513 1 1 -2.326 1 1 0.569 1 1 20 1 1 22.58 <math id="M292"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.67</mn></mrow><mrow><mo>−</mo><mn>11.78</mn></mrow></msubsup></mrow></math> 1 1 <math id="M293"><mrow><msubsup><mrow/><mrow><mn>56</mn></mrow><mrow><mn>147</mn></mrow></msubsup></mrow></math> Ba 1 1 6414 1 1 715 1 1 -0.112 1 1 -0.115 1 1 0.569 1 1 0.066 1 1 0.01 <math id="M294"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.02</mn></mrow><mrow><mo>−</mo><mn>0.01</mn></mrow></msubsup></mrow></math> 1 1 <math id="M295"><mrow><msubsup><mrow/><mrow><mn>56</mn></mrow><mrow><mn>148</mn></mrow></msubsup></mrow></math> Ba 1 1 5115 1 1 1013 1 1 -0.483 1 1 -0.184 1 1 0.579 1 1 0.39 1 1 0.10 <math id="M296"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.15</mn></mrow><mrow><mo>−</mo><mn>0.06</mn></mrow></msubsup></mrow></math> 1 1 <math id="M297"><mrow><msubsup><mrow/><mrow><mn>56</mn></mrow><mrow><mn>149</mn></mrow></msubsup></mrow></math> Ba 1 1 7100 1 1 1520 1 1 -1.044 1 1 -0.602 1 1 0.569 1 1 2.2 1 1 0.20 <math id="M298"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.30</mn></mrow><mrow><mo>−</mo><mn>0.12</mn></mrow></msubsup></mrow></math> 1 1 <math id="M299"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>148</mn></mrow></msubsup></mrow></math> La 1 1 7690 1 1 1234 1 1 0.293 1 1 -0.104 1 1 0.571 1 1 0.19 1 1 0.09 <math id="M300"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.13</mn></mrow><mrow><mo>−</mo><mn>0.05</mn></mrow></msubsup></mrow></math> 1 1 <math id="M301"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>149</mn></mrow></msubsup></mrow></math> La 1 1 6450 1 1 2110 1 1 0.087 1 1 -0.182 1 1 0.569 1 1 1.41 1 1 1.32 <math id="M302"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.82</mn></mrow><mrow><mo>−</mo><mn>0.77</mn></mrow></msubsup></mrow></math> 1 1 <math id="M303"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>150</mn></mrow></msubsup></mrow></math> La 1 1 8720 1 1 2470 1 1 -0.673 1 1 -0.709 1 1 0.571 1 1 2.69 1 1 1.14 <math id="M304"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.57</mn></mrow><mrow><mo>−</mo><mn>0.66</mn></mrow></msubsup></mrow></math> Because the uncertainties were estimated on a logarithmic scale, the distances from the upper and lower bounds to the predicted values were different when converting, and thus there were differences in the positive and negative directions of the uncertainties. For the sake of convenience, the half-lives are presented in natural logarithmic form with T in units of seconds so that the total uncertainty on the calculated values can be given in the same scale in the sixth column. Because the two formulas Eqs. (9) and (10) study different objects, the calculated values of probability were converted from the natural logarithm form. Predictions 2 According to the presented method, the predictions of β -decay half-lives and βn probabilities P βn could be given for nuclei without experimental data, and the uncertainties according to Eq. (14). The predictions for neutron-rich nuclei in the intermediate mass zone offer important nuclear input and relevant data for nuclear physics applications, such as fission product yields in nuclear reactors [ 16 16 ], and the half-lives of nuclei participating in the rapid neutron capture process ( r process) in astrophysics [ 51 51 ]. In TABLE 5 TABLE 5 , 123 nuclei without experimental values of P βn are listed, 18 of which also have no half-life (in the last eighteen lines of the table). The predictions corresponding to Eq. (10) and Eq. (4) are given for the probability and half-life, respectively. 1 1 Nucl. 1 1 Q β 1 1 Q βn 1 1 ln T exp 1 1 ln T pred 1 1 <math id="M305"><mrow><msub><mi>σ</mi><mrow><mi>ln</mi><msub><mi>T</mi><mrow><mtext>pred</mtext></mrow></msub></mrow></msub></mrow></math> 1 1 <math id="M306"><mrow><msub><mi>P</mi><mrow><mtext>cal</mtext></mrow></msub><mo stretchy="false">(</mo><mi>%</mi><mo stretchy="false">)</mo></mrow></math> 1 1 <math id="M307"><mrow><msubsup><mrow/><mrow><mn>29</mn></mrow><mrow><mn>82</mn></mrow></msubsup></mrow></math> Cu 1 1 16990 1 1 12810 1 1 -3.433 1 1 -2.444 1 1 0.517 1 1 69.09 <math id="M308"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.36</mn></mrow><mrow><mo>−</mo><mn>21.29</mn></mrow></msubsup></mrow></math> 1 1 <math id="M309"><mrow><msubsup><mrow/><mrow><mn>30</mn></mrow><mrow><mn>78</mn></mrow></msubsup></mrow></math> Zn 1 1 6222.7 1 1 437.8 1 1 0.385 1 1 0.750 1 1 0.522 1 1 0 1 1 <math id="M310"><mrow><msubsup><mrow/><mrow><mn>32</mn></mrow><mrow><mn>87</mn></mrow></msubsup></mrow></math> Ge 1 1 11540 1 1 6810 1 1 -2.271 1 1 -1.383 1 1 0.514 1 1 34.71 <math id="M311"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.53</mn></mrow><mrow><mo>−</mo><mn>16.65</mn></mrow></msubsup></mrow></math> 1 1 <math id="M312"><mrow><msubsup><mrow/><mrow><mn>32</mn></mrow><mrow><mn>88</mn></mrow></msubsup></mrow></math> Ge 1 1 10580 1 1 7410 1 1 -2.800 1 1 -1.914 1 1 0.523 1 1 43.62 <math id="M313"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.78</mn></mrow><mrow><mo>−</mo><mn>19.54</mn></mrow></msubsup></mrow></math> 1 1 <math id="M314"><mrow><msubsup><mrow/><mrow><mn>33</mn></mrow><mrow><mn>88</mn></mrow></msubsup></mrow></math> As 1 1 13160 1 1 7640 1 1 -1.609 1 1 -1.154 1 1 0.518 1 1 43.59 <math id="M315"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.61</mn></mrow><mrow><mo>−</mo><mn>19.41</mn></mrow></msubsup></mrow></math> 1 1 <math id="M316"><mrow><msubsup><mrow/><mrow><mn>34</mn></mrow><mrow><mn>90</mn></mrow></msubsup></mrow></math> Se 1 1 8200 1 1 4400 1 1 -1.635 1 1 -0.886 1 1 0.520 1 1 16.12 <math id="M317"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.56</mn></mrow><mrow><mo>−</mo><mn>8.70</mn></mrow></msubsup></mrow></math> 1 1 <math id="M318"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>100</mn></mrow></msubsup></mrow></math> Kr 1 1 11200 1 1 8000 1 1 -4.962 1 1 -3.289 1 1 0.518 1 1 22.99 <math id="M319"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.20</mn></mrow><mrow><mo>−</mo><mn>12.03</mn></mrow></msubsup></mrow></math> 1 1 <math id="M320"><mrow><msubsup><mrow/><mrow><mn>37</mn></mrow><mrow><mn>103</mn></mrow></msubsup></mrow></math> Rb 1 1 13810 1 1 10480 1 1 -3.772 1 1 -3.395 1 1 0.511 1 1 36.03 <math id="M321"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.58</mn></mrow><mrow><mo>−</mo><mn>17.08</mn></mrow></msubsup></mrow></math> 1 1 <math id="M322"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>96</mn></mrow></msubsup></mrow></math> Sr 1 1 5411.7 1 1 213 1 1 0.067 1 1 0.333 1 1 0.518 1 1 0 1 1 <math id="M323"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>103</mn></mrow></msubsup></mrow></math> Sr 1 1 11040 1 1 5680 1 1 -2.937 1 1 -2.292 1 1 0.511 1 1 9.15 <math id="M324"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>10.29</mn></mrow><mrow><mo>−</mo><mn>5.09</mn></mrow></msubsup></mrow></math> 1 1 <math id="M325"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>104</mn></mrow></msubsup></mrow></math> Sr 1 1 9960 1 1 6280 1 1 -2.937 1 1 -2.743 1 1 0.518 1 1 14.60 <math id="M326"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>14.74</mn></mrow><mrow><mo>−</mo><mn>7.95</mn></mrow></msubsup></mrow></math> 1 1 <math id="M327"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>105</mn></mrow></msubsup></mrow></math> Sr 1 1 12700 1 1 7380 1 1 -3.244 1 1 -2.993 1 1 0.511 1 1 14.73 <math id="M328"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>14.57</mn></mrow><mrow><mo>−</mo><mn>7.99</mn></mrow></msubsup></mrow></math> 1 1 <math id="M329"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>106</mn></mrow></msubsup></mrow></math> Sr 1 1 11260 1 1 8400 1 1 -3.912 1 1 -3.356 1 1 0.518 1 1 26.42 <math id="M330"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.39</mn></mrow><mrow><mo>−</mo><mn>13.56</mn></mrow></msubsup></mrow></math> 1 1 <math id="M331"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>106</mn></mrow></msubsup></mrow></math> Y 1 1 12500 1 1 7340 1 1 -2.501 1 1 -1.986 1 1 0.513 1 1 22.86 <math id="M332"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.93</mn></mrow><mrow><mo>−</mo><mn>11.91</mn></mrow></msubsup></mrow></math> 1 1 <math id="M333"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>107</mn></mrow></msubsup></mrow></math> Y 1 1 12000 1 1 8110 1 1 -3.396 1 1 -2.726 1 1 0.511 1 1 25.22 <math id="M334"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.57</mn></mrow><mrow><mo>−</mo><mn>12.89</mn></mrow></msubsup></mrow></math> 1 1 <math id="M335"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>108</mn></mrow></msubsup></mrow></math> Y 1 1 14060 1 1 9000 1 1 -3.507 1 1 -2.574 1 1 0.513 1 1 30.26 <math id="M336"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.09</mn></mrow><mrow><mo>−</mo><mn>15.07</mn></mrow></msubsup></mrow></math> 1 1 <math id="M337"><mrow><msubsup><mrow/><mrow><mn>39</mn></mrow><mrow><mn>109</mn></mrow></msubsup></mrow></math> Y 1 1 12990 1 1 10080 1 1 -3.689 1 1 -3.122 1 1 0.511 1 1 38.33 <math id="M338"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.68</mn></mrow><mrow><mo>−</mo><mn>17.83</mn></mrow></msubsup></mrow></math> 1 1 <math id="M339"><mrow><msubsup><mrow/><mrow><mn>40</mn></mrow><mrow><mn>108</mn></mrow></msubsup></mrow></math> Zr 1 1 8190 1 1 4300 1 1 -2.545 1 1 -1.797 1 1 0.518 1 1 7.06 <math id="M340"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>8.44</mn></mrow><mrow><mo>−</mo><mn>3.97</mn></mrow></msubsup></mrow></math> 1 1 <math id="M341"><mrow><msubsup><mrow/><mrow><mn>40</mn></mrow><mrow><mn>109</mn></mrow></msubsup></mrow></math> Zr 1 1 10500 1 1 5280 1 1 -2.882 1 1 -2.075 1 1 0.511 1 1 8.34 <math id="M342"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>9.56</mn></mrow><mrow><mo>−</mo><mn>4.66</mn></mrow></msubsup></mrow></math> 1 1 <math id="M343"><mrow><msubsup><mrow/><mrow><mn>40</mn></mrow><mrow><mn>110</mn></mrow></msubsup></mrow></math> Zr 1 1 9400 1 1 5730 1 1 -3.283 1 1 -2.486 1 1 0.518 1 1 12.83 <math id="M344"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>13.48</mn></mrow><mrow><mo>−</mo><mn>7.04</mn></mrow></msubsup></mrow></math> 1 1 <math id="M345"><mrow><msubsup><mrow/><mrow><mn>40</mn></mrow><mrow><mn>111</mn></mrow></msubsup></mrow></math> Zr 1 1 11320 1 1 6700 1 1 -3.730 1 1 -2.451 1 1 0.511 1 1 15.79 <math id="M346"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.24</mn></mrow><mrow><mo>−</mo><mn>8.51</mn></mrow></msubsup></mrow></math> 1 1 <math id="M347"><mrow><msubsup><mrow/><mrow><mn>40</mn></mrow><mrow><mn>112</mn></mrow></msubsup></mrow></math> Zr 1 1 10460 1 1 6990 1 1 -3.507 1 1 -3.021 1 1 0.518 1 1 18.1 <math id="M348"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>16.90</mn></mrow><mrow><mo>−</mo><mn>9.70</mn></mrow></msubsup></mrow></math> 1 1 <math id="M349"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>103</mn></mrow></msubsup></mrow></math> Nb 1 1 5932 1 1 466.1 1 1 0.307 1 1 0.764 1 1 0.511 1 1 0 1 1 <math id="M350"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>111</mn></mrow></msubsup></mrow></math> Nb 1 1 11060 1 1 7600 1 1 -2.919 1 1 -2.351 1 1 0.511 1 1 26.64 <math id="M351"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.99</mn></mrow><mrow><mo>−</mo><mn>13.50</mn></mrow></msubsup></mrow></math> 1 1 <math id="M352"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>112</mn></mrow></msubsup></mrow></math> Nb 1 1 13190 1 1 7600 1 1 -3.270 1 1 -2.288 1 1 0.513 1 1 21.42 <math id="M353"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.33</mn></mrow><mrow><mo>−</mo><mn>11.24</mn></mrow></msubsup></mrow></math> 1 1 <math id="M354"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>113</mn></mrow></msubsup></mrow></math> Nb 1 1 11980 1 1 8880 1 1 -3.442 1 1 -2.750 1 1 0.511 1 1 33.67 <math id="M355"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.37</mn></mrow><mrow><mo>−</mo><mn>16.25</mn></mrow></msubsup></mrow></math> 1 1 <math id="M356"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>114</mn></mrow></msubsup></mrow></math> Nb 1 1 14420 1 1 9030 1 1 -4.075 1 1 -2.734 1 1 0.513 1 1 28.25 <math id="M357"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.65</mn></mrow><mrow><mo>−</mo><mn>14.25</mn></mrow></msubsup></mrow></math> 1 1 <math id="M358"><mrow><msubsup><mrow/><mrow><mn>41</mn></mrow><mrow><mn>115</mn></mrow></msubsup></mrow></math> Nb 1 1 13400 1 1 10380 1 1 -3.772 1 1 -3.310 1 1 0.511 1 1 38.15 <math id="M359"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.68</mn></mrow><mrow><mo>−</mo><mn>17.78</mn></mrow></msubsup></mrow></math> 1 1 <math id="M360"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>112</mn></mrow></msubsup></mrow></math> Mo 1 1 7800 1 1 3490 1 1 -2.079 1 1 -1.586 1 1 0.518 1 1 3.60 <math id="M361"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>4.66</mn></mrow><mrow><mo>−</mo><mn>2.05</mn></mrow></msubsup></mrow></math> 1 1 <math id="M362"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>113</mn></mrow></msubsup></mrow></math> Mo 1 1 10320 1 1 4700 1 1 -2.526 1 1 -2.021 1 1 0.511 1 1 5.55 <math id="M363"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>6.79</mn></mrow><mrow><mo>−</mo><mn>3.14</mn></mrow></msubsup></mrow></math> 1 1 <math id="M364"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>114</mn></mrow></msubsup></mrow></math> Mo 1 1 8790 1 1 4930 1 1 -2.847 1 1 -2.184 1 1 0.518 1 1 9.24 <math id="M365"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>10.52</mn></mrow><mrow><mo>−</mo><mn>5.15</mn></mrow></msubsup></mrow></math> 1 1 <math id="M366"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>115</mn></mrow></msubsup></mrow></math> Mo 1 1 11570 1 1 5780 1 1 -3.090 1 1 -2.592 1 1 0.511 1 1 8.13 <math id="M367"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>9.36</mn></mrow><mrow><mo>−</mo><mn>4.54</mn></mrow></msubsup></mrow></math> 1 1 <math id="M368"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>116</mn></mrow></msubsup></mrow></math> Mo 1 1 9960 1 1 6750 1 1 -3.442 1 1 -2.807 1 1 0.518 1 1 19.06 <math id="M369"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.41</mn></mrow><mrow><mo>−</mo><mn>10.17</mn></mrow></msubsup></mrow></math> 1 1 <math id="M370"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>117</mn></mrow></msubsup></mrow></math> Mo 1 1 12210 1 1 7210 1 1 -3.817 1 1 -2.855 1 1 0.511 1 1 15.74 <math id="M371"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.21</mn></mrow><mrow><mo>−</mo><mn>8.49</mn></mrow></msubsup></mrow></math> 1 1 <math id="M372"><mrow><msubsup><mrow/><mrow><mn>42</mn></mrow><mrow><mn>118</mn></mrow></msubsup></mrow></math> Mo 1 1 11160 1 1 7680 1 1 -3.963 1 1 -3.351 1 1 0.518 1 1 20.52 <math id="M373"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.12</mn></mrow><mrow><mo>−</mo><mn>10.87</mn></mrow></msubsup></mrow></math> 1 1 <math id="M374"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>115</mn></mrow></msubsup></mrow></math> Tc 1 1 9870 1 1 5830 1 1 -2.551 1 1 -1.813 1 1 0.511 1 1 15.67 <math id="M375"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.17</mn></mrow><mrow><mo>−</mo><mn>8.45</mn></mrow></msubsup></mrow></math> 1 1 <math id="M376"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>116</mn></mrow></msubsup></mrow></math> Tc 1 1 12610 1 1 6660 1 1 -2.865 1 1 -2.093 1 1 0.513 1 1 15.66 <math id="M377"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.27</mn></mrow><mrow><mo>−</mo><mn>8.47</mn></mrow></msubsup></mrow></math> 1 1 <math id="M378"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>117</mn></mrow></msubsup></mrow></math> Tc 1 1 11110 1 1 7620 1 1 -3.112 1 1 -2.399 1 1 0.511 1 1 26.61 <math id="M379"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.98</mn></mrow><mrow><mo>−</mo><mn>13.48</mn></mrow></msubsup></mrow></math> 1 1 <math id="M380"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>118</mn></mrow></msubsup></mrow></math> Tc 1 1 13470 1 1 7630 1 1 -3.507 1 1 -2.403 1 1 0.513 1 1 20.54 <math id="M381"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.92</mn></mrow><mrow><mo>−</mo><mn>10.83</mn></mrow></msubsup></mrow></math> 1 1 <math id="M382"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>119</mn></mrow></msubsup></mrow></math> Tc 1 1 12190 1 1 8820 1 1 -3.817 1 1 -2.808 1 1 0.511 1 1 32.68 <math id="M383"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.22</mn></mrow><mrow><mo>−</mo><mn>15.88</mn></mrow></msubsup></mrow></math> 1 1 <math id="M384"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>120</mn></mrow></msubsup></mrow></math> Tc 1 1 14490 1 1 8980 1 1 -3.863 1 1 -2.645 1 1 0.513 1 1 30.35 <math id="M385"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.02</mn></mrow><mrow><mo>−</mo><mn>15.07</mn></mrow></msubsup></mrow></math> 1 1 <math id="M386"><mrow><msubsup><mrow/><mrow><mn>43</mn></mrow><mrow><mn>121</mn></mrow></msubsup></mrow></math> Tc 1 1 13270 1 1 10160 1 1 -3.817 1 1 -3.001 1 1 0.510 1 1 44.15 <math id="M387"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.40</mn></mrow><mrow><mo>−</mo><mn>19.42</mn></mrow></msubsup></mrow></math> 1 1 <math id="M388"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>114</mn></mrow></msubsup></mrow></math> Ru 1 1 5489 1 1 474.4 1 1 -0.611 1 1 0.139 1 1 0.518 1 1 0 1 1 <math id="M389"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>115</mn></mrow></msubsup></mrow></math> Ru 1 1 8040 1 1 1450 1 1 -1.146 1 1 -0.803 1 1 0.511 1 1 0.10 <math id="M390"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.14</mn></mrow><mrow><mo>−</mo><mn>0.06</mn></mrow></msubsup></mrow></math> 1 1 <math id="M391"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>116</mn></mrow></msubsup></mrow></math> Ru 1 1 6667 1 1 2089.6 1 1 -1.590 1 1 -0.830 1 1 0.518 1 1 0.77 <math id="M392"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.07</mn></mrow><mrow><mo>−</mo><mn>0.44</mn></mrow></msubsup></mrow></math> 1 1 <math id="M393"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>117</mn></mrow></msubsup></mrow></math> Ru 1 1 9410 1 1 3170 1 1 -1.890 1 1 -1.582 1 1 0.511 1 1 1.54 <math id="M394"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>2.08</mn></mrow><mrow><mo>−</mo><mn>0.88</mn></mrow></msubsup></mrow></math> 1 1 <math id="M395"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>118</mn></mrow></msubsup></mrow></math> Ru 1 1 7630 1 1 3570 1 1 -2.313 1 1 -1.482 1 1 0.518 1 1 4.47 <math id="M396"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.66</mn></mrow><mrow><mo>−</mo><mn>2.54</mn></mrow></msubsup></mrow></math> 1 1 <math id="M397"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>119</mn></mrow></msubsup></mrow></math> Ru 1 1 10260 1 1 4250 1 1 -2.666 1 1 -1.962 1 1 0.511 1 1 3.95 <math id="M398"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.01</mn></mrow><mrow><mo>−</mo><mn>2.25</mn></mrow></msubsup></mrow></math> 1 1 <math id="M399"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>120</mn></mrow></msubsup></mrow></math> Ru 1 1 8800 1 1 4740 1 1 -3.101 1 1 -2.092 1 1 0.518 1 1 8.84 <math id="M400"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>10.12</mn></mrow><mrow><mo>−</mo><mn>4.93</mn></mrow></msubsup></mrow></math> 1 1 <math id="M401"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>121</mn></mrow></msubsup></mrow></math> Ru 1 1 11200 1 1 5700 1 1 -3.540 1 1 -2.218 1 1 0.510 1 1 10.96 <math id="M402"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>11.79</mn></mrow><mrow><mo>−</mo><mn>6.05</mn></mrow></msubsup></mrow></math> 1 1 <math id="M403"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>122</mn></mrow></msubsup></mrow></math> Ru 1 1 9930 1 1 6030 1 1 -3.689 1 1 -2.416 1 1 0.518 1 1 17.97 <math id="M404"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>16.66</mn></mrow><mrow><mo>−</mo><mn>9.61</mn></mrow></msubsup></mrow></math> 1 1 <math id="M405"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>123</mn></mrow></msubsup></mrow></math> Ru 1 1 12280 1 1 6930 1 1 -3.963 1 1 -2.310 1 1 0.510 1 1 22.13 <math id="M406"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.39</mn></mrow><mrow><mo>−</mo><mn>11.51</mn></mrow></msubsup></mrow></math> 1 1 <math id="M407"><mrow><msubsup><mrow/><mrow><mn>44</mn></mrow><mrow><mn>124</mn></mrow></msubsup></mrow></math> Ru 1 1 10930 1 1 7330 1 1 -4.200 1 1 -2.489 1 1 0.520 1 1 33.99 <math id="M408"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.61</mn></mrow><mrow><mo>−</mo><mn>16.47</mn></mrow></msubsup></mrow></math> 1 1 <math id="M409"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>115</mn></mrow></msubsup></mrow></math> Rh 1 1 6197 1 1 1190 1 1 0.030 1 1 0.485 1 1 0.511 1 1 0.13 <math id="M410"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.19</mn></mrow><mrow><mo>−</mo><mn>0.08</mn></mrow></msubsup></mrow></math> 1 1 <math id="M411"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>121</mn></mrow></msubsup></mrow></math> Rh 1 1 9930 1 1 5960 1 1 -2.577 1 1 -1.632 1 1 0.510 1 1 20.36 <math id="M412"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.63</mn></mrow><mrow><mo>−</mo><mn>10.70</mn></mrow></msubsup></mrow></math> 1 1 <math id="M413"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>122</mn></mrow></msubsup></mrow></math> Rh 1 1 12540 1 1 6030 1 1 -2.976 1 1 -1.721 1 1 0.513 1 1 15.22 <math id="M414"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>14.88</mn></mrow><mrow><mo>−</mo><mn>8.23</mn></mrow></msubsup></mrow></math> 1 1 <math id="M415"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>123</mn></mrow></msubsup></mrow></math> Rh 1 1 11070 1 1 7190 1 1 -3.170 1 1 -1.877 1 1 0.510 1 1 33.01 <math id="M416"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.18</mn></mrow><mrow><mo>−</mo><mn>15.96</mn></mrow></msubsup></mrow></math> 1 1 <math id="M417"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>124</mn></mrow></msubsup></mrow></math> Rh 1 1 13500 1 1 7470 1 1 -3.507 1 1 -1.751 1 1 0.515 1 1 32.14 <math id="M418"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.18</mn></mrow><mrow><mo>−</mo><mn>15.69</mn></mrow></msubsup></mrow></math> 1 1 <math id="M419"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>125</mn></mrow></msubsup></mrow></math> Rh 1 1 12120 1 1 8320 1 1 -3.631 1 1 -1.997 1 1 0.512 1 1 46.99 <math id="M420"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.16</mn></mrow><mrow><mo>−</mo><mn>20.12</mn></mrow></msubsup></mrow></math> 1 1 <math id="M421"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>126</mn></mrow></msubsup></mrow></math> Rh 1 1 14560 1 1 8750 1 1 -3.963 1 1 -1.858 1 1 0.518 1 1 47.36 <math id="M422"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.23</mn></mrow><mrow><mo>−</mo><mn>20.31</mn></mrow></msubsup></mrow></math> 1 1 <math id="M423"><mrow><msubsup><mrow/><mrow><mn>45</mn></mrow><mrow><mn>127</mn></mrow></msubsup></mrow></math> Rh 1 1 13150 1 1 9760 1 1 -3.912 1 1 -2.252 1 1 0.514 1 1 59.36 <math id="M424"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.60</mn></mrow><mrow><mo>−</mo><mn>21.77</mn></mrow></msubsup></mrow></math> 1 1 <math id="M425"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>119</mn></mrow></msubsup></mrow></math> Pd 1 1 7238 1 1 74.6 1 1 -0.083 1 1 -0.181 1 1 0.510 1 1 0 1 1 <math id="M426"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>120</mn></mrow></msubsup></mrow></math> Pd 1 1 5371.5 1 1 294 1 1 -0.709 1 1 0.415 1 1 0.518 1 1 0 1 1 <math id="M427"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>121</mn></mrow></msubsup></mrow></math> Pd 1 1 8220 1 1 1397.9 1 1 -1.238 1 1 -0.653 1 1 0.510 1 1 0.10 <math id="M428"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.15</mn></mrow><mrow><mo>−</mo><mn>0.06</mn></mrow></msubsup></mrow></math> 1 1 <math id="M429"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>122</mn></mrow></msubsup></mrow></math> Pd 1 1 6490 1 1 1715 1 1 -1.645 1 1 -0.321 1 1 0.518 1 1 0.55 <math id="M430"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.76</mn></mrow><mrow><mo>−</mo><mn>0.31</mn></mrow></msubsup></mrow></math> 1 1 <math id="M431"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>128</mn></mrow></msubsup></mrow></math> Pd 1 1 10130 1 1 5880 1 1 -3.352 1 1 -1.929 1 1 0.523 1 1 25.28 <math id="M432"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.80</mn></mrow><mrow><mo>−</mo><mn>12.99</mn></mrow></msubsup></mrow></math> 1 1 <math id="M433"><mrow><msubsup><mrow/><mrow><mn>46</mn></mrow><mrow><mn>129</mn></mrow></msubsup></mrow></math> Pd 1 1 14370 1 1 8940 1 1 -3.474 1 1 -2.738 1 1 0.513 1 1 39.52 <math id="M434"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.72</mn></mrow><mrow><mo>−</mo><mn>18.22</mn></mrow></msubsup></mrow></math> 1 1 <math id="M435"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>130</mn></mrow></msubsup></mrow></math> Ag 1 1 15420 1 1 9290 1 1 -3.194 1 1 -2.151 1 1 0.519 1 1 48.29 <math id="M436"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.11</mn></mrow><mrow><mo>−</mo><mn>20.51</mn></mrow></msubsup></mrow></math> 1 1 <math id="M437"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>131</mn></mrow></msubsup></mrow></math> Ag 1 1 14840 1 1 12670 1 1 -3.352 1 1 -2.946 1 1 0.513 1 1 71.84 <math id="M438"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>14.20</mn></mrow><mrow><mo>−</mo><mn>20.58</mn></mrow></msubsup></mrow></math> 1 1 <math id="M439"><mrow><msubsup><mrow/><mrow><mn>47</mn></mrow><mrow><mn>132</mn></mrow></msubsup></mrow></math> Ag 1 1 16470 1 1 13360 1 1 -3.576 1 1 -2.590 1 1 0.517 1 1 75.48 <math id="M440"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.71</mn></mrow><mrow><mo>−</mo><mn>19.73</mn></mrow></msubsup></mrow></math> 1 1 <math id="M441"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>126</mn></mrow></msubsup></mrow></math> Cd 1 1 5516 1 1 149 1 1 -0.666 1 1 0.980 1 1 0.521 1 1 0 1 1 <math id="M442"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>127</mn></mrow></msubsup></mrow></math> Cd 1 1 8149 1 1 954 1 1 -0.799 1 1 0.036 1 1 0.513 1 1 0.04 <math id="M443"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.06</mn></mrow><mrow><mo>−</mo><mn>0.02</mn></mrow></msubsup></mrow></math> 1 1 <math id="M444"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>128</mn></mrow></msubsup></mrow></math> Cd 1 1 6900 1 1 1583 1 1 -1.402 1 1 -0.065 1 1 0.522 1 1 0.54 <math id="M445"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.76</mn></mrow><mrow><mo>−</mo><mn>0.31</mn></mrow></msubsup></mrow></math> 1 1 <math id="M446"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>129</mn></mrow></msubsup></mrow></math> Cd 1 1 9780 1 1 3020 1 1 -1.890 1 1 -0.825 1 1 0.514 1 1 2.94 <math id="M447"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>3.87</mn></mrow><mrow><mo>−</mo><mn>1.68</mn></mrow></msubsup></mrow></math> 1 1 <math id="M448"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>133</mn></mrow></msubsup></mrow></math> Cd 1 1 13540 1 1 10420 1 1 -2.749 1 1 -2.502 1 1 0.513 1 1 61.77 <math id="M449"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.86</mn></mrow><mrow><mo>−</mo><mn>21.77</mn></mrow></msubsup></mrow></math> 1 1 <math id="M450"><mrow><msubsup><mrow/><mrow><mn>48</mn></mrow><mrow><mn>134</mn></mrow></msubsup></mrow></math> Cd 1 1 12740 1 1 10470 1 1 -2.733 1 1 -3.206 1 1 0.521 1 1 58.49 <math id="M451"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.03</mn></mrow><mrow><mo>−</mo><mn>22.00</mn></mrow></msubsup></mrow></math> 1 1 <math id="M452"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>135</mn></mrow></msubsup></mrow></math> In 1 1 14100 1 1 11830 1 1 -2.293 1 1 -2.689 1 1 0.513 1 1 70.92 <math id="M453"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>14.58</mn></mrow><mrow><mo>−</mo><mn>20.80</mn></mrow></msubsup></mrow></math> 1 1 <math id="M454"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>136</mn></mrow></msubsup></mrow></math> In 1 1 15390 1 1 12050 1 1 -2.465 1 1 -2.197 1 1 0.518 1 1 74.18 <math id="M455"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>13.28</mn></mrow><mrow><mo>−</mo><mn>20.15</mn></mrow></msubsup></mrow></math> 1 1 <math id="M456"><mrow><msubsup><mrow/><mrow><mn>49</mn></mrow><mrow><mn>137</mn></mrow></msubsup></mrow></math> In 1 1 14750 1 1 12790 1 1 -2.733 1 1 -2.946 1 1 0.513 1 1 73.19 <math id="M457"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>13.64</mn></mrow><mrow><mo>−</mo><mn>20.24</mn></mrow></msubsup></mrow></math> 1 1 <math id="M458"><mrow><msubsup><mrow/><mrow><mn>50</mn></mrow><mrow><mn>138</mn></mrow></msubsup></mrow></math> Sn 1 1 9400 1 1 7130 1 1 -1.871 1 1 -1.616 1 1 0.523 1 1 52.33 <math id="M459"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.55</mn></mrow><mrow><mo>−</mo><mn>21.38</mn></mrow></msubsup></mrow></math> 1 1 <math id="M460"><mrow><msubsup><mrow/><mrow><mn>50</mn></mrow><mrow><mn>139</mn></mrow></msubsup></mrow></math> Sn 1 1 11350 1 1 7700 1 1 -2.120 1 1 -1.593 1 1 0.514 1 1 49.58 <math id="M461"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.85</mn></mrow><mrow><mo>−</mo><mn>20.70</mn></mrow></msubsup></mrow></math> 1 1 <math id="M462"><mrow><msubsup><mrow/><mrow><mn>51</mn></mrow><mrow><mn>134</mn></mrow></msubsup></mrow></math> Sb 1 1 8513.2 1 1 845.3 1 1 -0.393 1 1 0.772 1 1 0.519 1 1 0.03 <math id="M463"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>0.05</mn></mrow><mrow><mo>−</mo><mn>0.02</mn></mrow></msubsup></mrow></math> 1 1 <math id="M464"><mrow><msubsup><mrow/><mrow><mn>51</mn></mrow><mrow><mn>141</mn></mrow></msubsup></mrow></math> Sb 1 1 11380 1 1 9400 1 1 -2.273 1 1 -1.721 1 1 0.513 1 1 67.87 <math id="M465"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.75</mn></mrow><mrow><mo>−</mo><mn>21.30</mn></mrow></msubsup></mrow></math> 1 1 <math id="M466"><mrow><msubsup><mrow/><mrow><mn>52</mn></mrow><mrow><mn>139</mn></mrow></msubsup></mrow></math> Te 1 1 8265.9 1 1 3703.5 1 1 -0.298 1 1 -0.189 1 1 0.512 1 1 11.86 <math id="M467"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.56</mn></mrow><mrow><mo>−</mo><mn>6.52</mn></mrow></msubsup></mrow></math> 1 1 <math id="M468"><mrow><msubsup><mrow/><mrow><mn>52</mn></mrow><mrow><mn>140</mn></mrow></msubsup></mrow></math> Te 1 1 7030 1 1 3823 1 1 -1.047 1 1 -0.404 1 1 0.520 1 1 16.94 <math id="M469"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>16.05</mn></mrow><mrow><mo>−</mo><mn>9.10</mn></mrow></msubsup></mrow></math> 1 1 <math id="M470"><mrow><msubsup><mrow/><mrow><mn>52</mn></mrow><mrow><mn>141</mn></mrow></msubsup></mrow></math> Te 1 1 9440 1 1 5050 1 1 -1.645 1 1 -0.978 1 1 0.511 1 1 20.57 <math id="M471"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.76</mn></mrow><mrow><mo>−</mo><mn>10.80</mn></mrow></msubsup></mrow></math> 1 1 <math id="M472"><mrow><msubsup><mrow/><mrow><mn>52</mn></mrow><mrow><mn>142</mn></mrow></msubsup></mrow></math> Te 1 1 8400 1 1 5490 1 1 -1.917 1 1 -1.428 1 1 0.519 1 1 28.61 <math id="M473"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.69</mn></mrow><mrow><mo>−</mo><mn>14.39</mn></mrow></msubsup></mrow></math> 1 1 <math id="M474"><mrow><msubsup><mrow/><mrow><mn>52</mn></mrow><mrow><mn>143</mn></mrow></msubsup></mrow></math> Te 1 1 10350 1 1 6420 1 1 -2.120 1 1 -1.577 1 1 0.510 1 1 30.16 <math id="M475"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.74</mn></mrow><mrow><mo>−</mo><mn>14.89</mn></mrow></msubsup></mrow></math> 1 1 <math id="M476"><mrow><msubsup><mrow/><mrow><mn>53</mn></mrow><mrow><mn>142</mn></mrow></msubsup></mrow></math> I 1 1 10460 1 1 5360 1 1 -1.448 1 1 -0.806 1 1 0.514 1 1 21.38 <math id="M477"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.14</mn></mrow><mrow><mo>−</mo><mn>11.18</mn></mrow></msubsup></mrow></math> 1 1 <math id="M478"><mrow><msubsup><mrow/><mrow><mn>53</mn></mrow><mrow><mn>143</mn></mrow></msubsup></mrow></math> I 1 1 9570 1 1 6530 1 1 -1.704 1 1 -1.403 1 1 0.510 1 1 34.84 <math id="M479"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.37</mn></mrow><mrow><mo>−</mo><mn>16.61</mn></mrow></msubsup></mrow></math> 1 1 <math id="M480"><mrow><msubsup><mrow/><mrow><mn>53</mn></mrow><mrow><mn>144</mn></mrow></msubsup></mrow></math> I 1 1 11590 1 1 6850 1 1 -2.364 1 1 -1.506 1 1 0.513 1 1 29.69 <math id="M481"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.81</mn></mrow><mrow><mo>−</mo><mn>14.77</mn></mrow></msubsup></mrow></math> 1 1 <math id="M482"><mrow><msubsup><mrow/><mrow><mn>53</mn></mrow><mrow><mn>145</mn></mrow></msubsup></mrow></math> I 1 1 10550 1 1 7860 1 1 -2.411 1 1 -2.056 1 1 0.510 1 1 39.97 <math id="M483"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.60</mn></mrow><mrow><mo>−</mo><mn>18.28</mn></mrow></msubsup></mrow></math> 1 1 <math id="M484"><mrow><msubsup><mrow/><mrow><mn>54</mn></mrow><mrow><mn>148</mn></mrow></msubsup></mrow></math> Xe 1 1 8310 1 1 5250 1 1 -2.465 1 1 -2.060 1 1 0.518 1 1 15.04 <math id="M485"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>15.03</mn></mrow><mrow><mo>−</mo><mn>8.17</mn></mrow></msubsup></mrow></math> 1 1 <math id="M486"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>151</mn></mrow></msubsup></mrow></math> Cs 1 1 10710 1 1 7600 1 1 -2.830 1 1 -2.403 1 1 0.511 1 1 29.52 <math id="M487"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.70</mn></mrow><mrow><mo>−</mo><mn>14.67</mn></mrow></msubsup></mrow></math> 1 1 <math id="M488"><mrow><msubsup><mrow/><mrow><mn>56</mn></mrow><mrow><mn>150</mn></mrow></msubsup></mrow></math> Ba 1 1 6230 1 1 2250 1 1 -1.355 1 1 -0.674 1 1 0.518 1 1 1.43 <math id="M489"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>1.94</mn></mrow><mrow><mo>−</mo><mn>0.82</mn></mrow></msubsup></mrow></math> 1 1 <math id="M490"><mrow><msubsup><mrow/><mrow><mn>56</mn></mrow><mrow><mn>151</mn></mrow></msubsup></mrow></math> Ba 1 1 8370 1 1 3120 1 1 -1.790 1 1 -1.185 1 1 0.511 1 1 2.36 <math id="M491"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>3.12</mn></mrow><mrow><mo>−</mo><mn>1.35</mn></mrow></msubsup></mrow></math> 1 1 <math id="M492"><mrow><msubsup><mrow/><mrow><mn>56</mn></mrow><mrow><mn>152</mn></mrow></msubsup></mrow></math> Ba 1 1 7580 1 1 3530 1 1 -1.966 1 1 -1.655 1 1 0.518 1 1 4.27 <math id="M493"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.44</mn></mrow><mrow><mo>−</mo><mn>2.43</mn></mrow></msubsup></mrow></math> 1 1 <math id="M494"><mrow><msubsup><mrow/><mrow><mn>56</mn></mrow><mrow><mn>153</mn></mrow></msubsup></mrow></math> Ba 1 1 9590 1 1 4750 1 1 -2.180 1 1 -1.866 1 1 0.511 1 1 7.85 <math id="M495"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>9.10</mn></mrow><mrow><mo>−</mo><mn>4.39</mn></mrow></msubsup></mrow></math> 1 1 <math id="M496"><mrow><msubsup><mrow/><mrow><mn>56</mn></mrow><mrow><mn>154</mn></mrow></msubsup></mrow></math> Ba 1 1 8710 1 1 5170 1 1 -2.937 1 1 -2.350 1 1 0.518 1 1 11.57 <math id="M497"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.51</mn></mrow><mrow><mo>−</mo><mn>6.39</mn></mrow></msubsup></mrow></math> 1 1 <math id="M498"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>151</mn></mrow></msubsup></mrow></math> La 1 1 7910 1 1 3470 1 1 -0.783 1 1 -0.917 1 1 0.511 1 1 4.74 <math id="M499"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>5.91</mn></mrow><mrow><mo>−</mo><mn>2.69</mn></mrow></msubsup></mrow></math> 1 1 <math id="M500"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>152</mn></mrow></msubsup></mrow></math> La 1 1 9690 1 1 3860 1 1 -1.211 1 1 -0.988 1 1 0.513 1 1 5.03 <math id="M501"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>6.25</mn></mrow><mrow><mo>−</mo><mn>2.85</mn></mrow></msubsup></mrow></math> 1 1 <math id="M502"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>153</mn></mrow></msubsup></mrow></math> La 1 1 8850 1 1 4850 1 1 -1.406 1 1 -1.478 1 1 0.511 1 1 11.76 <math id="M503"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>12.45</mn></mrow><mrow><mo>−</mo><mn>6.47</mn></mrow></msubsup></mrow></math> 1 1 <math id="M504"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>154</mn></mrow></msubsup></mrow></math> La 1 1 10690 1 1 5310 1 1 -1.826 1 1 -1.479 1 1 0.513 1 1 12.37 <math id="M505"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>13.00</mn></mrow><mrow><mo>−</mo><mn>6.79</mn></mrow></msubsup></mrow></math> 1 1 <math id="M506"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>155</mn></mrow></msubsup></mrow></math> La 1 1 9850 1 1 6220 1 1 -2.293 1 1 -2.014 1 1 0.511 1 1 19.98 <math id="M507"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.51</mn></mrow><mrow><mo>−</mo><mn>10.53</mn></mrow></msubsup></mrow></math> 1 1 <math id="M508"><mrow><msubsup><mrow/><mrow><mn>57</mn></mrow><mrow><mn>156</mn></mrow></msubsup></mrow></math> La 1 1 11770 1 1 6660 1 1 -2.477 1 1 -1.961 1 1 0.513 1 1 20.1 <math id="M509"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.73</mn></mrow><mrow><mo>−</mo><mn>10.62</mn></mrow></msubsup></mrow></math> 1 1 <math id="M510"><mrow><msubsup><mrow/><mrow><mn>30</mn></mrow><mrow><mn>85</mn></mrow></msubsup></mrow></math> Zn 1 1 14620 1 1 10790 1 1 - 1 1 -2.682 1 1 0.512 1 1 54.96 <math id="M511"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.71</mn></mrow><mrow><mo>−</mo><mn>21.41</mn></mrow></msubsup></mrow></math> 1 1 <math id="M512"><mrow><msubsup><mrow/><mrow><mn>32</mn></mrow><mrow><mn>89</mn></mrow></msubsup></mrow></math> Ge 1 1 13070 1 1 8920 1 1 - 1 1 -2.005 1 1 0.514 1 1 50.23 <math id="M513"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.73</mn></mrow><mrow><mo>−</mo><mn>20.82</mn></mrow></msubsup></mrow></math> 1 1 <math id="M514"><mrow><msubsup><mrow/><mrow><mn>32</mn></mrow><mrow><mn>90</mn></mrow></msubsup></mrow></math> Ge 1 1 12110 1 1 9510 1 1 - 1 1 -2.589 1 1 0.523 1 1 56.10 <math id="M515"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.68</mn></mrow><mrow><mo>−</mo><mn>21.84</mn></mrow></msubsup></mrow></math> 1 1 <math id="M516"><mrow><msubsup><mrow/><mrow><mn>33</mn></mrow><mrow><mn>89</mn></mrow></msubsup></mrow></math> As 1 1 12190 1 1 9020 1 1 - 1 1 -1.732 1 1 0.513 1 1 57.61 <math id="M517"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.07</mn></mrow><mrow><mo>−</mo><mn>21.66</mn></mrow></msubsup></mrow></math> 1 1 <math id="M518"><mrow><msubsup><mrow/><mrow><mn>33</mn></mrow><mrow><mn>90</mn></mrow></msubsup></mrow></math> As 1 1 14470 1 1 9590 1 1 - 1 1 -1.666 1 1 0.518 1 1 57.12 <math id="M519"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.28</mn></mrow><mrow><mo>−</mo><mn>21.75</mn></mrow></msubsup></mrow></math> 1 1 <math id="M520"><mrow><msubsup><mrow/><mrow><mn>33</mn></mrow><mrow><mn>91</mn></mrow></msubsup></mrow></math> As 1 1 13680 1 1 10830 1 1 - 1 1 -2.351 1 1 0.513 1 1 63.67 <math id="M521"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>17.23</mn></mrow><mrow><mo>−</mo><mn>21.69</mn></mrow></msubsup></mrow></math> 1 1 <math id="M522"><mrow><msubsup><mrow/><mrow><mn>33</mn></mrow><mrow><mn>92</mn></mrow></msubsup></mrow></math> As 1 1 15740 1 1 11530 1 1 - 1 1 -2.134 1 1 0.517 1 1 66.32 <math id="M523"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>16.39</mn></mrow><mrow><mo>−</mo><mn>21.65</mn></mrow></msubsup></mrow></math> 1 1 <math id="M524"><mrow><msubsup><mrow/><mrow><mn>34</mn></mrow><mrow><mn>92</mn></mrow></msubsup></mrow></math> Se 1 1 9510 1 1 6310 1 1 - 1 1 -1.761 1 1 0.519 1 1 29.99 <math id="M525"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.99</mn></mrow><mrow><mo>−</mo><mn>14.94</mn></mrow></msubsup></mrow></math> 1 1 <math id="M526"><mrow><msubsup><mrow/><mrow><mn>34</mn></mrow><mrow><mn>93</mn></mrow></msubsup></mrow></math> Se 1 1 12180 1 1 7450 1 1 - 1 1 -2.103 1 1 0.510 1 1 28.87 <math id="M527"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.47</mn></mrow><mrow><mo>−</mo><mn>14.38</mn></mrow></msubsup></mrow></math> 1 1 <math id="M528"><mrow><msubsup><mrow/><mrow><mn>34</mn></mrow><mrow><mn>94</mn></mrow></msubsup></mrow></math> Se 1 1 10600 1 1 8020 1 1 - 1 1 -2.444 1 1 0.518 1 1 39.83 <math id="M529"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.94</mn></mrow><mrow><mo>−</mo><mn>18.46</mn></mrow></msubsup></mrow></math> 1 1 <math id="M530"><mrow><msubsup><mrow/><mrow><mn>34</mn></mrow><mrow><mn>95</mn></mrow></msubsup></mrow></math> Se 1 1 13310 1 1 8870 1 1 - 1 1 -2.685 1 1 0.510 1 1 33.98 <math id="M531"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.29</mn></mrow><mrow><mo>−</mo><mn>16.31</mn></mrow></msubsup></mrow></math> 1 1 <math id="M532"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>95</mn></mrow></msubsup></mrow></math> Br 1 1 12390 1 1 9510 1 1 - 1 1 -2.575 1 1 0.510 1 1 43.17 <math id="M533"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.48</mn></mrow><mrow><mo>−</mo><mn>19.18</mn></mrow></msubsup></mrow></math> 1 1 <math id="M534"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>96</mn></mrow></msubsup></mrow></math> Br 1 1 14920 1 1 9920 1 1 - 1 1 -2.624 1 1 0.513 1 1 38.11 <math id="M535"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.84</mn></mrow><mrow><mo>−</mo><mn>17.87</mn></mrow></msubsup></mrow></math> 1 1 <math id="M536"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>97</mn></mrow></msubsup></mrow></math> Br 1 1 13370 1 1 10950 1 1 - 1 1 -3.070 1 1 0.510 1 1 47.37 <math id="M537"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.11</mn></mrow><mrow><mo>−</mo><mn>20.20</mn></mrow></msubsup></mrow></math> 1 1 <math id="M538"><mrow><msubsup><mrow/><mrow><mn>35</mn></mrow><mrow><mn>98</mn></mrow></msubsup></mrow></math> Br 1 1 16060 1 1 11100 1 1 - 1 1 -3.082 1 1 0.513 1 1 40.00 <math id="M539"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>21.91</mn></mrow><mrow><mo>−</mo><mn>18.50</mn></mrow></msubsup></mrow></math> 1 1 <math id="M540"><mrow><msubsup><mrow/><mrow><mn>36</mn></mrow><mrow><mn>101</mn></mrow></msubsup></mrow></math> Kr 1 1 13720 1 1 9050 1 1 - 1 1 -3.342 1 1 0.511 1 1 23.31 <math id="M541"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>18.91</mn></mrow><mrow><mo>−</mo><mn>12.05</mn></mrow></msubsup></mrow></math> 1 1 <math id="M542"><mrow><msubsup><mrow/><mrow><mn>38</mn></mrow><mrow><mn>107</mn></mrow></msubsup></mrow></math> Sr 1 1 13470 1 1 9080 1 1 - 1 1 -3.287 1 1 0.511 1 1 25.01 <math id="M543"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>19.50</mn></mrow><mrow><mo>−</mo><mn>12.80</mn></mrow></msubsup></mrow></math> 1 1 <math id="M544"><mrow><msubsup><mrow/><mrow><mn>55</mn></mrow><mrow><mn>152</mn></mrow></msubsup></mrow></math> Cs 1 1 12780 1 1 7940 1 1 - 1 1 -2.344 1 1 0.513 1 1 27.55 <math id="M545"><mrow><msubsup><mrow/><mrow><mo>+</mo><mn>20.47</mn></mrow><mrow><mo>−</mo><mn>13.96</mn></mrow></msubsup></mrow></math> Conclusion 1 This study focused on the properties of β -decay, that is, the half-lives and probability of releasing the delayed neutrons of neutron-rich nuclei with atomic numbers from 29 to 57, which are important fission products. During the review phase of the paper, new experimental results were published [ 52 52 ]. Taking experimental uncertainty into account, the latest results are all within one standard deviation of our prediction, with an RMS equal to 16.752%. In considering the odevity as well as the shell effect, phenomenological formulas for β -decay were proposed on top of the classical formula. The β -decay neutron emission ( βn ) probability has a similar formula to the half-life based on their relationship analysis, except for the addition of new terms to include the differences between the decay energy when releasing delayed neutrons and that of not. Based on the fitting results, the β -decay half-lives, βn probabilities, and the corresponding uncertainties were calculated. The experimental half-lives were generally well reproduced. In particular, the shorter the half-life, the better the consistency. 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Material preparation, data collection and analysis were performed by Yu-Feng Gao and Bo-Shuai Cai. The first draft of the manuscript was written by Yu-Feng Gao and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. Discussions with Mr. Guang-Shang Chen, Jiong-Yu Xu, and Bo-Cong Liu are greatly appreciated. 10.1007/s41365-022-01153-4 This work was supported by the Guangdong Major Project of Basic and Applied Basic Research (No. 2021B0301030006), and computational resources from Sun Yat-Sen University and the National Supercomputer Center in Guangzhou. 2022-09-13 2022-10-25 2022-11-14 2023-01-18 2023-02-20 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2023 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-022-01153-4 http://dx.doi.org/10.1007/s41365-022-01153-4 . Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. 2023 Nuclear Science and Techniques 01 34