Charge resolution in the isochronous mass spectrometry and the mass of ⁵¹Co

Charge resolution in the isochronous mass spectrometry and the mass of 51 Co 1 2 first-author https://orcid.org/0000-0001-8744-2909 1 2 corresp Corresponding author, wangm@impcas.ac.cn Corresponding author, wangm@impcas.ac.cn wangm@impcas.ac.cn https://orcid.org/0000-0003-2408-8089 1 2 1 2 1 2 https://orcid.org/0000-0002-1761-9040} 1 2 https://orcid.org/0000-0002-8393-513X 1 3 https://orcid.org/0000-0002-7043-4993 1 3 1 4 1 5 1 6 1 1 1 3 1 1 1 7 https://orcid.org/0000-0001-9060-0357 1 1 2 1 2 1 1 2 1 8 1 2 1 2 1 2 1 2 1 2 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 GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany GSI Helmholtzzentrum für Schwerionenforschung, Planckstraße 1, 64291 Darmstadt, Germany 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 Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, IL 60439, USA Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, IL 60439, USA School of Science, Xi’an Jiaotong University, Xi’an 710049, China School of Science, Xi’an Jiaotong University, Xi’an 710049, China School of nuclear science and engineering, East China University of Technology, Nanchang 330013, China School of nuclear science and engineering, East China University of Technology, Nanchang 330013, China Université Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, France Université Paris-Saclay, CNRS/IN2P3, IJCLab, F-91405 Orsay, France Isochronous mass spectrometry (IMS) of heavy-ion storage rings is a powerful tool for the mass measurements of short-lived nuclei. In IMS experiments, masses are determined through precision measurements of the revolution times of the ions stored in the ring. However, the revolution times cannot be resolved for particles with nearly the same mass-to-charge ( m/q ) ratios. To overcome this limitation and to extract the accurate revolution times for such pairs of ion species with very close m/q ratios, in our early work on particle identification, we analyzed the amplitudes of the timing signals from the detector based on the emission of secondary electrons. Here, the previous data analysis method is further improved by considering the signal amplitudes, detection efficiencies, and number of stored ions in the ring. A sensitive Z -dependent parameter is introduced in the data analysis, leading to a better resolution of 34 Ar 18+ and 51 Co 27+ with A/Z =17/9. The mean revolution times of 34 Ar 18+ and 51 Co 27+ are deduced, although their time difference is merely 1.8 ps. The uncorrected, overlapped peak of these ions has a full width at half maximum of 7.7 ps. The mass excess of 51 Co was determined to be -27,332(41) keV, which is in agreement with the previous value of -27,342(48) keV. Isochronous mass spectrometry Charge resolution Signal amplitude Micro-channel plate 51 Co 1 Introduction 1 Isochronous mass spectrometry (IMS) of heavy-ion storage rings plays an important role in the mass measurements of short-lived nuclei [ 1 1 , 2 2 ]. There are three storage ring facilities that conduct such experiments worldwide [ 3 3 - 6 6 3-6 ], namely, the experimental cooler-storage ring (CSRe) in Lanzhou, China; the experimental storage ring (ESR) in Darmstadt, Germany; and the Rare-RI Ring (R3) in Saitama, Japan. In IMS experiments, the nuclei of interest are produced in projectile fragmentation (PF) or in in-flight fission nuclear reactions, where the production cross sections are related to the binding energies of the fragments [ 7 7 - 9 9 7-9 ]. The reaction products of interest are selected with a fragment separator and injected into the storage ring for mass measurements. The revolution times of the stored nuclides are directly related to their mass-to-charge ( m/q ) ratios. The revolution times are typically measured by using dedicated timing detectors [ 10 10 - 13 13 10-13 ]. It is obvious that only those revolution times that could unambiguously be assigned to a specific ion species can be used [ 14 14 , 15 15 ]. Particle identification (PID) is a prerequisite in experiments with radioactive ion beams (RIBs) produced in a nuclear reaction and is routinely accomplished along an RIB beam line by measuring the time of flight (TOF), energy loss ( Δ E), and magnetic rigidity (B ρ ) for each particle [ 16 16 , 17 17 ]. In particular, the atomic number Z is mainly determined by using the Δ E value, which is usually measured with various ionization-type detectors placed along the beam line. Among the storage-ring-based facilities, the R3 in RIKEN is the only one where a PID within a beam line can be performed [ 18 18 , 19 19 ], where the quasi-DC beam from the superconducting cyclotron is employed. Thus, the RIBs can indeed be identified on an event-by-event basis prior to their injection into the R3. It is very different in the cases of the CSRe and ESR. The driver accelerator at the facility in Lanzhou is the heavy-ion synchrotron CSRm [ 20 20 ]. The primary beams are rapidly extracted from the CSRm within ∼ 300 ns. Correspondingly, the produced RIBs have a similar bunched structure. Therefore, event-by-event PID is not feasible in the RIBLL2 radioactive-ion beam line connecting the CSRm and the CSRe. A similar situation can be observed at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany, where the ions are fast-extracted from the heavy-ion synchrotron SIS-18, analyzed in-flight with the fragment separator FRS, and injected into the ESR for isochronous mass measurements [ 21 21 ]. In this work, we examined the sensitivity of the timing detectors to the charge of the stored ions for the purpose of performing in-ring PID. Using IMS at the CSRe, we measured the masses of more than 30 short-lived nuclei [ 22 22 - 32 32 22-32 ]. For a recent review, the reader is referred to Refs. [ 5 5 , 6 6 , 27 27 ] and the references cited therein. In these experiments, the ions were identified almost solely through their m/q ratios by comparing the revolution time spectrum obtained experimentally with the simulated one [ 14 14 , 15 15 ]. An m/q resolving power of 3 × 10 5 was achieved at the CSRe, which was sufficient to identify the isomeric states in 101 In and 52 Co [ 24 24 , 28 28 ]. However, for some pairs of ions with very similar m/q ratios, such as 51 Co 27+ and 34 Ar 18+ , the revolution times were too close to each other to be resolved clearly. Charge determination can provide crucial information for PID in these cases. Charge-resolved IMS was developed by analyzing the average amplitudes of the signals from the timing detector induced by the stored ions [ 33 33 ]. This method was used successfully to determine the mass of 51 Co for the first time. Although the charge difference (Δ Z ) of 51 Co 27+ and 34 Ar 18+ was relatively large, some events could not be unambiguously identified because of the limited charge resolution in a previous study [ 33 33 ]. A higher charge resolution is desired. For example, the masses of 54,56 Ti nuclides were measured in an earlier experiment at the CSRe [ 23 23 , 29 29 ]. The 55 Ti nuclide must have been produced in significant amounts in this experiment according to the yields of the neighboring nuclei; however, it could not be separated from 50 Ca. To measure the mass of 55 Ti, we need to resolve 55 Ti 22+ and 50 Ca 20+ by charge, where Δ Z is only 2. Such high charge resolution was not realized in that experiment. Owing to the limited charge resolution, mass measurements of N = Z nuclides with conventional IMS at the CSRe or ESR are usually regarded as unfeasible. The N = Z nuclides with Δ Z =2 must be resolved by charge, whereas the neighboring N = Z (Δ Z =1) nuclides can be resolved by their revolution times because the difference in their m/q ratios is sufficiently large, owing to the odd-even staggering of the binding energies. If ions with Δ Z =2 can be resolved by charge, then, in principle, all nuclides can be identified and measured in IMS experiments. In this paper, we describe a new method in which the detailed characteristics of the timing detector are considered in the data analysis. The charge resolution of the IMS was improved significantly, leading to a complete separation of 34 Ar and 51 Co. Possible future developments are discussed as well. 2 Experiment and the timing detector 1 The following discussions are based on the same experimental data that were analyzed in an earlier study [ 33 33 ]. More details about the experiment can be found in Refs. [ 33 33 - 35 35 33-35 ]. This experiment aimed to measure the masses of T z =-3/2 nuclei in the pf shell. The nuclei of interest were produced using a projectile fragmentation of 463 MeV/u of 58 Ni 19+ primary beams in a 15-mm 9 Be production target. At this energy, the fragments emerged from the target predominantly as bare ions. Therefore, in the following, we assume the atomic charge q to be equal to the atomic number Z . The RIBLL2 and CSRe were set to a fixed magnetic rigidity of Bρ = 5.677 Tm. All fragments within the Bρ acceptance of ∼±0.2% were injected into the CSRe. The revolution times of the stored ions were measured by using a timing detector equipped with a carbon foil of 19 μ g/cm 2 in thickness and 40 mm in diameter [ 11 11 ]. The foil was positioned in the circulation path of the stored ions. When an ion passed through the carbon foil, secondary electrons were released from the foil surface and guided isochronously to a set of micro-channel plates (MCP) in the Chevron configuration [ 36 36 ]. The MCP had the same diameter as that of the carbon foil, and the micro-channels were 5 μ m in diameter. When an electron hit a channel of the MCP, an avalanche of further secondary electrons propagated through the channel. A bunch of electrons exiting from the rear side of the channel was collected by a conical anode. A signal can be generated with the activation of one or more channels. The negative-voltage signal was directly transmitted from the anode to a digital oscilloscope for data acquisition. The recording time was 200 μ s for each injection in this experiment. The number of electrons from the carbon foil induced by an ion was roughly proportional to the energy loss, which scales with q 2 = Z 2 [ 11 11 ]. Consequently, both the average signal amplitude ( A 0 ) and the detection efficiency ( η ) of an ion depended strongly on its atomic number Z . Figure 1 (a) Figure 1 (a) shows a two-dimensional plot of the revolution time T vs. A 0 obtained in the experiment, and this plot is similar to that in Fig. 3 Fig. 3 given in an earlier work [ 33 33 ]. The 51 Co 27+ and 34 Ar 18+ ions can be resolved using the A 0 value, albeit not completely separated. Figure 1 (a) Figure 1 (a) is an analogue of the typical PID plots at an in-flight separator [ 16 16 , 17 17 ], although with a lower charge resolution but with a higher m/q resolution. Figure 1(b) Figure 1(b) shows a two-dimensional plot of the revolution time T vs. η . The two plots in Fig. 1 Fig. 1 are quite similar. It seems that A 0 provides a better charge resolution for heavier ions, whereas η provides a better charge resolution for lighter ones. 3 Analysis of the signal amplitudes 1 In an earlier study, the average signal amplitude ( A 0 ) was used to resolve the 51 Co 27+ and 34 Ar 18+ ions [ 33 33 ]. Figure 1(a) Figure 1(a) shows a scatter plot of the revolution time T vs. A 0 and the projected histogram for 34 Ar and 51 Co. Although the two ion species can be well resolved, there still exists an overlap between the two Gaussian-like distributions. Assuming that each microchannel was fully discharged after the electron impact and thus provided the same contribution to the signal, we found that A 0 was roughly proportional to the average number of activated microchannels and, in turn, to the number of secondary electrons released from the foil surface. However, there were ion passages through the detector, which did not generate signals. This reflects the finite detection efficiency η [ 33 33 ], which includes electron hits in between the channels (geometrical efficiency) and hits into the already discharged channels (dynamic efficiency). We define an average signal amplitude corrected by the total efficiency as A 1 : <math display="block" id="M1"><mrow><msub><mi>A</mi><mn>1</mn></msub><mo>=</mo><msub><mi>A</mi><mn>0</mn></msub><mo>×</mo><mi>η</mi><mn>.</mn></mrow></math> Clearly, A 1 is proportional to the total number of micro-channels activated by an ion. Figure 2(b) Figure 2(b) shows a scatter plot of the revolution time T vs. A 1 and the projected histogram for 34 Ar and 51 Co. It can be seen clearly from the figure that the separation of these two ions became better. After a micro-channel was activated to output the avalanche electrons, it took 10 ms to recharge the channel. During this period, the channel did not respond to other coming electrons. Because the measurement time is much shorter than the recharging time, each micro-channel can be used at most once during the measurement [ 37 37 ]. If the number of stored ions is too large for one injection into the CSRe, the tot al number of activated microchannels would be large and the chance for each electron to activate a microchannel would be reduced, leading to reduced A 0 and η values. This dynamic efficiency obviously depends on the number of stored ions and their charge. The sum amplitude of all signals ( A s ) was a direct measure of the total number of activated channels in one injection. Thus, it is expected that the A 1 values have a negative correlation with the A s values for one ion species. In the present experiment, the number of stored ions ranged from 2 to 46 in various injections, with the most probable value being 21. The A s values ranged from 50 to 300 V. The relationship between the A 1 and the A s values was similar for all ion species, as shown in Fig. 3 Fig. 3 for the example of the 36 K and 53 Ni ions, which can be clearly identified using their revolution times. The mean <math id="M2"><mrow><msub><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mn>1</mn></msub></mrow></math> values are calculated for these two ion species. The <math id="M3"><mrow><msub><mi>A</mi><mn>1</mn></msub><mo>/</mo><msub><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mn>1</mn></msub></mrow></math> ratios are calculated for each individual ion, and a scatter plot of <math id="M4"><mrow><msub><mi>A</mi><mn>1</mn></msub><mo>/</mo><msub><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mn>1</mn></msub></mrow></math> vs. A s is shown in Fig. 3 Fig. 3 ). The <math id="M5"><mrow><msub><mi>A</mi><mn>1</mn></msub><mo>/</mo><msub><mover accent="true"><mi>A</mi><mo>¯</mo></mover><mn>1</mn></msub></mrow></math> values for both ion species are described by a linear function of A s . The two slopes obtained are very similar, indicating a constant slope for all the ion species. If the observed correlation of A 1 and A s values is considered, the charge resolution can be improved. A new parameter A 2 is defined as an estimate of the A 1 value at A s = 0 V. The A 2 value is proportional to the number of channels that should be activated by the ion if all the micro-channels are available. Thus, it is directly related to the number of electrons released from the detector foil owing to this ion. Considering the constant slope for different ion species, as shown in Fig. 3 Fig. 3 , we can calculate the A 2 value as <math display="block" id="M7"><mrow><msub><mi>A</mi><mn>2</mn></msub><mo>=</mo><msub><mi>A</mi><mn>1</mn></msub><mo>×</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><mi>B</mi><mo>×</mo><msub><mi>A</mi><mi>s</mi></msub><mo stretchy="false">)</mo><mn>.</mn></mrow></math> Here, the parameter B represents the slope shown in Fig. 2 Fig. 2 and is determined by using all ion species with a proton number of Z > 8 and more than 100 counts. It is equal to B =-9.05(7) × 10 -4 V -1 . Figure 2(c) Figure 2(c) shows a scatter plot of the revolution time T vs. A 2 and the projected histogram for 34 Ar and 51 Co ions. It can be seen from the figure that the two ions are completely separated. Because the revolution time T is Bρ dependent on the ions of 34 Ar and 51 Co [ 3 3 , 4 4 ], the T values should depend on the average passage position of the ions through the detector. As shown in Fig. 2 Fig. 2 , the values of A 0 , A 1 , and A 2 have no correlation with the revolution time T , proving the position independence of A 0 , A 1 , and A 2 in this experiment. Using A 2 for the PID, we determined the mass excess of 51 Co to be -27,332(41) keV, which is in agreement with the previously obtained value of -27,342(48) [ 33 33 ]. The smaller mass uncertainty in this analysis was mainly due to the larger statistics obtained under less strict constraints. In an earlier work [ 33 33 ], only the particles that were stored for more than 300 revolutions in the CSRe were used in the analysis. Using the improved data analysis methods, we lowered the threshold in the present work to 80 revolutions, thus increasing the statistics. 4 Charge resolution 1 The A 0 , A 1 , and A 2 values were calculated for all ions. Figure 4(a) Figure 4(a) shows the average values of these three parameters for ions with the same proton number Z . As can be seen in the figure, the A 1 and A 2 values are very similar, whereas A 0 is larger than the other two parameters for lighter ions. A 2 increases rapidly with the proton number and approaches A 0 . It is evident that A 2 is more sensitive to proton number Z . The standard deviations of these three parameters are shown in Fig. 4(b) Fig. 4(b) as a function of Z . For heavy ions ( Z ∼20), they are similar for all three parameters, whereas for lighter ions, the standard deviation of A 0 is considerably larger. The charge resolution ratio R was introduced to represent the separation of the two ion species. R is defined as <math display="block" id="M8"><mrow><mi>R</mi><mo stretchy="false">(</mo><mi>A</mi><mo>;</mo><mi>Z</mi><mn>,</mn><msub><mi>Δ</mi><mi>Z</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><msub><mi>A</mi><mi>Z</mi></msub><mo>−</mo><msub><mi>A</mi><mrow><mi>Z</mi><mo>−</mo><mi>Δ</mi><mi>Z</mi></mrow></msub></mrow><mrow><msub><mi>σ</mi><mrow><msub><mi>A</mi><mi>Z</mi></msub></mrow></msub><mo>+</mo><msub><mi>σ</mi><mrow><msub><mi>A</mi><mrow><mi>Z</mi><mo>−</mo><mi>Δ</mi><mi>Z</mi></mrow></msub></mrow></msub></mrow></mfrac><mn>,</mn></mrow></math> where A indicates the parameters used in the charge identification, Z is the proton number, and Δ Z is the proton number difference between the two ion species. For the normal distribution, two peaks can be resolved if R 2, corresponding to less than 2.5In the case of R =1, two peaks can be identified with 16% overlapping events. Figure 5 Figure 5 shows the charge resolution ratios for different pairs of ions with Δ Z =2. The charge resolution ratios for A 2 ( R ( A 2 )) were the largest for all ions, with an increase of 10The A 2 parameter provided the highest charge resolution. With the use of the A 2 values in the calculation, Figure 6 Figure 6 shows the R ( A 2 ) for pairs of ions with various Δ Z values as a function of Z . The R values are directly related to Δ Z/Z . In this experiment, pairs of ions with Δ Z/Z > 0.22 can be clearly resolved. Only a moderate charge resolution was achieved in this experiment because the charge resolution was not particularly optimized. A better charge resolution can be realized with several technical improvements. The charge resolution can be improved by extending the recording time for each injection, i.e., from the present 200 μ s to 400-600 μ s. A lower number of stored ions in an individual injection will also lead to a higher resolution. Two timing detectors, a new IMS method that is under development and which will be applied in future experiments at the CSRe [ 12 12 , 29 29 , 39 39 - 41 41 39-41 ], could also increase the charge resolution. Finally, MCP plates with 2 μ m of pore size will be adopted, thus boosting the number of microchannels. 5 Summary 1 In the IMS experiments, charge resolution provides crucial information for the particle identification of ion pairs with m/q ratios that are too similar to be resolved by their revolution times. In an earlier study, a charge-resolved IMS was developed at the CSRe to resolve the 51 Co 27+ and 34 Ar 18+ ions. However, the two ion types were not completely separated owing to the limited charge resolution. In this paper, a new analysis method is presented that explicitly considers the average signal amplitudes, detection efficiencies, and number of stored ions in the data analysis. 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Zhang , et al ., An improvement of isochronous mass spectrometry: Velocity measurements using two time-of-flight detectors . Nucl. Instrum Meth. Phys. Res. B , 376 , 311 - 315 ( 2016 ). doi: 10.1016/j.nimb.2016.02.006 http://doi.org/10.1016/j.nimb.2016.02.006 An improvement of isochronous mass spectrometry: Velocity measurements using two time-of-flight detectors X. L. Yan , R. J. Chen , M. Wang , et al ., Characterization of a double Time-Of-Flight detector system for accurate velocity measurement in a storage ring using laser beams . Nucl. Instrum. Meth. Phys. Res. A , 931 , 52 ( 2019 ). doi: 10.1016/j.nima.2019.03.058 http://doi.org/10.1016/j.nima.2019.03.058 Characterization of a double Time-Of-Flight detector system for accurate velocity measurement in a storage ring using laser beams All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Xu Zhou, Meng Wang, Yu-Hu Zhang, Xin-Liang Yan and Peng Shuai. The first draft of the manuscript was written by Xu Zhou and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript. 10.1007/s41365-021-00876-0 This work is supported by the National Key R&D Program of China (Nos. 2016YFA0400504 and 2018YFA0404401), the Strategic Priority Research Program of the Chinese Academy of Sciences (No. XDB34000000), the National Natural Science Foundation of China (Nos. 11905261, 11805032, 11975280, and 11605248), the CAS "Light of West China" Program, the China Postdoctoral Science Foundation (No. 2019M660250), the FRIB-CSC Fellowship, China (No. 201704910964), the International Postdoctoral Exchange Fellowship Program 2017 by the Office of China Postdoctoral Council (No. 60 Document of OCPC, 2017), and the European Research Council (ERC) under the European Union’s Horizon 2020 Research and Innovation Programme (No. 682841 "ASTRUm"). 2021-01-04 2021-01-22 2021-01-29 2021-04-11 2021-04-01 2021-05-09 © 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. 2021 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/s41365-021-00876-0 http://dx.doi.org/10.1007/s41365-021-00876-0 . 2021 Nuclear Science and Techniques 04 32