Production of p-rich nuclei with Z=20-25 based on radioactive ion beams 封面论文

Production of p-rich nuclei with Z=20-25 based on radioactive ion beams 1 2 first-author 1 2 1 2 1 2 3 corresp fszhang@bnu.edu.cn fszhang@bnu.edu.cn fszhang@bnu.edu.cn https://orcid.org/0000-0003-0507-0983 The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China The Key Laboratory of Beam Technology and Material Modification of Ministry of Education, College of Nuclear Science and Technology, Beijing Normal University, Beijing 100875, China Institute of Radiation Technology, Beijing Academy of Science and Technology, Beijing 100875, China Institute of Radiation Technology, Beijing Academy of Science and Technology, Beijing 100875, China Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China Center of Theoretical Nuclear Physics, National Laboratory of Heavy Ion Accelerator of Lanzhou, Lanzhou 730000, China Within the framework of isospin-dependent Boltzmann-Langevin model, the production cross sections of proton-rich nuclei with Z = 20-25 are investigated. According to the reaction results for different isospin of projectiles 48 Ni, 49 Ni, and 50 Ni, proton-rich fragments tend to be more easily produced in reactions with the proton-rich projectile 48 Ni. The production cross-sections of the unknown nuclei in the vicinity of the projectile are sensitive to incident energy. It is observed that incident energy of 345 MeV/u is appropriate for producing proton-rich nuclei with Z = 20-25. In projectile fragmentation reactions based on the radioactive ion beam of 48 Ni at 345 MeV/u, several unknown proton-rich nuclei near the proton drip line are generated in the simulations. All these new nuclei are near-projectile elements near Z = 28. The production cross sections of the new nuclei 34 Ca, 37,38 Sc, 38 Ti, 40,41,42 V, 40,41 Cr, and 42,43,44,45 Mn are in the range of 10 -2 – 10 2 mb. Hence, projectile fragmentation of radioactive ion beams of Ni is a potential method for generating new proton-rich nuclei with Z = 20-25. Production cross sections Radioactive ion beams Isospin-dependent Boltzmann-Langevin model Introduction 1 The production of new exotic isotopes and determination of drip lines are frontier topics in nuclear physics [ 1 1 - 6 6 1-6 ]. To date, 3327 nuclides have been experimentally observed [ 7 7 ]. Erler et al. predicted the presence of approximately 7000 nuclides; therefore, more than half of these nuclides remain undiscovered [ 1 1 , 8 8 ]. Investigation of exotic isotopes provides valuable information for understanding the processes of nuclear astrophysics and nuclear structure [ 9 9 - 12 12 9-12 ]. Moreover, this types of nuclear reactions provide further information on isospin dependent nucleon-nucleon interactions, offering a powerful method to study the nuclear equation of state and even the symmetry energy, which is important for the physics of neutron stars and supernovas [ 13 13 - 18 18 13-18 ]. To date, the proton drip line experimentally reached the medium-mass region, whereas the neutron drip line has only recently been detected up to Z = 10 [ 8 8 - 20 20 8-20 ]. The prot on drip line is closer to the stable region because of the Coulomb repulsion between protons, which leads to a long lifetime even for nuclides outside the proton drip line [ 21 21 ]. This results in shallow regions or sandbanks, which serve to bridge gaps of unbound nuclei along the path of the astrophysical rapid-proton capture ( rp ) process [ 22 22 ]. Additionally, approximately 200 proton unbound nuclides remain to be discovered [ 8 8 ]. Some of these nuclides are reconstructed through their decay products, and some even have lifetimes long enough to be experimentally observable. With the establishment of sophisticated facilities, radioactive ion beams (RIBs) of nuclei with large excesses of neutrons or protons allow a deeper investigation of exotic isotopes, which has led to new discoveries such as halo nuclei and the change of magic numbers with isospin [ 23 23 - 26 26 23-26 ]. The separation and identification of exotic nuclei has become principally possible using two techniques: isotope separation online (ISOL) and in-flight separation techniques [ 27 27 - 32 32 27-32 ]. In particular, the cross-sections of intermediate mass fragments under projectile fragmentation reactions at 140 MeV/u were investigated at the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University (MSU) using an A1900 fragment separator [ 4 4 ]. Recently, the proton-rich isotope 68 Br was discovered in secondary fragmentation reactions at the RIKEN Nishina Center in 2019, suggesting that secondary fragmentation reactions offer an alternative way to search for new isotopes [ 21 21 ]. Similar experimental and theoretical studies have been conducted [ 33 33 - 39 39 33-39 ]. Exotic nuclei can be generated via projectile fragmentation, fission, and spallation [ 40 40 , 41 41 , 2 2 ]. Spallation is an effective reaction mechanism for the production of exotic nuclei for time-of-flight particle identification [ 42 42 - 44 44 42-44 ]. High-energy projectile fission is appropriate for light and heavy fission fragments [ 45 45 - 47 47 45-47 ]. Projectile fragmentation is a common reaction mechanism that has recently been used to study the production of new exotic nuclei, and many new nuclides have been discovered [ 48 48 - 52 52 48-52 ]. Recently, multinucleon transfer in peripheral reactions at beam energies from the Coulomb barrier to the Fermi energy has been considered to exhibit the potential of producing exotic nuclei because the projectile can pick up neutrons from the neutron-rich target [ 53 53 - 57 57 53-57 ]. The development of projectile fragmentation for producing new radioactive nuclides has led to a new era, not only in the discovery of new nuclides but also in the generation and utilization of unstable RIBs. Models describing projectile fragmentation reactions deliver important inputs for yield predictions that are useful for planning experiments and future accelerator facilities [ 58 58 ]. The models include Boltzmann-Uehling-Uhlenbeck (BUU) model [ 59 59 - 61 61 59-61 ], quantum molecular dynamics (QMD) model [ 62 62 - 66 66 62-66 ], the stochastic mean-field approach (SMF) [ 67 67 , 68 68 , 14 14 ], the abrasion-ablation (AA) model [ 69 69 - 71 71 69-71 ], the empirical parametrization of fragmentation cross sections (EPAX) [ 72 72 - 74 74 72-74 ], and the FRACS parameterization [ 75 75 - 77 77 75-77 ]. Transport models are good event generators and exhibit applications, for example, to design or simulate new detectors, and empirical approaches also provide better agreement with the experimental data within a large range of incident energy [ 78 78 , 79 79 ]. For a thorough review, refer to Refs. [ 80 80 - 85 85 80-85 ]. The theoretical method applied in this study was developed by adding the fluctuating collision term to the BUU equation and introducing the isospin effect, which is the isospin-dependent Boltzmann-Langevin equation (IBLE) [ 86 86 - 95 95 86-95 ]. In this study, we investigate the production cross-sections of nuclei near the proton drip line with charge number Z = 20-25 by using RIBs in an isospin-dependent Boltzmann-Langevin approach. A good description of the experimental data with the IBLE model suggests the possibility of using the present theoretical framework for the prediction of exotic nuclei using RIBs, which will soon be available in upcoming facilities [ 21 21 , 8 8 , 54 54 , 35 35 ]. The remainder of this paper is organized as follows. A brief introduction to the IBLE model is provided in Sect. 2. The model test, calculation results, and discussion are presented in Sect. 3. Finally, the conclusions of the study are presented in Sect. 4. Theoretical descriptions 1 In the IBLE model, the transport equation of motion for fluctuating single-particle density <math id="M1"><mrow><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>,</mn><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo></mrow></math> can be expressed in the following form [ 87 87 - 89 89 87-89 , 93 93 ]: <math display="block" id="M2"><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mrow><mo>(</mo><mrow><mfrac><mo>∂</mo><mrow><mo>∂</mo><mi>t</mi></mrow></mfrac><mo>+</mo><mfrac><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mi>m</mi></mfrac><mo>⋅</mo><msub><mo>∇</mo><mi>r</mi></msub><mo>−</mo><msub><mo>∇</mo><mi>r</mi></msub><mi>U</mi><mo stretchy="false">(</mo><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">)</mo><mo>⋅</mo><msub><mo>∇</mo><mi>p</mi></msub></mrow><mo>)</mo></mrow></mrow></mtd><mtd columnalign="left"><mrow><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>,</mn><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow/></mtd><mtd columnalign="left"><mrow><mo>=</mo><mi>K</mi><mo stretchy="false">(</mo><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">)</mo><mo>+</mo><mi>δ</mi><mi>K</mi><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>,</mn><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo><mn>,</mn></mrow></mtd></mtr></mtable></mrow></math> where the left side expresses the Vlasov propagation of the individual particles in the nuclear mean field <math id="M3"><mrow><mi>U</mi><mo stretchy="false">(</mo><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">)</mo></mrow></math> , while the right side describes the residual binary collisions. <math id="M4"><mrow><mi>K</mi><mo stretchy="false">(</mo><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">)</mo></mrow></math> denotes the collision term that has the usual BUU form but a stochastic character manifested by the fluctuating density <math id="M5"><mrow><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>,</mn><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo></mrow></math> : <math display="block" id="M6"><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mi>K</mi><mo stretchy="false">(</mo><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>1</mn></msub><mo stretchy="false">)</mo><mo>=</mo></mrow></mtd><mtd columnalign="left"><mrow><mstyle displaystyle="true"><mrow><mo>∫</mo></mrow></mstyle><mi>d</mi><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>2</mn></msub><mi>d</mi><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>3</mn></msub><mi>d</mi><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>4</mn></msub><mi>W</mi><mo stretchy="false">(</mo><mn>12</mn><mo>;</mo><mn>34</mn><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow/></mtd><mtd columnalign="left"><mrow><mo stretchy="false">[</mo><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>3</mn></msub><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>4</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>1</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>2</mn></msub><mo stretchy="false">)</mo><mo>−</mo><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>1</mn></msub><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>3</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mn>4</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">]</mo><mn>.</mn></mrow></mtd></mtr></mtable></mrow></math> Here the <math id="M7"><mrow><msub><mover accent="true"><mi>f</mi><mo>^</mo></mover><mi>i</mi></msub></mrow></math> = <math id="M8"><mrow><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mi>i</mi></msub><mn>,</mn><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mi>i</mi></msub><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo></mrow></math> denotes the diagonal elements of single particle density and W (12;34) denotes the transition rate, which is related to the cross section of the corresponding two-body scattering process. δ K ( r,p,t ) is the fluctuating collision term, whose second moment is characterized by a correlation function <math display="block" id="M9"><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><mo>〈</mo><mi>δ</mi><mi>K</mi><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>1</mn></msub><mn>,</mn><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>1</mn></msub><mn>,</mn><msub><mi>t</mi><mn>1</mn></msub><mo stretchy="false">)</mo><mi>δ</mi><mi>K</mi><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>2</mn></msub><mn>,</mn><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>2</mn></msub><mn>,</mn><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mo>〉</mo><mo>=</mo></mrow></mtd><mtd columnalign="left"><mrow><mi>C</mi><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>,</mn><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>1</mn></msub><mn>,</mn><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>2</mn></msub><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow/></mtd><mtd columnalign="left"><mrow><mi>δ</mi><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>1</mn></msub><mo>−</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>2</mn></msub><mo stretchy="false">)</mo><mi>δ</mi><mo stretchy="false">(</mo><msub><mi>t</mi><mn>1</mn></msub><mo>−</mo><msub><mi>t</mi><mn>2</mn></msub><mo stretchy="false">)</mo><mn>,</mn></mrow></mtd></mtr></mtable></mrow></math> where ⟨⋅s⟩ presents the average over the local ensemble of BLE events, which is the local average [ 87 87 - 89 89 87-89 , 93 93 ]. The fluctuating collision term acts as a stochastic force acting on <math id="M10"><mover accent="true"><mi>f</mi><mo>^</mo></mover></math> , which is consistent with the “fluctuation-dissipation theorem". The correlation function C ( p 1 , p 2 ) is assumed as local in space and time, and it is coherent with the Markovian treatment of the Boltzmann collision term [ 88 88 , 96 96 ]. In the semi-classical limit, the correlation function is determined by the local averaged single-particle density f ( r,p,t ) as detailed in Ref. [ 88 88 ]. To obtain approximate solutions of the IBLE transport equation, a projection method was introduced and applied [ 86 86 , 92 92 ]. The fluctuations were projected onto a set of low-order multipole moments of the momentum distribution. The zero order multipole moment is constant along with the first multipole moment because of mass conservation and momentum conservation. The quadrupole moment of the momentum distribution exhibits a strong dissipative phenomenon, and it can describe the fluctuations very well. The propagation of fluctuations in the quadrupole moment of the momentum distribution alone does not provide a detailed description of the momentum space fluctuations. Thus, the octupole moment of the momentum distribution is also introduced, although its dissipative effect is not evident. We expect that such an approximation can provide a reasonable description of the gross properties of the dynamics of density fluctuations in heavy-ion collisions [ 86 86 ]. The local multipole moments of the momentum distribution are defined as follows: <math display="block" id="M11"><mrow><msub><mover accent="true"><mi>Q</mi><mo>^</mo></mover><mrow><mi>L</mi><mi>M</mi></mrow></msub><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo><mo>=</mo><mstyle displaystyle="true"><mrow><mo>∫</mo></mrow></mstyle><mi>d</mi><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><msub><mi>Q</mi><mrow><mi>L</mi><mi>M</mi></mrow></msub><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mo stretchy="false">)</mo><mover accent="true"><mi>f</mi><mo>^</mo></mover><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>,</mn><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo><mn>,</mn></mrow></math> where Q LM ( p ) is the fluctuating multipole moments of order L with magnetic quantum number M in the momentum space. The fluctuations of multipole moments can be expressed by the diffusion matrix provided by [ 88 88 ] <math display="block" id="M12"><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><msub><mi>C</mi><mrow><mi>L</mi><mi>M</mi><msup><mi>L</mi><mo>'</mo></msup><msup><mi>M</mi><mo>'</mo></msup></mrow></msub><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>r</mi></mstyle><mn>,</mn><mi>t</mi><mo stretchy="false">)</mo></mrow></mtd><mtd columnalign="left"><mrow><mo>=</mo><mstyle displaystyle="true"><mrow><mo>∫</mo></mrow></mstyle><mi>d</mi><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mi>d</mi><msup><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mo>'</mo></msup><msub><mi>Q</mi><mrow><mi>L</mi><mi>M</mi></mrow></msub><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mo stretchy="false">)</mo><msub><mi>Q</mi><mrow><msup><mi>L</mi><mo>'</mo></msup><msup><mi>M</mi><mo>'</mo></msup></mrow></msub><mo stretchy="false">(</mo><msup><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mstyle mathvariant="bold-italic" mathsize="normal"><mo>'</mo></mstyle></msup><mo stretchy="false">)</mo><mi>C</mi><mo stretchy="false">(</mo><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>,</mn><msup><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mo>'</mo></msup><mo stretchy="false">)</mo></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow/></mtd><mtd columnalign="left"><mrow><mo>=</mo><mstyle displaystyle="true"><mrow><mo>∫</mo></mrow></mstyle><mi>d</mi><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>1</mn></msub><mi>d</mi><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>2</mn></msub><mi>d</mi><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>3</mn></msub><mi>d</mi><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>4</mn></msub><mi>Δ</mi><msub><mi>Q</mi><mrow><mi>L</mi><mi>M</mi></mrow></msub><mi>Δ</mi><msub><mi>Q</mi><mrow><msup><mi>L</mi><mo>'</mo></msup><msup><mi>M</mi><mo>'</mo></msup></mrow></msub></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow/></mtd><mtd columnalign="left"><mrow><mo>×</mo><mi>W</mi><mo stretchy="false">(</mo><mn>12,34</mn><mo stretchy="false">)</mo><msub><mi>f</mi><mn>1</mn></msub><msub><mi>f</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>f</mi><mn>3</mn></msub><mo stretchy="false">)</mo><mo stretchy="false">(</mo><mn>1</mn><mo>−</mo><msub><mi>f</mi><mn>4</mn></msub><mo stretchy="false">)</mo><mn>,</mn></mrow></mtd></mtr></mtable></mrow></math> with <math id="M13"><mrow><mi>Δ</mi><msub><mi>Q</mi><mrow><mi>L</mi><mi>M</mi></mrow></msub><mo>=</mo><msub><mi>Q</mi><mrow><mi>L</mi><mi>M</mi></mrow></msub><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>1</mn></msub><mo stretchy="false">)</mo><mo>+</mo><msub><mi>Q</mi><mrow><mi>L</mi><mi>M</mi></mrow></msub><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>2</mn></msub><mo stretchy="false">)</mo><mo>−</mo><msub><mi>Q</mi><mrow><mi>L</mi><mi>M</mi></mrow></msub><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>3</mn></msub><mo stretchy="false">)</mo><mo>−</mo><msub><mi>Q</mi><mrow><mi>L</mi><mi>M</mi></mrow></msub><mo stretchy="false">(</mo><msub><mstyle mathvariant="bold-italic" mathsize="normal"><mi>p</mi></mstyle><mn>4</mn></msub><mo stretchy="false">)</mo></mrow></math> . f 1 f 2 (1- f 3 )(1- f 4 ) describes the Pauli-blocking effect. The diffusion matrix C LML’ M’ can reliably describe the dynamics of multipole moments, although it contains less information on the dynamics than the correlation function C ( p,p’ ) [ 86 86 ]. In this model, the isospin dependent interaction nuclear potential is provided as follows: <math display="block" id="M14"><mrow><mtable columnalign="left"><mtr columnalign="left"><mtd columnalign="left"><mrow><msub><mi>U</mi><mi>τ</mi></msub><mo stretchy="false">(</mo><mi>ρ</mi><mn>,</mn><mi>δ</mi><mo stretchy="false">)</mo><mo>=</mo></mrow></mtd><mtd columnalign="left"><mrow><mi>α</mi><mfrac><mi>ρ</mi><mrow><msub><mi>ρ</mi><mn>0</mn></msub></mrow></mfrac><mo>+</mo><mi>β</mi><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mi>ρ</mi><mrow><msub><mi>ρ</mi><mn>0</mn></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mi>γ</mi></msup><mo>+</mo><msubsup><mi>E</mi><mrow><mtext>sym</mtext></mrow><mrow><mtext>loc</mtext></mrow></msubsup><mo stretchy="false">(</mo><mi>ρ</mi><mo stretchy="false">)</mo><msup><mi>δ</mi><mn>2</mn></msup></mrow></mtd></mtr><mtr columnalign="left"><mtd columnalign="left"><mrow/></mtd><mtd columnalign="left"><mrow><mo>+</mo><mfrac><mrow><mo>∂</mo><msubsup><mi>E</mi><mrow><mtext>sym</mtext></mrow><mrow><mtext>loc</mtext></mrow></msubsup><mo stretchy="false">(</mo><mi>ρ</mi><mo stretchy="false">)</mo></mrow><mrow><mo>∂</mo><mi>ρ</mi></mrow></mfrac><mi>ρ</mi><msup><mi>δ</mi><mn>2</mn></msup><mo>+</mo><msubsup><mi>E</mi><mrow><mtext>sym</mtext></mrow><mrow><mtext>loc</mtext></mrow></msubsup><mo stretchy="false">(</mo><mi>ρ</mi><mo stretchy="false">)</mo><mi>ρ</mi><mfrac><mrow><mo>∂</mo><msup><mi>δ</mi><mn>2</mn></msup></mrow><mrow><mo>∂</mo><msub><mi>ρ</mi><mi>τ</mi></msub></mrow></mfrac><mn>,</mn></mrow></mtd></mtr></mtable></mrow></math> where δ =( ρ n - ρ p )/ ρ is the isospin asymmetry; ρ 0 is normal nuclear matter density; ρ , ρ p , and ρ n denote the total, proton, and neutron densities, respectively. We adopted the soft equation of state, which is widely applied in heavy-ion collisions at intermediate and high incident energies [ 96 96 , 88 88 ]. The coefficient values of α , β , and γ are -356 MeV, 303 MeV and 7/6, respectively. <math id="M15"><mrow><msubsup><mi>E</mi><mrow><mtext>sym</mtext></mrow><mrow><mtext>loc</mtext></mrow></msubsup></mrow></math> is the local part of the symmetry energy, which is provided by <math display="block" id="M16"><mrow><msubsup><mi>E</mi><mrow><mtext>sym</mtext></mrow><mrow><mtext>loc</mtext></mrow></msubsup><mo stretchy="false">(</mo><mi>ρ</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msub><mi>C</mi><mrow><mtext>sym</mtext></mrow></msub><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mi>ρ</mi><mrow><msub><mi>ρ</mi><mn>0</mn></msub></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><msub><mi>γ</mi><mi>s</mi></msub></mrow></msup><mn>,</mn></mrow></math> where γ s = 0.5 and 2.0 correspond to the soft and hard symmetry energies, respectively [ 94 94 ]. The coefficient value of C sym was 29.4 MeV. The details on the symmetry energy are provided in Ref. [ 94 94 , 95 95 ]. The cross sections of each channel used in the IBLE model are experimental parameterizations, which are isospin-dependent [ 97 97 - 99 99 97-99 ]. Additionally, the in-medium cross-sections for each channel were used in the model as detailed in Ref. [ 94 94 ]. In this study, we construct clusters using the coalescence model, in which parameters R 0 and P 0 are set as 3.5 fm and 300 MeV/ c , respectively [ 95 95 ]. Calculations were performed with 20 test particles, and simulations were conducted for 10,000 events, with impact parameter values ranging from 0 to 7 fm. The excitation energy of the produced light fragments is not sufficient to evaporate neutrons; therefore, the difference between the cross-sections before and after de-excitation is small. In this study, we focus on the production cross sections of light fragments around Z=20. Results and discussion 1 To test the feasibility of using the IBLE model to predict the production cross sections of nuclei in projectile fragmentation, we calculated the cross-sections of nuclei with 19 ≤ Z ≤ 24 in the reaction of 58 Ni+ 9 Be at 140 MeV/u as shown in Fig. 1 Fig. 1 . The solid and dashed lines denote the results of the IBLE model for the hard and soft symmetry energies, respectively. The solid circles denote the experimental data obtained from Ref. [ 4 4 ]. As shown, the measured cross-sections of the fragments are reasonably reproduced by the IBLE model for hard and soft symmetry energies. The peak locations of the calculated cross sections are close to those o btained via experiments. With respect to K and Ca, the peaks of the calculated cross-sections overestimated the experimental value, and the difference was within one order of magnitude. The number of calculated isotopes is less than the experimental value, especially for fragments near the projectile, which is a limitation of dynamical simulations in IBLE, i.e., it is dependent on the number of simulated events. For the simulations of different symmetry energies, it is observed that the results are very close and differ only slightly in the proton-rich and neutron-rich regions. In the proton-rich region, more isotopes are calculated for soft symmetry energy than for hard symmetry energy. By comparing the two calculations with the experimental data, we observe that the IBLE model realizes a good description of the cross-section distributions but slightly underestimates the neutron-rich tails. The calculations for the soft symmetry energy produced more isotopes, especially for proton-rich nuclei. Therefore, it is reasonable to apply the IBLE model with soft symmetry energy to predict the production cross-sections of proton-rich fragments in projectile fragmentation reactions. Radioactive ion beams became possible with the development of large scientific installations worldwide [ 21 21 , 2 2 , 33 33 ]. To produce proton-rich nuclei with charge number <math id="M17"><mrow><mi>Z</mi><mo>≈</mo></mrow></math> 20, proton-rich beams should be used in projectile fragmentation reactions. 48,49,50 Ni are good candidates for radioactive beams because they exhibit small N/Z ratios near <math id="M18"><mrow><mi>Z</mi><mo>≈</mo></mrow></math> 20. They are most likely generated via projectile fragmentation in a newly built FRIB facility, such as the fragmentation of a 58 Ni beam on a beryllium target at an incident energy of several hundred MeV/u. To study the effect of isospin of the projectile on the fragments produced by projectile fragmentation, the isotopic distributions of fragments with Z = 20-25 for the 48 Ni+ 9 Be (circles), 49 Ni+ 9 Be (squares), and 50 Ni+ 9 Be (triangles) reactions at 140 MeV/u are shown in Fig. 2 Fig. 2 . Unknown nuclei are denoted by open symbols. The isospin T z of projectiles 48 Ni, 49 Ni, and 50 Ni are -4, -7/2, and -3, respectively. It is observed that the produced fragments tend to be proton-rich because of proton-rich radioactive ion beams. In Fig. 2 Fig. 2 , several new nuclei near the proton drip line, such as 37,38 Sc, 38 Ti, 40,41,42 V, 41 Cr, and 43,44,45 Mn, are generated during simulations. The predicted production cross-sections of these nuclei ranged from 10 -2 to 10 2 mb. The number and cross-sections of proton-rich new nuclei in the reaction with 48 Ni projectile are the highest, which is due to the highest absolute value of the projectile isospin and the lowest N/Z ratio. As the mass number of the projectile increases by 1, the peak of the isotopic distribution shifts to the right by approximately one unit, which shows a strong isospin effect in the projectile fragmentation reactions because the isospin effect is dependent on the density distribution of protons and neutrons. When the absolute value of the projectile isospin decreases or when the N/Z ratio increases, the produced fragments are closer to the stability line. The absolute values of isospins of newly produced nuclei are smaller than those of the projectile because as the reaction proceeds the isospin of the reaction system gradually tends towards equilibrium, which is the isospin diffusion process. According to the above results for different isospin of projectiles, reaction 48 Ni+ 9 Be exhibits the advantage of producing rare proton-rich nuclei. To observe the incident energy effect, the production cross-sections of the fragments in the 48 Ni+ 9 Be reaction at 140 MeV/u (circles), 240 MeV/u (squares), and 345 MeV/u (triangles) are presented in Fig. 3 Fig. 3 . As shown, the production cross-sections of new nuclei at 345 MeV/u are the largest, especially the nuclei near the projectile. However, the difference among the results for different incident energies is not large. The discrepancy between the fragment cross-sections at the three energies increased as the charge number of the generated fragments increased. Heavy fragments are mainly produced from peripheral collisions, which vary significantly with incident energies below 200 MeV/u [ 4 4 ]. Additionally, the number of new nuclei produced in the simulations was consistent at incident energies of 240 and 345 MeV/u. In the 48 Ni+ 9 Be reaction at 140 MeV/u, the production cross-sections of the produced fragments with Z = 20–25 decrease as charge number increases, whereas at 345 MeV/u, the production cross-sections of the corresponding fragments do not show a significant decreasing trend. At 345 MeV/u, the projectile and target collide quickly with each other, resulting in fragments produced by the reaction. Furthermore, when compared to the reaction 140 MeV/u, the characteristics of the initial entrance channel are retained to the maximum extent at 345 MeV/u. To analyze the characteristics of the fragments produced by different projectiles in projectile fragmentation reactions, the production cross-sections as functions of Z and A for the fragments in the 48 Ni+ 9 Be (a), 49 Ni+ 9 Be (b), and 50 Ni+ 9 Be (c) reactions at 140 MeV/u are presented in Fig. 4 Fig. 4 . As the mass number of the projectile increases, the mass of the fragments produced slightly increases. Additionally, there was a plateau near Z = 16 in all three reaction systems, where most of the fragments in this region were produced from the projectiles. The dashed lines indicate the general trends in the three distributions. The slopes of the dashed lines are 1.54, 1.62, and 1.69, corresponding to the reactions 48 Ni+ 9 Be, 49 Ni+ 9 Be, and 50 Ni+ 9 Be, respectively. An increase in the slope indicates that proton-rich fragments are difficult to produce in the reaction induced by the 50 Ni projectile, which is consistent with Fig. 2 Fig. 2 . The 48 Ni+ 9 Be reaction at 345 MeV/u provides a significant advantage for producing new proton-rich nuclei with Z = 20-25 as discussed above. To observe the relationship between the calculated nuclei near the proton drip line and experimentally synthesized nuclei with higher intuition, a nuclear chart of the predicted fragments with Z = 20-25 for the 48 Ni+ 9 Be reaction at 345 MeV/u is shown in Fig. 5 Fig. 5 . The filled and open squares denote known and unknown nuclei, respectively. Black, red, and brown are stable, β + decay, and p decay, respectively. The production cross-sections of unknown nuclei in the 48 Ni+ 9 Be reaction at 345 MeV/u are indicated by open squares in the figure. From the figure, it can be observed that the produced new nuclei are mainly distributed in the vicinity of the projectile (Z = 28) because the new nuclei are almost formed by the projectile sources in the region of highly peripheral collisions [ 30 30 ]. In the projectile fragmentation of 48 Ni+ 9 Be, 13 new proton-rich nuclei with Z = 20-25 have been predicted as follows: 34 Ca (0.14 mb), 37 Sc (18.2 mb), 38 Sc (60.3 mb), 38 Ti (2.61 mb), 40 V (12.8 mb), 41 V (46.5 mb), 42 V (17.2 mb), 40 Cr (15.7 μ b), 41 Cr (1.70 mb), 42 Mn (75.4 μ b), 43 Mn (9.53 mb), 44 Mn (21.1 mb), and 45 Mn (2.08 mb). Additionally, an empirical approach was applied to determine the binding energies and to predict the cross sections for isotopes with Z = 22-28 near the proton drip line (see Ref. [ 100 100 , 101 101 ]). It is evident that the selection of the optimal reaction system should consider not only the production cross-sections of fragments but also various factors such as experimental feasibility and detection efficiency. In any case, with the improvement of the experimental condition technology, it is expected that the generation of new proton-rich nuclei with Z = 20-25 via the 48,49,50 Ni+ 9 Be reaction is imminent. Summary 1 In conclusion, fragmentation isotopic distributions were calculated for 58 Ni on 9 Be targets using the IBLE model for hard and soft symmetry energies. The IBLE model for soft symmetry energy leads to a good description of the cross-section distributions, and the measured cross-sections of fragments are reasonably reproduced by the IBLE model, which indicates that the IBLE model can be applied to predict the production cross-sections of proton-rich fragments in projectile fragmentation. When considering isospin effects, the 48 Ni-induced reaction produces more new nuclei and has the largest production cross sections when compared to the 49 Ni and 50 Ni projectiles because it has the largest absolute value of isospin and can produce fragments with the greatest proton abundance. Therefore, the 48 Ni+ 9 Be reaction is promising for producing proton-rich nuclei with Z = 20-25. The production cross-sections of the new nuclei become larger as the incident energy increases, but this effect becomes weak when the incident energy is higher than 200 MeV/u. The results show that when compared to 140 and 240 MeV/u, the predicted cross-sections of new proton-rich nuclei with Z = 20-25 are the highest at 345 MeV/u. The isospin of the projectile and incident energy play important roles in projectile fragmentations. In the reaction of 48 Ni+ 9 Be at 345 MeV/u, 13 new nuclei near the proton drip line were produced in simulations in the vicinity of the projectile (Z = 28). The predicted production cross-sections of the new nuclei 34 Ca, 37,38 Sc, 38 Ti, 40,41,42 V, 40,41 Cr, and 42,43,44,45 Mn range from 10 -2 to 10 2 mb. Hence, the generation of new proton-rich nuclei with Z = 20-25 via projectile fragmentations using secondary radioactive ion beams of 48,49,50 Ni is promising for future studies. References J. Erler , N. Birge , M. Kortelainen et al. , The limits of the nuclear landscape . Nature 486 , 509 - 512 ( 2012 ). doi: 10.1038/nature11188 http://doi.org/10.1038/nature11188 The limits of the nuclear landscape O. Fasoula , G. A. Souliotis , Y. K. Kwon et al. , Production cross sections and angular distributions of neutron-rich rare isotopes from 15 MeV/nucleon Kr-induced collisions: toward the r-process path (2021) . arXiv: 2103.10688 [nucl-th] Production cross sections and angular distributions of neutron-rich rare isotopes from 15 MeV/nucleon Kr-induced collisions: toward the r-process path (2021) D. Y. Tao , T. K. Dong , S. J. Yun et al. , Short-lived radionuclide production cross sections calculated by the Liège intranuclear cascade model . Phys. Rev. C 103 , 044606 ( 2021 ). doi: 10.1103/PhysRevC.103.044606 http://doi.org/10.1103/PhysRevC.103.044606 Short-lived radionuclide production cross sections calculated by the Liège intranuclear cascade model M. Mocko , M. B. Tsang , L. Andronenko et al. , Projectile fragmentation of 40 Ca, 48 Ca, 58 Ni, and 64 Ni at 140 MeV/nucleon . Phys. Rev. C 74 , 054612 ( 2006 ). doi: 10.1103/PhysRevC.74.054612 http://doi.org/10.1103/PhysRevC.74.054612 Projectile fragmentation of 40Ca, 48Ca, 58Ni, and 64Ni at 140 MeV/nucleon Z. J. Wu , L. Guo , Production of proton-rich actinide nuclei in the multinucleon transfer reaction 58 Ni+ 232 Th . Sci. China-Phys. Mech. Astron. 63 , 242021 ( 2020 ). doi: 10.1007/s11433-019-1484-0 http://doi.org/10.1007/s11433-019-1484-0 Production of proton-rich actinide nuclei in the multinucleon transfer reaction 58Ni+232Th Y. Jin , C. Y. Niu , K. W. Brown et al. , First observation of the four-proton unbound nucleus 18 Mg . Phys. Rev. Lett. 127 , 262502 ( 2021 ). doi: 10.1103/PhysRevLett.127.262502 http://doi.org/10.1103/PhysRevLett.127.262502 First observation of the four-proton unbound nucleus 18Mg M. Thoennessen , Discovery of nuclides project ( 2021 ), https://people.nscl.msu.edu/thoennes/isotopes https://people.nscl.msu.edu/thoennes/isotopes . Accessed 31 Dec 2021 Discovery of nuclides project M. Thoennessen , Exploring new neutron-rich nuclei with the facility for rare isotope beams . Nuclear Data Sheets 118 , 85 - 90 ( 2014 ). doi: 10.1016/j.nds.2014.04.008 http://doi.org/10.1016/j.nds.2014.04.008 Exploring new neutron-rich nuclei with the facility for rare isotope beams K. Langanke , M. Wiescher , Nuclear reactions and stellar processes . Rep. Prog. Phys. 64 , 1657 - 1701 ( 2001 ). doi: 10.1088/0034-4885/64/12/202 http://doi.org/10.1088/0034-4885/64/12/202 Nuclear reactions and stellar processes X. F. Li , D. Q. Fang , Y. G. Ma , Determination of the neutron skin thickness from interaction cross section and charge-changing cross section for B, C, N, O, F isotopes . Nucl. Sci. Tech. 27 , 71 ( 2016 ). doi: 10.1007/s41365-016-0064-z http://doi.org/10.1007/s41365-016-0064-z Determination of the neutron skin thickness from interaction cross section and charge-changing cross section for B, C, N, O, F isotopes M. Arnould , S. Goriely , Astronuclear Physics: A tale of the atomic nuclei in the skies . Prog. Part. Nucl. Phys. 112 , 103766 ( 2020 ). doi: 10.1016/j.ppnp.2020.103766 http://doi.org/10.1016/j.ppnp.2020.103766 Astronuclear Physics: A tale of the atomic nuclei in the skies C. Li , P. W. Wen , J. J. Li et al. , Production of heavy neutron-rich nuclei with radioactive beams in multinucleon transfer reactions . Nucl. Sci. Tech. 28 , 110 ( 2017 ). doi: 10.1007/s41365-017-0266-z http://doi.org/10.1007/s41365-017-0266-z Production of heavy neutron-rich nuclei with radioactive beams in multinucleon transfer reactions P. Danielewicz , R. Lacey , W. G. Lynch , Determination of the equation of state of dense matter . Science 298 , 1592 - 1596 ( 2002 ). doi: 10.1126/science.1078070 http://doi.org/10.1126/science.1078070 Determination of the equation of state of dense matter V. Baran , M. Colonna , V. Greco et al. , Reaction dynamics with exotic nuclei . Phys. Rep. 410 , 335 - 466 ( 2005 ). doi: 10.1016/j.physrep.2004.12.004 http://doi.org/10.1016/j.physrep.2004.12.004 Reaction dynamics with exotic nuclei D. V. Shetty , S. J. Yennello , G. A. Souliotis , Density dependence of the symmetry energy and the nuclear equation of state: A dynamical and statistical model perspective . Phys. Rev. C 76 , 024606 ( 2007 ). doi: 10.1103/PhysRevC.76.024606 http://doi.org/10.1103/PhysRevC.76.024606 Density dependence of the symmetry energy and the nuclear equation of state: A dynamical and statistical model perspective B. A. Li , L. W. Chen , C. M. Ko , Recent progress and new challenges in isospin physics with heavy-ion reactions . Phys. Rep. 464 , 113 - 281 ( 2008 ). https://www.sciencedirect.com/science/article/pii/S037015730800126910.1016/j.physrep.2008.04.005 https://www.sciencedirect.com/science/article/pii/S037015730800126910.1016/j.physrep.2008.04.005 Recent progress and new challenges in isospin physics with heavy-ion reactions J. M. Lattimer , M. Prakash , Neutron star observations: Prognosis for equation of state constraints . Phys. Rep. 442 , 109 - 165 ( 2007 ). doi: 10.1016/j.physrep.2007.02.003 http://doi.org/10.1016/j.physrep.2007.02.003 Neutron star observations: Prognosis for equation of state constraints H. Yu , D. Q. Fang , Y. G. Ma , Investigation of the symmetry energy of nuclear matter using isospin-dependent quantum molecular dynamics . Nucl. Sci. Tech. 31 , 61 ( 2020 ). doi: 10.1007/s41365-020-00766-x http://doi.org/10.1007/s41365-020-00766-x Investigation of the symmetry energy of nuclear matter using isospin-dependent quantum molecular dynamics M. Thoennessen , The Discovery of Isotopes . ( Springer , Cham , 2016 ). doi: 10.1007/978-3-319-31763-2 http://doi.org/10.1007/978-3-319-31763-2 The Discovery of Isotopes D. S. Ahn , N. Fukuda , H. Geissel et al. , Location of the neutron dripline at Fluorine and Neon . Phys. Rev. Lett. 123 , 212501 ( 2019 ). doi: 10.1103/PhysRevLett.123.212501 http://doi.org/10.1103/PhysRevLett.123.212501 Location of the neutron dripline at Fluorine and Neon K. Wimmer , P. Doornenbal , W. Korten et al. , Discovery of 68 Br in secondary reactions of radioactive beams . Phys. Lett. B 795 , 266 - 270 ( 2019 ). doi: 10.1016/j.physletb.2019.06.014 http://doi.org/10.1016/j.physletb.2019.06.014 Discovery of 68Br in secondary reactions of radioactive beams H. Suzuki , L. Sinclair , P. A. Söderström et al. , Discovery of 72 Rb: A nuclear sandbank beyond the proton drip line . Phys. Rev. Lett. 119 , 192503 ( 2017 ). doi: 10.1103/PhysRevLett.119.192503 http://doi.org/10.1103/PhysRevLett.119.192503 Discovery of 72Rb: A nuclear sandbank beyond the proton drip line K. Riisager , Halos and related structures . Phys. Scr. T152 , 014001 ( 2013 ). doi: 10.1088/0031-8949/2013/t152/014001 http://doi.org/10.1088/0031-8949/2013/t152/014001 Halos and related structures R. Kanungo , A new view of nuclear shells . Phys. Scr. T152 , 014002 ( 2013 ). doi: 10.1088/0031-8949/2013/t152/014002 http://doi.org/10.1088/0031-8949/2013/t152/014002 A new view of nuclear shells H. Geissel , P. Armbruster , K. Behr et al. , The GSI projectile fragment separator (FRS): a versatile magnetic system for relativistic heavy ions . Nucl. Instrum. Methods B , 70 , 286 - 297 ( 1992 ). doi: 10.1016/0168-583X(92)95944-M http://doi.org/10.1016/0168-583X(92)95944-M The GSI projectile fragment separator (FRS): a versatile magnetic system for relativistic heavy ions H. Geissel , K. Beckert , F. Bosch et al. , First storage and cooling of secondary heavy-ion beams at relativistic energies . Phys. Rev. Lett. 68 , 3412 - 3415 ( 1992 ). doi: 10.1103/PhysRevLett.68.3412 http://doi.org/10.1103/PhysRevLett.68.3412 First storage and cooling of secondary heavy-ion beams at relativistic energies H. L. Ravn , Experiments with intense secondary beams of radioactive ions . Phys. Rep. , 54 , 201 - 259 ( 1979 ). doi: 10.1016/0370-1573(79)90045-0 http://doi.org/10.1016/0370-1573(79)90045-0 Experiments with intense secondary beams of radioactive ions S. Galès , Towards the next generation of radioactive ion beam facilities . Nucl. Phys. A 722 , C148 - C156 ( 2003 ). doi: 10.1016/S0375-9474(03)01351-4 http://doi.org/10.1016/S0375-9474(03)01351-4 Towards the next generation of radioactive ion beam facilities T. J. M. Symons , Y. P. Viyogi , G. D. Westfall et al. , Observation of new neutron-rich isotopes by fragmentation of 205-MeV/nucleon 40 Ar ions . Phys. Rev. Lett. 42 , 40 - 43 ( 1979 ). doi: 10.1103/PhysRevLett.42.40 http://doi.org/10.1103/PhysRevLett.42.40 Observation of new neutron-rich isotopes by fragmentation of 205-MeV/nucleon 40Ar ions H. Imal , R. Ogul , Theoretical study of isotope production in the peripheral heavy-ion collision 136 Xe+Pb at 1 GeV/nucleon . Nucl. Phys. A 1014 , 122261 ( 2021 ). doi: 10.1016/j.nuclphysa.2021.122261 http://doi.org/10.1016/j.nuclphysa.2021.122261 Theoretical study of isotope production in the peripheral heavy-ion collision 136Xe+Pb at 1 GeV/nucleon F. F. Duan , Y. Y. Yang , B. T. Hu et al. , Silicon detector array for radioactive beam experiments at HIRFL-RIBLL . Nucl. Sci. Tech. 29 , 165 ( 2018 ). doi: 10.1007/s41365-018-0499-5 http://doi.org/10.1007/s41365-018-0499-5 Silicon detector array for radioactive beam experiments at HIRFL-RIBLL Z. Y. Sun , W. L. Zhan , Z. Y. Guo et al. , Separation and Identification of Isotopes Produced from 20 Ne+Be Reaction by Radioactive Ion Beam Line in Lanzhou . Chin. Phys. Lett. 15 , 790 - 792 ( 1998 ). doi: 10.1088/0256-307X/15/11/004 http://doi.org/10.1088/0256-307X/15/11/004 Separation and Identification of Isotopes Produced from 20Ne+Be Reaction by Radioactive Ion Beam Line in Lanzhou S. Lukyanov , M. Mocko , L. Andronenko et al. , Projectile fragmentation of radioactive beams of 68 Ni, 69 Cu, and 72 Zn . Phys. Rev. C , 80 , 014609 ( 2009 ). doi: 10.1103/PhysRevC.80.014609 http://doi.org/10.1103/PhysRevC.80.014609 Projectile fragmentation of radioactive beams of 68Ni, 69Cu, and 72Zn R. J. Charity , T. B. Webb , J. M. Elson et al. , Observation of the exotic isotope 13 F located four neutrons beyond the proton drip line . Phys. Rev. Lett. 126 , 132501 ( 2021 ). doi: 10.1103/PhysRevLett.126.132501 http://doi.org/10.1103/PhysRevLett.126.132501 Observation of the exotic isotope 13F located four neutrons beyond the proton drip line T. Sumikama , N. Fukuda , N. Inabe et al. , Observation of new neutron-rich isotopes in the vicinity of 110 Zr . Phys. Rev. C 103 , 014614 ( 2021 ). doi: 10.1103/PhysRevC.103.014614 http://doi.org/10.1103/PhysRevC.103.014614 Observation of new neutron-rich isotopes in the vicinity of 110Zr K. Wang , Y. Y. Yang , A. M. Moro et al. , Elastic scattering and breakup reactions of the proton drip-line nucleus 8 B on 208 Pb at 238 MeV . Phys. Rev. C 103 , 024606 ( 2021 ). doi: 10.1103/PhysRevC.103.024606 http://doi.org/10.1103/PhysRevC.103.024606 Elastic scattering and breakup reactions of the proton drip-line nucleus 8B on 208Pb at 238 MeV G. G. Adamian , N. V. Antonenko , A. Diaz-Torres et al. , How to extend the chart of nuclides? Eur. Phys. J. A 56 , 47 ( 2020 ). doi: 10.1140/epja/s10050-020-00046-7 http://doi.org/10.1140/epja/s10050-020-00046-7 How to extend the chart of nuclides? D. Q. Fang , W. Q. Shen , J. Feng et al. , Measurements of total reaction cross sections for exotic nuclei close to the proton drip-line at intermediate energies and observation of a proton halo in 27 P . Chin. Phys. Lett. 18 , 1033 - 1036 ( 2001 ). doi: 10.1088/0256-307X/18/8/312 http://doi.org/10.1088/0256-307X/18/8/312 Measurements of total reaction cross sections for exotic nuclei close to the proton drip-line at intermediate energies and observation of a proton halo in 27P C.W. Ma , X.B. Wei , X.X. Chen et al. , Precise machine learning models for fragment production in projectile fragmentation reactions by Bayesian neural networks . Chin. Phys. C 46 , 074104 ( 2022 ). doi: 10.1088/1674-1137/ac5efb http://doi.org/10.1088/1674-1137/ac5efb Precise machine learning models for fragment production in projectile fragmentation reactions by Bayesian neural networks H. Geissel , G. Munzenberg , K. Riisager , Secondary exotic nuclear beams . Annu. Rev. Nucl. Part. Sci. , 45 , 163 - 203 ( 1995 ). doi: 10.1146/annurev.ns.45.120195.001115 http://doi.org/10.1146/annurev.ns.45.120195.001115 Secondary exotic nuclear beams Y. Blumenfeld , T. Nilsson , P. Van Duppen , Facilities and methods for radioactive ion beam production . Phys. Scr. T152 , 014023 ( 2013 ). doi: 10.1088/0031-8949/2013/t152/014023 http://doi.org/10.1088/0031-8949/2013/t152/014023 Facilities and methods for radioactive ion beam production A. M. Poskanzer , G. Butler , E. Hyde et al. , Observation of the new isotope 17 C using a combined time-of-flight particle-identification technique . Phys. Lett. B 27 , 414 - 416 ( 1968 ). doi: 10.1016/0370-2693(68)90222-0 http://doi.org/10.1016/0370-2693(68)90222-0 Observation of the new isotope 17C using a combined time-of-flight particle-identification technique A. M. Poskanzer , S. W. Cosper , E. K. Hyde et al. , New Isotopes: 11 Li, 14 B, and 15 B . Phys. Rev. Lett. 17 , 1271 - 1274 ( 1966 ). doi: 10.1103/PhysRevLett.17.1271 http://doi.org/10.1103/PhysRevLett.17.1271 New Isotopes: 11Li, 14B, and 15B J. C. David , Spallation reactions: A successful interplay between modeling and applications . Eur. Phys. J. A 51 , 68 ( 2015 ). doi: 10.1140/epja/i2015-15068-1 http://doi.org/10.1140/epja/i2015-15068-1 Spallation reactions: A successful interplay between modeling and applications H. Alvarez-Pol , J. Benlliure , E. Casarejos et al. , Production of new neutron-rich isotopes of heavy elements in fragmentation reactions of 238 U projectiles at 1 A GeV . Phys. Rev. C 82 , 041602 ( 2010 ). doi: 10.1103/PhysRevC.82.041602 http://doi.org/10.1103/PhysRevC.82.041602 Production of new neutron-rich isotopes of heavy elements in fragmentation reactions of 238U projectiles at 1A GeV N. Vonta , G. A. Souliotis , W. Loveland et al. , Neutron-rich rare-isotope production from projectile fission of heavy nuclei near 20 MeV/nucleon beam energy . Phys. Rev. C 94 , 064611 ( 2016 ). doi: 10.1103/PhysRevC.94.064611 http://doi.org/10.1103/PhysRevC.94.064611 Neutron-rich rare-isotope production from projectile fission of heavy nuclei near 20 MeV/nucleon beam energy J. Kurcewicz , F. Farinon , H. Geissel et al. , Discovery and cross-section measurement of neutron-rich isotopes in the element range from neodymium to platinum with the FRS . Phys. Lett. B 717 , 371 - 375 ( 2012 ). doi: 10.1016/j.physletb.2012.09.021 http://doi.org/10.1016/j.physletb.2012.09.021 Discovery and cross-section measurement of neutron-rich isotopes in the element range from neodymium to platinum with the FRS O. B. Tarasov , M. Portillo , A. M. Amthor et al. , Production of very neutron-rich nuclei with a 76 Ge beam . Phys. Rev. C 80 , 034609 ( 2009 ). doi: 10.1103/PhysRevC.80.034609 http://doi.org/10.1103/PhysRevC.80.034609 Production of very neutron-rich nuclei with a 76Ge beam T. Kurtukian-Nieto , J. Benlliure , K. H. Schmidt et al. , Production cross sections of heavy neutron-rich nuclei approaching the nucleosynthesis r-process path around A =195 . Phys. Rev. C 89 , 024616 ( 2014 ). doi: 10.1103/PhysRevC.89.024616 http://doi.org/10.1103/PhysRevC.89.024616 Production cross sections of heavy neutron-rich nuclei approaching the nucleosynthesis r-process path around A=195 Z. Meisel , S. George , S. Ahn et al. , Time-of-flight mass measurements of neutron-rich chromium isotopes up to N =40 and implications for the accreted neutron star crust . Phys. Rev. C 93 , 035805 ( 2016 ). doi: 10.1103/PhysRevC.93.035805 http://doi.org/10.1103/PhysRevC.93.035805 Time-of-flight mass measurements of neutron-rich chromium isotopes up to N=40 and implications for the accreted neutron star crust C. Santamaria , C. Louchart , A. Obertelli et al. , Extension of the N =40 island of inversion towards N =50: Spectroscopy of 66 Cr, 70,72 Fe . Phys. Rev. Lett. 115 , 192501 ( 2015 ). doi: 10.1103/PhysRevLett.115.192501 http://doi.org/10.1103/PhysRevLett.115.192501 Extension of the N=40 island of inversion towards N=50: Spectroscopy of 66Cr, 70,72Fe R. Caballero-Folch , C. Domingo-Pardo , J. Agramunt et al. , First measurement of several β -delayed neutron emitting isotopes beyond N =126 . Phys. Rev. Lett. 117 , 012501 ( 2016 ). doi: 10.1103/PhysRevLett.117.012501 http://doi.org/10.1103/PhysRevLett.117.012501 First measurement of several β-delayed neutron emitting isotopes beyond N=126 K. Palli , G. A. Souliotis , T. Depastas et al. , Microscopic dynamical description of multinucleon transfer in 40 Ar induced peripheral collisions at 15 MeV/nucleon . EPJ Web Conf. 252 , 07002 ( 2021 ). doi: 10.1051/epjconf/202125207002 http://doi.org/10.1051/epjconf/202125207002 Microscopic dynamical description of multinucleon transfer in 40Ar induced peripheral collisions at 15 MeV/nucleon A. Papageorgiou , G. A. Souliotis , K. Tshoo et al. , Neutron-rich rare isotope production with stable and radioactive beams in the mass range A ∼ 40-60 at beam energy around 15 MeV/nucleon . J. Phys. G 45 , 095105 ( 2018 ). doi: 10.1088/1361-6471/aad7df http://doi.org/10.1088/1361-6471/aad7df Neutron-rich rare isotope production with stable and radioactive beams in the mass range A ∼ 40-60 at beam energy around 15 MeV/nucleon G. A. Souliotis , M. Veselsky , G. Chubarian et al. , Enhanced production of neutron-rich rare isotopes in peripheral collisions at Fermi energies . Phys. Rev. Lett. 91 , 022701 ( 2003 ). doi: 10.1103/PhysRevLett.91.022701 http://doi.org/10.1103/PhysRevLett.91.022701 Enhanced production of neutron-rich rare isotopes in peripheral collisions at Fermi energies G. A. Souliotis , M. Veselsky , G. Chubarian et al. , Enhanced production of neutron-rich rare isotopes in the reaction of 25 MeV/nucleon 86 Kr on 64 Ni . Phys. Lett. B 543 , 163 - 172 ( 2002 ). doi: 10.1016/S0370-2693(02)02459-0 http://doi.org/10.1016/S0370-2693(02)02459-0 Enhanced production of neutron-rich rare isotopes in the reaction of 25 MeV/nucleon 86Kr on 64Ni R. Ogul , N. Buyukcizmeci , A. Ergun et al. , Production of neutron-rich exotic nuclei in projectile fragmentation at Fermi energies . Nucl. Sci. Tech. 28 , 18 ( 2016 ). doi: 10.1007/s41365-016-0175-6 http://doi.org/10.1007/s41365-016-0175-6 Production of neutron-rich exotic nuclei in projectile fragmentation at Fermi energies R. Thies , A. Heinz , T. Adachi et al. , Systematic investigation of projectile fragmentation using beams of unstable B and C isotopes . Phys. Rev. C 93 , 054601 ( 2016 ). doi: 10.1103/PhysRevC.93.054601 http://doi.org/10.1103/PhysRevC.93.054601 Systematic investigation of projectile fragmentation using beams of unstable B and C isotopes G. F. Bertsch , H. Kruse , S. D. Gupta , Boltzmann equation for heavy ion collisions . Phys. Rev. C 29 , 673 - 675 ( 1984 ). doi: 10.1103/PhysRevC.29.673 http://doi.org/10.1103/PhysRevC.29.673 Boltzmann equation for heavy ion collisions G. F. Bertsch , S. Das Gupta , A guide to microscopic models for intermediate energy heavy ion collisions . Phys. Rep. 160 , 189 - 233 ( 1988 ). doi: 10.1016/0370-1573(88)90170-6 http://doi.org/10.1016/0370-1573(88)90170-6 A guide to microscopic models for intermediate energy heavy ion collisions O. Buss , T. Gaitanos , K. Gallmeister et al. , Transport-theoretical description of nuclear reactions . Phys. Rep. 512 , 1 - 124 ( 2012 ). doi: 10.1016/j.physrep.2011.12.001 http://doi.org/10.1016/j.physrep.2011.12.001 Transport-theoretical description of nuclear reactions J. Aichelin , “Quantum” molecular dynamics-a dynamical microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions . Phys. Rep. 202 , 233 - 360 ( 1991 ). doi: 10.1016/0370-1573(91)90094-3 http://doi.org/10.1016/0370-1573(91)90094-3 “Quantum” molecular dynamics-a dynamical microscopic n-body approach to investigate fragment formation and the nuclear equation of state in heavy ion collisions G. Tian , R. Wada , Z. Chen et al. , Nuclear stopping and light charged particle emission in 12 C+ 12 C at 95 MeV/nucleon . Phys. Rev. C 95 , 044613 ( 2017 ). doi: 10.1103/PhysRevC.95.044613 http://doi.org/10.1103/PhysRevC.95.044613 Nuclear stopping and light charged particle emission in 12C+12C at 95 MeV/nucleon J. Su , L. Zhu , C. C. Guo et al. , Uniform description of breakup mechanisms in central collision, projectile fragmentation, and proton-induced spallation . Phys. Rev. C 100 , 014602 ( 2019 ). doi: 10.1103/PhysRevC.100.014602 http://doi.org/10.1103/PhysRevC.100.014602 Uniform description of breakup mechanisms in central collision, projectile fragmentation, and proton-induced spallation Z. Q. Feng , Nuclear dynamics and particle production near threshold energies in heavy-ion collisions . Nucl. Sci. Tech. 29 , 40 ( 2018 ). doi: 10.1007/s41365-018-0379-z http://doi.org/10.1007/s41365-018-0379-z Nuclear dynamics and particle production near threshold energies in heavy-ion collisions C. W. Ma , C. Y. Qiao , T. T. Ding et al. , Temperature of intermediate mass fragments in simulated 40 Ca+ 40 Ca reactions around the Fermi energies by AMD model . Nucl. Sci. Tech. 27 , 111 ( 2016 ). doi: 10.1007/s41365-016-0112-8 http://doi.org/10.1007/s41365-016-0112-8 Temperature of intermediate mass fragments in simulated 40Ca+40Ca reactions around the Fermi energies by AMD model A. Guarnera , M. Colonna , P. Chomaz , 3D stochastic mean-field simulations of the spinodal fragmentation of dilute nuclei . Phys. Lett. B 373 , 267 - 274 ( 1996 ). doi: 10.1016/0370-2693(96)00152-9 http://doi.org/10.1016/0370-2693(96)00152-9 3D stochastic mean-field simulations of the spinodal fragmentation of dilute nuclei M. Colonna , M. Di Toro , A. Guarnera et al. , Fluctuations and dynamical instabilities in heavy-ion reactions . Nucl. Phys. A 642 , 449 - 460 ( 1998 ). doi: 10.1016/S0375-9474(98)00542-9 http://doi.org/10.1016/S0375-9474(98)00542-9 Fluctuations and dynamical instabilities in heavy-ion reactions J. J. Gaimard , K. H. Schmidt , A reexamination of the abrasion-ablation model for the description of the nuclear fragmentation reaction . Nucl. Phys. A 531 , 709 - 745 ( 1991 ). doi: 10.1016/0375-9474(91)90748-U http://doi.org/10.1016/0375-9474(91)90748-U A reexamination of the abrasion-ablation model for the description of the nuclear fragmentation reaction C. W. Ma , H. L. Wei , J. Y. Wang et al. , Isospin dependence of projectile-like fragment production at intermediate energies . Phys. Rev. C 79 , 034606 ( 2009 ). doi: 10.1103/PhysRevC.79.034606 http://doi.org/10.1103/PhysRevC.79.034606 Isospin dependence of projectile-like fragment production at intermediate energies D. Q. Fang , W. Q. Shen , J. Feng et al. , Isospin effect of fragmentation reactions induced by intermediate energy heavy ions and its disappearance . Phys. Rev. C 61 , 044610 ( 2000 ). doi: 10.1103/PhysRevC.61.044610 http://doi.org/10.1103/PhysRevC.61.044610 Isospin effect of fragmentation reactions induced by intermediate energy heavy ions and its disappearance K. Sümmerer , Erratum: Improved empirical parametrization of fragmentation cross sections [Phys. Rev. C 86, 014601 (2012)] . Phys. Rev. C 87 , 039903 ( 2013 ). doi: 10.1103/PhysRevC.87.039903 http://doi.org/10.1103/PhysRevC.87.039903 Erratum: Improved empirical parametrization of fragmentation cross sections [Phys. Rev. C 86, 014601 (2012)] K. Sümmerer , Improved empirical parametrization of fragmentation cross sections . Phys. Rev. C 86 , 014601 ( 2012 ). doi: 10.1103/PhysRevC.86.014601 http://doi.org/10.1103/PhysRevC.86.014601 Improved empirical parametrization of fragmentation cross sections K. Sümmerer , B. Blank , Modified empirical parametrization of fragmentation cross sections . Phys. Rev. C 61 , 034607 ( 2000 ). doi: 10.1103/PhysRevC.61.034607 http://doi.org/10.1103/PhysRevC.61.034607 Modified empirical parametrization of fragmentation cross sections G. Rudstam , Systematics of spallation yields . Z. Naturforsch. Teil A 21 , 1027 - 1041 ( 1966 ). doi: 10.1515/zna-1966-0724 http://doi.org/10.1515/zna-1966-0724 Systematics of spallation yields B. Mei , Improved empirical parameterization for projectile fragmentation cross sections . Phys. Rev. C 95 , 034608 ( 2017 ). doi: 10.1103/PhysRevC.95.034608 http://doi.org/10.1103/PhysRevC.95.034608 Improved empirical parameterization for projectile fragmentation cross sections Y. D. Song , H. L. Wei , C. W. Ma et al. , Improved fracs parameterizations for cross sections of isotopes near the proton drip line in projectile fragmentation reactions . Nucl. Sci. Tech. 29 , 96 ( 2018 ). doi: 10.1007/s41365-018-0439-4 http://doi.org/10.1007/s41365-018-0439-4 Improved fracs parameterizations for cross sections of isotopes near the proton drip line in projectile fragmentation reactions H. Wolter , M. Colonna , D. Cozma et al. , Transport model comparison studies of intermediate-energy heavy-ion collisions (2022) . arXiv: 2202.06672 [nucl-th] Transport model comparison studies of intermediate-energy heavy-ion collisions (2022) C. W. Ma , Y. L. Zhang , S. S. Wang et al. , A model comparison study of fragment production in 140 A MeV 58,64 Ni+ 9 Be reactions . Chin. Phys. Lett. 32 , 072501 ( 2015 ). doi: 10.1088/0256-307X/32/7/072501 http://doi.org/10.1088/0256-307X/32/7/072501 A model comparison study of fragment production in 140 A MeV 58,64Ni+9Be reactions Y. X. Zhang , N. Wang , Q. F. Li et al. , Progress of quantum molecular dynamics model and its applications in heavy ion collisions . Front. Phys. 15 , 54301 ( 2020 ). doi: 10.1007/s11467-020-0961-9 http://doi.org/10.1007/s11467-020-0961-9 Progress of quantum molecular dynamics model and its applications in heavy ion collisions M. Colonna , Collision dynamics at medium and relativistic energies . Prog. Part. Nucl. Phys. 113 , 103775 ( 2020 ). doi: 10.1016/j.ppnp.2020.103775 http://doi.org/10.1016/j.ppnp.2020.103775 Collision dynamics at medium and relativistic energies J. Xu , Transport approaches for the description of intermediate-energy heavy-ion collisions . Prog. Part. Nucl. Phys. 106 , 312 - 359 ( 2019 ). doi: 10.1016/j.ppnp.2019.02.009 http://doi.org/10.1016/j.ppnp.2019.02.009 Transport approaches for the description of intermediate-energy heavy-ion collisions A. Ono , Dynamics of clusters and fragments in heavy-ion collisions . Prog. Part. Nucl. Phys. 105 , 139 - 179 ( 2019 ). doi: 10.1016/j.ppnp.2018.11.001 http://doi.org/10.1016/j.ppnp.2018.11.001 Dynamics of clusters and fragments in heavy-ion collisions C. W. Ma , Y. G. Ma , Shannon information entropy in heavy-ion collisions . Prog. Part. Nucl. Phys. 99 , 120 - 158 ( 2018 ). doi: 10.1016/j.ppnp.2018.01.002 http://doi.org/10.1016/j.ppnp.2018.01.002 Shannon information entropy in heavy-ion collisions C. W. Ma , H. L. Wei , X. Q. Liu et al. , Nuclear fragments in projectile fragmentation reactions . Prog. Part. Nucl. Phys. 121 , 103911 ( 2021 ). doi: 10.1016/j.ppnp.2021.103911 http://doi.org/10.1016/j.ppnp.2021.103911 Nuclear fragments in projectile fragmentation reactions Y. Abe , S. Ayik , P. G. Reinhard et al. , On stochastic approaches of nuclear dynamics . Phys. Rep. 275 , 49 - 196 ( 1996 ). doi: 10.1016/0370-1573(96)00003-8 http://doi.org/10.1016/0370-1573(96)00003-8 On stochastic approaches of nuclear dynamics F. S. Zhang , E. Suraud , Boltzmann-Langevin equation, dynamical instability and multifragmentation . Phys. Lett. B 319 , 35 - 40 ( 1993 ). doi: 10.1016/0370-2693(93)90777-F http://doi.org/10.1016/0370-2693(93)90777-F Boltzmann-Langevin equation, dynamical instability and multifragmentation F. S. Zhang , E. Suraud , Analysis of multifragmentation in a Boltzmann-Langevin approach . Phys. Rev. C 51 , 3201 ( 1995 ). doi: 10.1103/PhysRevC.51.3201 http://doi.org/10.1103/PhysRevC.51.3201 Analysis of multifragmentation in a Boltzmann-Langevin approach S. Ayik , C. Grégoire , Fluctuations of single-particle density in nuclear collisions . Phys. Lett. B 212 , 269 - 272 ( 1988 ). doi: 10.1016/0370-2693(88)91315-9 http://doi.org/10.1016/0370-2693(88)91315-9 Fluctuations of single-particle density in nuclear collisions W. Bauer , G. F. Bertsch , S. Das Gupta , Fluctuations and clustering in heavy-ion collisions . Phys. Rev. Lett. 58 , 863 - 866 ( 1987 ). doi: 10.1103/PhysRevLett.58.863 http://doi.org/10.1103/PhysRevLett.58.863 Fluctuations and clustering in heavy-ion collisions P. Chomaz , G. Burgio , J. Randrup , Inclusion of fluctuations in nuclear dynamics . Phys. Lett. B 254 , 340 - 346 ( 1991 ). doi: 10.1016/0370-2693(91)91166-S http://doi.org/10.1016/0370-2693(91)91166-S Inclusion of fluctuations in nuclear dynamics E. Suraud , S. Ayik , M. Belkacem et al. , Applications of Boltzmann-Langevin equation to nuclear collisions . Nucl. Phys. A 542 , 141 - 158 ( 1992 ). doi: 10.1016/0375-9474(92)90403-7 http://doi.org/10.1016/0375-9474(92)90403-7 Applications of Boltzmann-Langevin equation to nuclear collisions J. Randrup , B. Remaud , Fluctuations in one-body dynamics . Nucl. Phys. A 514 , 339 - 366 ( 1990 ). doi: 10.1016/0375-9474(90)90075-W http://doi.org/10.1016/0375-9474(90)90075-W Fluctuations in one-body dynamics W. J. Xie , J. Su , L. Zhu et al. , Symmetry energy and pion production in the Boltzmann-Langevin approach . Phys. Lett. B 718 , 1510 - 1514 ( 2013 ). doi: 10.1016/j.physletb.2012.12.021 http://doi.org/10.1016/j.physletb.2012.12.021 Symmetry energy and pion production in the Boltzmann-Langevin approach B. Li , N. Tang , F. S. Zhang , Isospin effects of projectile fragmentation in a Boltzmann-Langevin approach . Chin. Phys. C 45 , 084103 ( 2021 ). doi: 10.1088/1674-1137/ac009a http://doi.org/10.1088/1674-1137/ac009a Isospin effects of projectile fragmentation in a Boltzmann-Langevin approach B. A. Bian , F. S. Zhang , H. Y. Zhou , Fragmentation cross sections of 20 Ne collisions with different targets at 600 MeV/nucleon . Nucl. Phys. A 807 , 71 - 78 ( 2008 ). doi: 10.1016/j.nuclphysa.2008.03.014 http://doi.org/10.1016/j.nuclphysa.2008.03.014 Fragmentation cross sections of 20Ne collisions with different targets at 600 MeV/nucleon K. Chen , Z. Fraenkel , G. Friedlander et al. , VEGAS: A monte carlo simulation of intranuclear cascades . Phys. Rev. 166 , 949 - 967 ( 1968 ). doi: 10.1103/PhysRev.166.949 http://doi.org/10.1103/PhysRev.166.949 VEGAS: A monte carlo simulation of intranuclear cascades S. Huber , J. Aichelin , Production of Δ - and N * -resonances in the one-boson exchange model . Nucl. Phys. A 573 , 587 - 625 ( 1994 ). doi: 10.1016/0375-9474(94)90232-1 http://doi.org/10.1016/0375-9474(94)90232-1 Production of Δ- and N*-resonances in the one-boson exchange model J. Cugnon , D. L’Hôte , J. Vandermeulen , Simple parametrization of cross-sections for nuclear transport studies up to the GeV range . Nucl. Instr. Meth. B 111 , 215 - 220 ( 1996 ). doi: 10.1016/0168-583X(95)01384-9 http://doi.org/10.1016/0168-583X(95)01384-9 Simple parametrization of cross-sections for nuclear transport studies up to the GeV range Y. D. Song , H. L. Wei , C. W. Ma , Fragmentation binding energies and cross sections of isotopes near the proton dripline . Phys. Rev. C 98 , 024620 ( 2018 ). doi: 10.1103/PhysRevC.98.024620 http://doi.org/10.1103/PhysRevC.98.024620 Fragmentation binding energies and cross sections of isotopes near the proton dripline C. W. Ma , Y. D. Song , H. L. Wei , Binding energies of near proton-drip line Z = 22-28 isotopes determined from measured isotopic cross section distributions . Sci. China-Phys. Mech. Astron. 62 , 012013 ( 2019 ). doi: 10.1007/s11433-018-9256-8 http://doi.org/10.1007/s11433-018-9256-8 Binding energies of near proton-drip line Z = 22-28 isotopes determined from measured isotopic cross section distributions 10.1007/s41365-022-01048-4 This work was Supported by the National Natural Science Foundation of China (No.12135004, No.11635003 and No.11961141004) 2022-02-22 2022-03-27 2022-04-01 2022-06-15 2022-07-26 © 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. 2022 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/s41365-022-01048-4 http://dx.doi.org/10.1007/s41365-022-01048-4 . 2022 Nuclear Science and Techniques 05 33