Configurational information entropy analysis of fragment mass cross distributions to determine the neutron skin thickness of projectile nuclei

Configurational information entropy(CIE)analysis has been shown to be applicable for determining the neutron skin thickness(δnp)of neutron-rich nuclei from fragment production in projectile fragmentation reactions.The BNN+FRACS machine learning model was adopted to predict the fragment mass cross-sections(σ_(A))of the projectile fragmentation reactions induced by calcium isotopes from ^(36)Ca to ^(56)Ca on a ^(9)Be target at 140MeV/u.The fast Fourier transform was adopted to decompose the possible information compositions inσA distributions and determine the quantity of CIE(S_(A)[f]).It was found that the range of fragments significantly influences the quantity of S_(A)[f],which results in different trends of S_(A)[f]~δnp correlation.The linear S_(A)[f]~δnp correlation in a previous study[Nucl.Sci.Tech.33,6(2022)]could be reproduced using fragments with relatively large mass fragments,which verifies that S_(A)[f]determined from fragmentσAis sensitive to the neutron skin thickness of neutron-rich isotopes.

Determination of neutron-skin thickness using configurational information entropy

Configurational information entropy(CIE)theory was employed to determine the neutron-skin thickness of neutron-rich calcium isotopes.The nuclear density distributions and fragment cross sections in 350 MeV/u ^(40-60)Ca+^(9)Be projectile fragmentation reactions were calculated using a modified statistical abrasion-ablation model.CIE quantities were determined from the nuclear density,isotopic,mass,and charge distributions.The linear correlations between the CIE determined using the isotopic,mass,and charge distributions and the neutron-skin thickness of the projectile nucleus show that CIE provides new methods to extract the neutron-skin thickness of neutron-rich nuclei.

Improved FRACS parameterizations for cross sections of isotopes near the proton drip line in projectile fragmentation reactions

The FRACS parameterizations,labeled as FRACS-C,have been improved in order to predict the presence of isotopes near the proton drip line produced in projectile fragmentation reactions.By investigating the cross sections for proton-rich isotopes in a series of reactions with energies ranging from intermediate to relativistic,it is shown that the FRACS-C parameterizations can predict isotopes near the proton drip line considerably well.The FRACS-C parameterizations are suggested to serve as an effective tool for predicting the presence of proton-rich isotopes with large asymmetry in a projectile fragmentation reaction.Different reactions have been investigated to check these results.

Multiple-models predictions for drip line nuclides in projectile fragmentation of^(40,48)Ca,^(58,64)Ni,and^(78,86)Kr at 140 MeV/u

Modern rare isotope beam(RIB)factories will significantly enhance the production of extremely rare isotopes(ERI)at or near drip lines.As one of the most important methods employed in RIB factories,the production of ERIs in projectile fragmentation reactions should be theoretically improved to provide better guidance for experimental research.The cross-sections of ERIs produced in 140 MeV/u^(78,86)Kr/^(58,64)Ni/^(40,48)Ca+9Be projectile fragmentation reactions were predicted using the newly proposed models[i.e.,Bayesian neural network(BNN),BNN+FRACS,and FRACS,see Chin.Phys.C,46:074104(2022)]and the frequently used EPAX3 model.With a minimum cross-section of 1015 mb,the possibilities of ERIs discovery in a new facility for rare isotope beams(FRIB)are discussed.

Isotopic cross-sections in proton induced spallation reactions based on the Bayesian neural network method

The Bayesian neural network(BNN)method is proposed to predict the isotopic cross-sections in proton induced spallation reactions.Learning from more than 4000 data sets of isotopic cross-sections from 19 experimental measurements and 5 theoretical predictions with the SPACS parametrization,in which the mass of the spallation system ranges from 36 to 238,and the incident energy from 200 MeV/u to 1500 MeV/u,it is demonstrated that the BNN method can provide good predictions of the residue fragment cross-sections in spallation reactions.

Binding energies of near proton-drip line Z = 22-28 isotopes determined from measured isotopic cross section distributions

A new method is proposed to determine the binding energy(B)of near proton-drip line isotopes from isotopic cross section distribution.To determine B of Z=22-28 isotopes(with T_z=-2 and-5/2),the lack of cross sections for proton-rich isotopes in the 345A MeV^(78)Kr+~9Be is overcome by predicting the proton-rich isotopes from a newly discovered scaling phenomenon found in the proton-rich isotopes measured in the 140A MeV^(40,48)Ca(^(58,64)Ni)+~9Be reactions.The cross sections for proton-rich isotopes are verified to exponentially depend on the average binding energy per nucleon,based on which B of the Z=22-28 isotopes with T_z=-2 and-5/2 are determined from cross sections.The determined B of the isotopes are justified from obeying the scaling phenomenon of the difference between the mass of mirror nuclei.The cross sections for the Z=22-28 isotopes with T_z=-1 and-3/2,which in potential can be experimentally studied in mass storage ring,are also predicted.

A Bayesian-neural-network prediction for fragment production in proton induced spallation reaction

Fragment production in spallation reactions yields key infrastructure data for various applications.Based on the empirical SPACS parameterizations,a Bayesian-neural-network(BNN)approach is established to predict the fragment cross sections in proton-induced spallation reactions.A systematic investigation has been performed for the measured proton-induced spallation reactions of systems ranging from intermediate to heavy nuclei systems and incident energies ranging from 168 MeV/u to 1500 MeV/u.By learning the residuals between the experimental measurements and SPACS predictions,it is found that the BNN-predicted results are in good agreement with the measured results.The established method is suggested to benefit the related research on nuclear astrophysics,nuclear radioactive beam sources,accelerator driven systems,proton therapy,etc.

A scaling phenomenon for the cross section of fragment produced in projectile fragmentation reactions

A scaling phenomenon has been found for the cross section of a fragment, which is defined as a "square" cross section(SCS).This phenomenon can unify the cross sections of fragments in projectile fragmentation(PF) reactions. An empirical formula is proposed to calculate SCSfor a fragment with parameters determined by an extensive investigation of measured reactions ranging from Fermi energies to relativistic energies. The scaling phenomenon of SCShas been verified using different techniques,showing that the scaling of SCSgenerally exists in PF reactions. The concept of SCS, which can be assumed as a standard value for a fragment, is shown to accurately predict the cross sections of isotopes in PF reactions with incident energies ranging from tens of A MeV to approximately 1000 A MeV.

Cross-section prediction for isotopes near neutron drip line in 70, 80Zn projectile fragmentation reactions

The cross sections for 59,60Ca, recently measured in the 345 A MeV 70Zn+9 Be reaction,were estimated using the FRACS parametrization and an empirical formula,which are in good agreement.The FRACS parametrization and the empirical formula are combined to predict the cross sections for extreme calcium isotopes 66,70Ca in the70,80Zn+9 Be reactions at the incident energies of 60,80,and 345 A MeV.The dependence of emperical formula parameters on the reaction system,as well as the incident energy,are discussed.The results indicate that 66,70Ca can be discovered in reactions of 60,80A MeV 80Zn+9 Be.The predicted binding energy for extreme neutron-rich isotopes by the spherical relativistic continuum Hartree-Bogoliubov theory was adopted in the calculation.Hence,the planned Beijing Isotope-Separation-On Line Neutron-Rich Beam Facility(BISOL),which is a third generation radioactive ion beam facility,could provide the opportunity to discover 66,70 Ca and neighboring neutron-drip line nuclei.

Predictions for cross sections of light proton-rich isotopes in the ^(40)Ca + ~9Be reaction

The cross sections for Z=10-19 with isotopes Tz=-3/2 to -5 in the 140A MeV 40Ca ＋ 9Be projectile fragmentation reaction have been predicted. An empirical formula based on the correlation between the cross section and average binding energy of an isotope has been adopted to predict the cross section. The binding energies in the AME16, WS4, and the theoretical prediction by the spherical relativistic continuum Hartree-Bogoliubov theory have been used. Meanwhile, the FRACS parametrization and the modified statistical abrasion-ablation model are also used to predict the cross sections for the proton-rich isotopes. The predicted cross sections for the Tz=-3 isotopes are close to 10-10 mb, which hopefully can be studied experimentally. In addition, based on the predicted cross sections, Z=14 is suggested to be a new magic number in the light proton-rich nuclei with Tz ≤ -3/2, for which the phenomenon is much more evident than it is from the average binding energy per nucleon.