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

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 protonrich 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 of48Ni at 345MeV/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,37,38Sc,^(38)Ti,^(40,41,42)V,^(40,41)Cr,and^(42,43,44,45)Mn are in the range of 10-2-102mb.Hence,projectile fragmentation of radioactive ion beams of Ni is a potential method for generating new proton-rich nuclei with Z=20-25.

Isospin-dependent relativistic microscopic optical potential in the Dirac Brueckner-Hartree-Fock method

The relativistic microscopic optical potential in the asymmetric nuclear matter is studied in the framework of the Dirac Brueckner-Hartree-Fock method. A new decomposition of the Dirac structure of the nuclear self-energy in nuclear matter is adopted. The self-energy of a nucleon with E > 0 in nuclear matter is calculated with the G matrix in the Hartree-Fock approach. The optical potential of a nucleon in the nuclear medium is identified with the nucleon self-energy. The energy and asymmetric parameter dependence of the relativistic optical potentials for proton and neutron are discussed. The resulting Schroedinger equivalent potentials have reasonable behaviors of the energy dependence. The asymmetric parameter dependence of relativistic optical potentials and Schroedinger potentials are emphasized.

Uncertainties of critical temperatures based on higher-order fluctuations of the largest fragment charge

The new signature of liquid-gas phase transition has been well indicated by the higher-order fluctuations of the largest fragment charge,but the uncertainties of critical temperatures based on this signature have not been revealed.This study extracts the critical temperatures of liquid-gas phase transition in nuclear reactions and investigates their uncertainties.Utilizing the isospin-dependent quantum molecular dynamics model in conjunction with the statistical model GEMINI enables us to describe the dynamical path from the initial to the final state.An isotope thermometer and a quantum fluctuation thermometer are employed to extract the nuclear temperature.The higher-order fluctuations of the largest fragment charge and critical temperatures are studied in^(124)Sn+^(120)Sn collisions ranging from 400 to 1000 MeV/nucleon and^(124)Sn+AZ collisions at 600 MeV/nucleon.Observations revealed that the pseudo-critical point is robustly indicated by the higher-order fluctuations of the largest fragment charge.The critical temperatures extracted by the isotope thermometer are relatively consistent,with an uncertainty of 15%,while those obtained by the quantum fluctuation thermometer are heavily influenced by the incident energy and mass number of target nuclei.The excitation energy E∗and bound charge Zbound are used for event-sorting.These two ensembles represent the statistical properties of the initial and final states of the system,respectively.The initial-final correlations of statistical properties might lead to two phenomena.First,the size distribution of the largest fragment at the pseudo-critical point based on the Zbound ensemble is wide,while that based on E∗ensemble exhibits bimodality,which is a typical characteristic in the liquid-gas coexistence of a finite system.Second,the temperature at the pseudo-critical point based on the Zbound ensemble is higher than that based on the E∗ensemble.Furthermore,the projectile-like system exhibits a significant dynamical effect in its evolution path from the initial to final state,closely associated with the fluctuation of critical temperature.

Covariance analysis of an isospin-dependent probe

Based on a modified quantum molecular the nuclear stopping of reaction systems with different dynamics model, we calculate the neutron-proton ratio and symmetry potentials and collision cross sections. We perform correlations of several probes using the covariance data processing method. It is shown that the correlation between the nuclear stopping and the isospin-dependent nucleon-nucleon cross sections is strong, but the nuclear stopping and symmetry potentials have a weak correlation. The correlation between neutron-proton ratio and symmetry potentials in the case of low energy is stronger. The correlation between neutron-proton ratio and isospin-dependent collision cross sections is enhanced with the increase of energy, but remains weak. In addition, the correlations of the emission numbers of the deuteron with the symmetry potentials and collision cross sections at different beam energies are not obvious compared to two prior physical quantities. In this paper, we define a parameter to quantitatively describe the sensitivity of isospin-dependent probes. By analyzing this parameter, one can extract more information about the isospin effects of the physical quantity.

Production of neutron-deficient nuclei around N=126 by proton-induced spallation

Many isotopes of Np,Pu,Am,and Cm around the N=126 shell still have not been produced in the laboratory.This study aims to investigate the cross sections and yields of the neutron-deficient nuclei of Np,Pu,Am,and Cm produced in the proton-induced spallations of transuranium elements.The isospin-dependent quantum molecular dynamics(IQMD)model is applied to study the dynamical process of reaction,and the subsequent decay process is simulated by the GEMINI++model.The IQMD-GEMINI++model is applied to calculate the cross section,kinetic energy,and angular distribution of the isotopic productions around N=126.The Lindhand,Scharff,and Schiott theory is applied to calculate the energy loss of different heavy nuclei in the target material.A comparison between the data and the calculations shows that the IQMD-GEMINI++model can reproduce the production cross sections of the neutron-deficient nuclei in spallation within approximately 1.5 orders of magnitude.The maximum cross section of the undiscovered isotopes of Np,Pu,Am,and Cm is about 10-5 mb,while the kinetic energies of the productions are all less than 16 MeV.The angular distribution shows that the emission direction of production is mostly at a backward angle.The range of production in the target is within the range of 10-7to 10-5cm.This range is the effective target thickness for the online identification of undiscovered isotopes.Based on the effective thickness of the target and assuming an intensity of 120μA for the proton beam,the yields of the undiscovered neutron-deficient nuclei are calculated.Productions of the undiscovered isotopes of Np,Pu,Am,and Cm by the proton-induced spallations of transuranium elements are feasible.However,experimental techniques for online identification of neutron-deficient nuclei produced in proton-induced spallation should be developed.

Target dependence of isotopic cross sections in the spallation reactions^(238)U+p,d and^(9)Be at 1 A GeV

The spallation of ^(238)U is an important way to produce rare isotopes.This work aims at studying the cross sections of isotopes produced in ^(238)U+p,d and^9 Be reactions at 1 A GeV and their target dependence.(1)A physical model dependent(Bayesian neural network)BNN,which includes the details of IQMD-GEMINI++model and BNN,was developed for a more accurate evaluation of production cross sections.The isospin-dependent quantum molecular dynamics(IQMD)model is used to study the non-equilibrium thermalization of the ^(238)U nuclei and fragmentation of the hot system.The subsequent decay of the pre-fragments is simulated by the GEMINI++model.The BNN algorithm is used to improve the prediction accuracy after learning the residual error between experimental data and calculations by the IQMD-GEMINI++model.It is shown that the IQMD-GEMINI++model can reproduce the available experimental data(3282 points)within 1.5 orders of magnitude.After being fine tuned by the BNN algorithm,the deviation between calculations and experimental data were reduced to within 0.4 order of magnitude.(2)Based on the predictions by the IQMD-GEMINI++-BNN framework,the target dependence of isotopic cross sections was studied.The cross sections to produce the rare isotopes by the ^(238)U+p,d and^9 Be reactions at 1 A GeV are compared.For the generation of neutron-rich fission products,the cross sections for the ^(238)U+^(9)Be are the largest.For the generation of neutron-deficient nuclei in the region of A=200–220,the cross sections for ^(238)U+p reaction are the largest.Considering the largest cross sections and the atomic density,the beryllium target is recommended to produce the neutron-rich fission products by the ^(238)U beam at 1 A GeV,while the liquid-hydrogen target is suggested to produce the neutron-deficient nuclei in the region of A=200–220.

Isospin effects of projectile fragmentation in a Boltzmann-Langevin approach

The isospin effects of projectile fragmentation at intermediate energies are investigated using an isospin-dependent Boltzmann-Langevin model.The collisions of mass-symmetric reactions including 58Fe,58Ni+58Fe,and Ni at intermediate energies,in the 30 to 100 MeV/A range,are studied for different symmetry energies.Yield ratios of the isotopic,isobaric,and isotonic pairs of fragments from the intermediate-mass region using three symmetry energies are extracted as functions of the N/Z ratio of the composite systems in the entrance channel and the incident energies.It is found that the yield ratios are sensitive to symmetry energies,especially for neutron-rich systems,and the calculations using soft symmetry energy are closer to the experimental data.The isospin effect is stronger for the soft symmetry energy,owing to the competition of the repulsive Coulomb force and the symmetry energy attractive force on the proton.For the first time,the splits are presented,revealing a transition from the isospin equilibrium at lower energies to translucency at intermediate energies.The results show a degree of transparency in that intermediate mass fragments undergo a transition from dependence on the composite systems in the entrance channel to reliance on the projectile and target nuclei.

Isospin dependence of projectile fragmentation at hundreds of MeV/u

By modeling the fragmentation process using a dynamic model and permitting only evaporation in the statistical code,the main features of a projectile fragmentation at 600 MeV/u were considered in our previous study[Phys.Rev.C,98:014610(2018)].In this study,we extend this to the isospin dependence of a projectile fragmentation at several hundreds of MeV/u.We searched for isospin observables related to the isospin fractionation to extract the symmetry energy,and found that at the pre-equilibrium stage of the collisions an isospin diffusion will take place and affect the isospin of the final fragments.The isospin fractionation plays a part during the fragmenting stage.Compared to the soft symmetry energy,the stiff symmetry energy provides a smaller repulsive force for neutrons and an attractive force for the protons in a neutron-rich system at a subnormal density,and hence causes a smaller isospin asymmetry of the gas phase,leaving a more neutron-rich liquid phase.An observable robust isospin is proposed to extract the slope of the symmetry energy at normal density based on the isospin dependence of the projectile fragmentation at hundreds of MeV/u.

Dynamical fluctuations in fragmentation reactions in a Boltzmann-Langevin approach

Based on the isospin-dependent Boltzmann-Langevin model,the dynamical fluctuations in the fragmentation reaction of^(112)Sn+^(112)Sn are investigated.The quadrupole moment and octupole moment with zero magnetic quantum number have large fluctuations in the early time of the collisions.The dynamical fluctuations in momentum space show a strong dependence on the incident energy.The effects of using different fluctuations on the fragment cross sections are also studied in the fragmentation reactions.The results by using Q_(20)+Q_(30)fluctuation have a better agreement with the experimental data.Calculations using Q_(20)+Q_(30)fluctuation produce more proton-rich and neutron-rich nuclei than those using Q_(20)fluctuation only.Besides,the difference between the production cross sections of fragments calculated by using Q_(20)and Q_(20)+Q_(30)fluctuations is larger in the vicinity of the projectile.These results present that the dynamical fluctuations may affect the whole dynamical process of fragmentation reactions including the production of fragments,due to the nonlinear nature of the Boltzmann-Langevin equation.