A possible probe to neutron-skin thickness by fragment parallel momentum distribution in projectile fragmentation reactions

Neutron-skin thickness is a key parameter for a neutron-rich nucleus;however,it is difficult to determine.In the framework of the Lanzhou Quantum Molecular Dynamics(LQMD)model,a possible probe for the neutron-skin thickness(δ_(np))of neutron-rich ^(48)Ca was studied in the 140A MeV ^(48)Ca+^(9)Be projectile fragmentation reaction based on the parallel momentum distribution(p∥)of the residual fragments.A Fermi-type density distribution was employed to initiate the neutron density distributions in the LQMD simulations.A combined Gaussian function with different width parameters for the left side(Γ_(L))and the right side(Γ_(R))in the distribution was used to describe the p∥of the residual fragments.Taking neutron-rich sulfur isotopes as examples,Γ_(L) shows a sensitive correlation withδ_(np) of ^(48)Ca,and is proposed as a probe for determining the neutron skin thickness of the projectile nucleus.

Single source emission of proton projectile fragments in nucleus-emulsion interactions

The projected angular distribution and transverse momentum distribution of proton projectile fragments produced in 3.7A GeV 160, 500A MeV 56Fe, and 1.7A GeV S4Kr induced by different kinds of emulsion target （H, CNO, and AgBr） interactions are investigated. It is found that the projected angular distribution and transverse momentum distribution can be well represented by a single Gaussian distribution. Comparison of transverse momentum distribution with the Maxwell-Boltzmann distribution reveals that proton projectile fragments are emitted from a single-temperature emission source. The temperature is different for different colliding systems, and linearly depends on the target size.

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.

Disappearance of isospin effect in projectile fragmentation at intermediate energy

The 140 MeV/u ^40,48Ca＋^9Be and ^58,64Ni＋^9Be reactions are simulated by the statistical abrasion ablation model, and the simulation results are compared to the National Superconducting Cyclotron Laboratory （NSCL） experimental data. By comparing the fragment isotopic distributions of ^40,48Ca and ^58,64Ni, we study the isospin effect in the projectile fragmentation induced by the neutron-rich nuclei at intermediate energy experimentally and theoretically. It is found that the isospin effect in projectile fragmentation decreases and even disappears as the violence of the collision increases.

Predicting ^(28)Si projectile fragmentation cross sections with Bayesian neural network method

This study utilizes the Bayesian neural network(BNN)method in machine learning to learn and predict the cross-sectional data of ^(28)Si projectile fragmentation for different targets at different energies and to quantify the uncertainty.The detailed modeling process of the BNN is presented,and its prediction results are compared with those of the Cummings,Nilsen,EPAX2,EPAX3,and FRACS models and experimental measurement values.The results reveal that,compared with other models,the BNN method achieves the smallest root-mean-square error(RMSE)and the highest agreement with the experimental values.Only the BNN method and FRACS model show a significant odd-even staggering effect;however,the results of the BNN method are closer to the experimental values.Furthermore,the BNN method is the only model capable of reproducing data features with low cross-section values at Z=9,and the average ratio of the predicted to experimental values of the BNN is close to 1.0.These results indicate that the BNN method can accurately reproduce and predict the fragment production cross sections of ^(28)Si projectile fragmentation and demonstrate its ability to capture key data characteristics.

Precise machine learning models for fragment production in projectile fragmentation reactions using Bayesian neural networks

Machine learning models are constructed to predict fragment production cross sections in projectile fragmentation(PF)reactions using Bayesian neural network(BNN)techniques.The massive learning for BNN models is based on 6393 fragments from 53 measured projectile fragmentation reactions.A direct BNN model and physical guiding BNN via FRACS parametrization(BNN+FRACS)model have been constructed to predict the fragment cross section in projectile fragmentation reactions.It is verified that the BNN and BNN+FRACS models can reproduce a wide range of fragment productions in PF reactions with incident energies from 40 MeV/u to 1 GeV/u,reaction systems with projectile nuclei from^40 Ar to^208 Pb,and various target nuclei.The high precision of the BNN and BNN+FRACS models makes them applicable for the low production rate of extremely rare isotopes in future PF reactions with large projectile nucleus asymmetry in the new generation of radioactive nuclear beam factories.

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.

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 and neutron-skin thickness of neutron-rich nuclei

By investigating the cross section distributions of fragments produced in the 140 A MeV 40,48Ca＋9Be and 1 A GeV 124,136Xe＋Pb reactions, the isospin dependence of projectile fragmentation in fragment production is studied. In the framework of the statistical abrasion-ablation model, the 1 A GeV 136Xe＋ 208Pb reaction is calculated. By adjusting the diffuseness parameter in neutron density distribution of 136Xe, we find the isospin dependence of projectile fragmentation in fragment production is sensitive to the neutron-skin thickness of the projectile nucleus.

Projectile fragment emission in the fragmentation of ^(56)Fe on C,Al and CH_2 targets at 471 A MeV

The emission angle and the transverse momentum distributions of projectile fragments produced in the fragmentation of 56Fe on CHs, C and A1 targets at 471 A MeV are measured. It is found that for the same target, the average value and width of the angular distribution decrease with an increase of the projectile fragment charge; for the same projectile fragment, the average value of the distribution increases and the width of the distribution decreases with increasing the target charge number. The transverse momentum distribution of a projectile fragment can be explained by a single Gaussian distribution and the averaged transverse momentum per nucleon decreases with the increase of the charge of projectile fragment. The cumulated squared transverse momentum distribution of a projectile fragment can be explained well by a single Rayleigh distribution. The temperature parameter of the emission source of the projectile fragment, calculated from the cumulated squared transverse momentum distribution, decreases with the increase of the size of the projectile fragment.

Isoscaling of projectile-like fragments

In this paper, the isotopic and isotonic distributions of projectile fragmentation products have been simulated by a modified statistical abrasion-ablation model and the isoscaling behaviour of projectile-like fragments has been discussed. The isoscaling parameters α and β have been extracted respectively, for hot fragments before evaporation and cold fragments after evaporation. It looks that the evaporation has stronger effect on α than β. For cold fragments, a monotonic increase of α and ｜β｜ with the increase of Z and N is observed. The relation between isoscaling parameter and the change of isospin content is discussed.

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.

Study of Isotopic Distribution of the Projectile-like Fragments Produced in the ^(17,18)N + ^(197)Au Reactions at 33 MeV/u

The experimental data of the isotopic distribution for projectile-like fragments are presented for the 17,18N ＋ 197Au reaction at 33 MeV/u. The width of the isotopic distributions for lSN projectile is significantly broader than that for 17N projectile, and the average N/Z ratio of the former shifts to higher neutron number side. As long as the realistic nucleon density distribution is used, the isotopic distribution for fragments is reproduced by the simple abrasion-ablation model calculation, which thus provides an independent way to determine the surface distribution of the nuclear matter density for neutron-rich nuclei.

Fracture behavior and mechanism of highly fragmented steel cylindrical shell under explosive loading

An in-depth understanding of the fracture behavior and mechanism of metallic shells under internal explosive loading can help develop material designs for warheads and regulate the quantity and mass distribution of the fragments formed.This study investigated the fragmentation performance of a new high-carbon silicon-manganese(HCSiMn)steel cylindrical shell through fragment recovery experiments.Compared with the conventional 45Cr steel shell,the number of small mass fragments produced by the HCSi Mn steel shell was significantly increased with a scale parameter of 0.57 g fitted by the Weibull distribution model.The fragmentation process of the HCSi Mn shell exhibited more brittle tensile fracture characteristics,with the microcrack damage zone on the outer surface being the direct cause of its high fragmentation.On the one hand,the doping of alloy elements resulted in grain refinement by forming metallographic structure of tempered sorbite,so that microscopic intergranular fracture reduces the characteristic mass of the fragments;on the other hand,the distribution of alloy carbides can exert a"pinning"effect on the substrate grains,causing more initial cracks to form and propagate along the brittle carbides,further improving the shell fragmentation.Although the killing power radius for light armored vehicles was slightly reduced by about 6%,the dense killing radius of HCSiMn steel projectile against personnel can be significantly increased by about 26%based on theoretical assessment.These results provided an experimental basis for high fragmentation warhead design,and to some extent,revealed the correlation mechanism between metallographic structure and shell fragmentation.

Fragmentation in ^16 O-emulsion interactions at 3.7 A GeV

The topology of ^16 O fragmentation at 3.7 A GeV in reactions with emulsion nuclei is presented. The multiplicity distributions of projectile fragments, charged secondaries and their dependences on the projectile residues are discussed.

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.

Isospin Effects of Threshold Energy of Radial Flow in Heavy Ion Collisions

The threshold energies of radial flow in reactions of ^40 Ca-^40Ca and ^48Ca＋ ^48Ca in central collisions are investigated within an isospin dependent quantum molecular dynamics model by using three different forms of symmetry energy. It is found that the neutron-rich system has smaller threshold energy of radial flow and this quantity depends on the form of symmetry potential. It is indicated that the threshold energy of radial flow can provide a new method to determine the symmetry energy of asymmetric nuclear matter.

Helium production from ^84Kr- and ^197Au-emulsion interactions at high energies

The properties of the relativistic helium fragments produced in interactions of ^84Kr at 1.8 A GeV and ^197Au at 10.7 A GeV in emulsion are investigated. The experimental results are compared with those obtained from various projectiles with emulsion collisions at different energies. It is found that the multiplicity distribution of helium projectile fragments （HPFs） is well described by the Koba-Nielsen Olesen （KNO） scaling presentation. The second Mueller moment f2 of the HPF multiplicity distribution is independent of the projectile energy for the same projectile, but it is dependent on the projectile mass number. The value of f2 increases with the increase of projectile mass number Ap. The negative value of f2, when Ap 〈 69, means that the emission of HPFs is anticorrelated, but positive value of f2, when Ap 〉 69, refers to that the emission of HPFs is correlated. The non-zero f2 moment in this experiment implies the strong correlation existing between the HPFs.

Isotopic production cross sections of fragmentation residues produced by ^(18)O ions on a carbon target near 260 MeV/nucleon

The isotopic cross sections of residual nuclei produced in fragmentation reactions of ^(18)O projectiles impinging on a carbon target at energies near 260 MeV/nucleon were measured at the HIRFL facility in Lanzhou(China).A full identification of atomic and mass numbers of fragments was achieved from the determination of their magnetic rigidity,energy loss,and time of flight.The production cross sections for a dozen of nitrogen,carbon,and boron isotopes were determined with uncertainties below 30% for most of the cases.The obtained cross sections for N and B isotopes show a rather good agreement with previous experimental data obtained with different projectile energies.The cross sections for some C isotopes seem to exhibit a dependence on the projectile energy.A comparison of the data and several theoretical model calculations are presented.

An Isoratio Method to Study Free Energy and Temperature Effects in Intermediate Mass Fragments Produced in Heavy-Ion Collisions

An isoratio method, i.e., the isotopic(isotonic) ratio among three isotopes(isotones), is proposed to study the free energy and temperature effects in the intermediate mass fragments produced in heavy-ion collisions. The parameterizations for the free energy of nucleus at low temperature, which have been proposed in the framework of the density functional theory using the SKM skymre interaction, are adopted to calculate the temperature-dependent free energy of fragment. By analyzing the measured yields of fragments in the 140 A MeV ^(58),^(64) Ni +~9Be reactions,it is verified that the free energy in the isoratio is almost the same for different reactions. A temperature-dependent pairing-energy is introduced into the parameterizations for free energy, which reveals that the weakened pairing energy at the low temperature accounts for the weakened or disappearing odd-even staggering in isoratio.