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.

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.

Nucleon stripping in deuteron-induced spallation reactions at hundreds MeV/nucleon

A nucleon-nucleus dynamics model was developed to investigate the proton-,neutron-,and deuteron-induced reactions at hundreds of MeV/nucleon.In this model,the trajectory of incident nucleon is described by classical mechanics,and the probability of reaction between the nucleon and nucleus is calculated by exponential damping.It is shown that the total reaction cross sections calculated by the model agree in general with the predictions by the CDCC and the experimental data.The model was applied to investigate the nucleon stripping in deuteron-induced reactions and its symmetry energy dependence.

Pairing-energy coefficients of neutron-rich fragments in spallation reactions

The ratio of pairing-energy coefficient to temperature （ap/T） of neutron-rich fragments produced in spallation reactions has been investigated by adopting an isobaric yield ratio method deduced in the framework of a modified Fisher model. A series of spallation reactions, 0.5A and 1A GeV 208Pb ＋ p, 1A GeV 238U ＋ p, 0.5A GeV 136Xe ＋ d, 0.2A, 0.5A and 1A GeV 136Xe ＋ p, and 56Fe ＋ p with incident energy ranging from 0.3A to 1.5A GeV, has been analysed. An obvious odd-even staggering is shown in the fragments with small neutron excess （I=N-Z）, and in the relatively small-A fragments which have large I. The values of ap/T for the fragments, with I from 0 to 36, have been found to be in a range from -4 to 4, and most values of ap/T fall in the range from -1 to 1. It is suggested that a small pairing-energy coefficient should be considered in predicting the cross sections of fragments in spallation reactions. It is also concluded that the method proposed in this article is not good for fragments with A/As〉 85% （where As is the mass number of the spallation system）.

Light fragment and neutron emission in high-energy proton induced spallation reactions

The dynamics of high-energy proton-induced spallation reactions on target nuclides of 56Fe,58Ni,107Ag,112d,184W,181Ta,197Au,and 208Pb are investigated with the quantum molecular dynamics transport model motivated by the China initiative Accelerator Driven System(CiADS)in Huizhou and the China Spallation Neutron Source(CSNS)in Dongguan.The production mechanism of light nuclides and fission fragments is thoroughly analyzed,and the results obtained thereby are compared with available experimental data.The statistical code GEMINI is employed in conjunction with a transport model for describing the decay of primary fragments.For the treatment of cluster emission during the preequilibrium stage,a surface coalescence model is implemented into the model.It is found that the available data in terms of total fragment yields are well reproduced in the combined approach for spallation reactions both on the heavy and light targets.The energetic light nuclides(deuteron,triton,helium isotopes etc)mainly created during the preequilibrium stage are treated within the framework of surface coalescence,whereas their evaporation is described in the conventional manner by the GEMINI code.With this combined approach,a good overall description of light clusters and neutron emission is obtained,and some discrepancies with the experimental data are discussed.Possible production of radioactive isotopes in the spallation reactions is also analyzed,i.e.,the 6.8He energy spectra.

Study of neutron activation yields in spallation reaction of 400 MeV/u carbon on a thick lead target

The spallation-neutron yield was studied experimentally by bombarding a thick lead target with 400 MeV/u carbon beam. The data were obtained with the activation analysis method using foils of Au, Mn, Al, Fe and In. The yields of produced isotopes were deduced by analyzing the measured γ spectra of the irradiated foils. According to the isotopes yields, the spatial and energy distributions of the neutron field were discussed. The experimental results were compared with Monte Carlo simulations performed by the GEANT4＋FLUKA code.

SPAGINS:semiempirical parameterization for fragments in gamma-induced nuclear spallation

From the empirical phenomena of fragment distributions in nuclear spallation reactions,semiempirical formulas named SPAGINS were constructed to predict fragment cross-sections in high-energyγ-induced nuclear spallation reactions(PNSR).In constructing the SPAGINS formulas,theoretical models,including the TALYS toolkit,SPACS,and Rudstam formulas,were employed to study the general phenomenon of fragment distributions in PNSR with incident energies ranging from 100 to 1000 MeV.Considering the primary characteristics of PNSR,the SPAGINS formulas modify the EPAX and SPACS formulas and efficiently reproduce the measured data.The SPAGINS formulas provide a new and effective tool for predicting fragment production in PNSR.

Odd-even staggering for production cross sections of nuclei near the neutron drip-line

In our previous studies[Phys.Rev.C 97,044619(2018);Phys.Rev.C 103,044610(2021)],a universal odd-even staggering(OES)has been observed in extensive cross sections of isotopes not far from stability,measured for different fragmentation and spallation reactions.Four OES relations have been proposed on the basis of this OES universality.However,it is still unclear whether this OES universality and OES relations are applicable to many isotopes near the drip-lines.Here,the OES in recent experimental cross sections of very neutron-rich nuclei approaching the drip-line(from ^(76)Ge,^(82)Se+^(9)Be)is quantitatively investigated,to further validate the OES universality and OES relations.The OES magnitudes in these experimental data approaching the neutron drip-line generally agree with those evaluated previously,mainly from experimental data near stability.New OES evaluations de-rived from these experimental data are also recommended for more exotic nuclei near the neutron drip-line,which extends the conclusions of our previous OES studies.In addition,the OES relation calculations are consistent with these experimental data of very neutron-rich nuclides according to their comparisons in this work.Finally,comparisons with additional experimental data(from ^(238)U+^(9)Be)also support that new OES evaluations and OES relation calculations can be applied for exotic nuclei near the neutron drip-line.

Study of neutron spectra in a water bath from a Pb target irradiated by 250 MeV protons

Spallation neutrons were produced by the irradiation of Pb with 250 MeV protons. The Pb target was surrounded by water which was used to slow down the emitted neutrons. The moderated neutrons in the water bath were measured by using the resonance detectors of Au, Mn and In with a cadmium （Cd） cover. According to the measured activities of the foils, the neutron flux at different resonance energies were deduced and the epithermal neutron spectra were proposed. Corresponding results calculated with the Monte Carlo code MCNPX were compared with the experimental data to check the validity of the code. The comparison showed that the simulation could give a good prediction for the neutron spectra above 50 eV, while the finite thickness of the foils greatly effected the experimental data in low energy. It was also found that the resonance detectors themselves had great impact on the simulated energy spectra.

Production rates of cosmogenic nuclei on the lunar surface

A physical model for Geant4-based simulation of the galactic cosmic ray （GCR） particles＇ interaction with the lunar surface matter has been developed to investigate the production rates of cosmogenic nuclei. In this model the GCRs, mainly very high energy protons and 0c particles, bombard the surface of the Moon and produce many secondary particles, such as protons and neutrons. The energies of protons and neutrons at different depths are recorded and saved as ROOT files, and the analytical expressions for the differential proton and neutron fluxes are obtained through the best-fit procedure using ROOT software. To test the validity of this model, we calculate the production rates of the long-lived nuclei 10Be and 26Al in the Apollo 15 long drill core by combining the above differential fluxes and the newly evaluated spallation reaction cross sections. Our numerical results show that the theoretical production rates agree quite well with the measured data, which means that this model works well. Therefore, it can be expected that this model can be used to investigate the cosmogenic nuclei in future lunar samples returned by the Chinese lunar exploration program and can be extended to study other objects, such as meteorites and the Earth＇s atmosphere.