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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 40Ar to 208Pb, 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.

In this study, the Pauli blocking potential between two colliding nuclei in the density overlapping region is applied to describe the heavy nuclei fusion process. Inspired by the Pauli blocking effect in the -decay of heavy nuclei, the Pauli blocking potential of single nucleon from the surrounding matter is obtained. In fusion reactions with strong density overlap, the Pauli blocking potential between the projectile and target can be constructed using a single folding model. By considering this potential, the double folding model with a new parameter set is employed to analyze the fusion processes of 95 systems. A wider Coulomb barrier and shallower potential pocket are formed in the inner part of the potential between the two colliding nuclei, compared to that calculated using the Akyüz-Winther potential. The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems O + Pb and Ni + Ni.

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.

The ratio of pairing-energy coefficient to temperature ($a_{p}/T$) 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, 0.5$A$ and 1$A$ GeV $^{208}$Pb + $p$, 1$A$ GeV $^{238}$U + $p$, 0.5$A$ GeV $^{136}$Xe + $d$, 0.2$A$, 0.5$A$ and 1$A$ GeV $^{136}$Xe + $p$, and $^{56}$Fe + $p$ with incident energy ranging from 0.3$A$ to 1.5$A$ GeV, has been analysed. An obvious odd-even staggering is shown in the fragments with small neutron excess ($I\equiv N - Z$), and in the relatively small-$A$ fragments which have large $I$. The values of $a_{p}/T$ 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 $a_{p}/T$ 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 $A/A_{s} >$ 85\% (where $A_{s}$ is the mass number of the spallation system)., 8 pages, 6 figures, to appear on Chinese Physics C

The neutron induced reactions on 23Na are investigated by using the Talys1.4 program. The calculated results for the 23Na(n, 2n)22Na reaction are found to agree with the experimental results. The cross sections of the residues of the (n, n), (n, γ), (n, p), and (n, np) channels in the reactions are presented, and at the same time, the neutron induced reactions on 22Ne are also investigated.