Statistical theory of light-nucleus reactions and application to the ${}^9\text{Be}(p,xn)$ reaction

A statistical theory of light nucleus reactions (STLN) is proposed to describe both neutron and light charged particle induced nuclear reactions with $1p\text{-shell}$ light nuclei involved. The dynamics of STLN is described by the unified Hauser-Feshbach and exciton model, in which the angular momentum and parity conservations are strictly considered in equilibrium and pre-equilibrium processes. The Coulomb barriers of the incoming and outgoing charged particles, which significantly influence the open channels of the reaction, can be reasonably considered in the incident channel and different outgoing channels. In kinematics, the recoiling effects in various emission processes are strictly taken into account. The analytical double-differential cross sections of the reaction products in sequential and simultaneous emission processes are obtained in terms of the new integral formula proposed in our recent paper [Phys. Rev. C 92, 061601(R) (2015)]. Taking the ${}^9\text{Be}(p,xn)$ reaction as an example, we calculate the double-differential cross sections of outgoing neutrons and charged particles using the punf code in the frame of STLN. The existing experimental double-differential cross sections of neutrons at $E_p=18$ MeV can be remarkably well reproduced, which indicates that the punf code is a powerful tool to set up “file-6” in the reaction data library for light charged particle induced nuclear reactions with $1p\text{-shell}$ light nuclei involved.

Figure 1

The partial double-differential cross sections of outgoing neutrons from reaction channel $(p,n){}^9\text{B}$ with outgoing angle ${60}^{\circ }$ at $E_p=18$ MeV in LS. The points denote the experimental data taken from Ref. [42], and the red solid line denotes the calculated total double-differential cross sections. The black solid lines denote the partial spectra of the first emitted neutron from the compound nucleus to the ground state, up to the ninth excited energy levels (as labeled in the figure) of the first residual nucleus ${}^9\text{B}$, in which broadening effects must be taken into account. Only the cross sections with values larger than 0.1 mb are given.

Figure 2

The same as Fig. 1, but for the partial double-differential cross sections from reaction channel $(p,pn){}^8\text{Be}\to (p,pn+2\alpha )$. The black solid lines denote the partial spectra of the secondary emitted neutron from the first to 17th excited energy levels (as labeled in the figure) of the first residual nucleus ${}^9\text{Be}$ to the ground state of the secondary residual nucleus ${}^8\text{Be}$.

Figure 3

The same as Fig. 2, but the black solid lines denote the partial spectra from the sixth to 17th excited energy levels (as labeled in the figure) of ${}^9\text{Be}$ to the first excited energy level of ${}^8\text{Be}$. The green dashed lines denote the partial spectra from the 12th to 17th excited energy levels of ${}^9\text{Be}$ to the second excited energy level of ${}^8\text{Be}$, and the blue dotted lines denote the partial spectra from the 14th and 17th excited energy levels of ${}^9\text{Be}$ to the third excited energy level of ${}^8\text{Be}$.

Figure 4

The same as Fig. 1, but the black solid lines denote the partial spectra of the emitted neutron in reaction channel $(p,p\alpha ){}^5\text{He}\to (p,p\alpha +n\alpha )$ from the fourth to 17th excited energy levels of ${}^9\text{Be}$ to the lowest two energy levels of the secondary residual nucleus ${}^5\text{He}$, which can spontaneously break up a neutron and an $\alpha$. The blue dashed lines denote the partial spectra of the emitted neutron in double two-body breakup channel $(p,{}^5\text{He}){}^5\text{Li}\to (p,n\alpha +p\alpha )$ from the ground state and first excited energy level of the ${}^5\text{He}$.

Figure 5

The total double-differential cross sections of outgoing neutron for the reaction ${}^9\text{Be}(p,xn)$ with outgoing angles $0^{\circ },{20}^{\circ },{40}^{\circ },{60}^{\circ }$, and ${80}^{\circ }$ at $E_p=18$ MeV in LS. The points denote to the experimental data taken from Ref. [42]. The red solid lines denote the calculated results using the real and two predicted energy levels of ${}^9\text{Be}$, and the green dashed lines denote the calculated results only using the real energy levels of ${}^9\text{Be}$.

Figure 6

The same as Fig. 5, but with outgoing angles ${100}^{\circ },{120}^{\circ },{145}^{\circ }$, and ${170}^{\circ }$, respectively.