Deuteron-induced nonelastic cross sections based on the intranuclear cascade model with independent incident particles under interaction potentials

Deuteron-induced nonelastic cross sections are studied in an extended intranuclear cascade (INC) model. A three-body framework of proton, neutron, and target is introduced into the INC model to incorporate naturally the decomposition and capture reactions from weakly bound deuterons. This framework includes three types of interaction potential, namely proton-target, neutron-target, and proton-neutron, the last of which causes the two nucleons in the deuteron to oscillate and play an important role in its breakup. The calculated results reproduce well the experimental data for ${}^{12}\mathrm{C}, {}^{40}\mathrm{Ca}, {}^{58}\mathrm{Ni}$, and ${}^{208}\mathrm{Pb}$ targets with almost the same parameters as those determined previously for nucleon-induced nonelastic reactions. It is found that the contribution of the two-nucleon collision process increases with target size, that the contribution of the capture processes is limited to a narrow region at low energy for lighter targets, and that the contribution of the breakup process is relatively small compared to other processes. It is also concluded that discrete-level-constraint effects dominate in the low-energy region for light nuclei such as ${}^{12}\mathrm{C}$, while Coulomb effects dominate in the low-energy region for heavy nuclei. This result is consistent with the INC model of nucleon incidence, which explains well the nucleon-induced nonelastic cross sections at low energies.

Figure 1

Proton transition process $\left(d,nx\right)$ in which a proton collides with one of the target's nucleons. In this example, the impact parameter of the deuteron center is $b=6\mathrm{fm}$, the incident energy is $T_d=100\mathrm{MeV}$, and the angles are $\alpha ,\beta ,\gamma =0$. The red and blue lines indicate the motions of the proton and neutron, respectively, and the black line indicates the motion of the target center. The dotted green line is the radius $r_0$ of ${}^{58}\mathrm{Ni}$ in the initial stage, and the solid green line is the radius of the maximum height of the potential, which is the sum of the nuclear potential and the finite-size Coulomb potential. The figure is displayed in the laboratory system. The nucleons in the target are not shown.

Figure 2

Neutron transition process $\left(d,px\right)$ for $b=6\mathrm{fm}$ and $T_d=100\mathrm{MeV}$. The lines mean the same as in Fig. 1. In this case, the initial positions of the proton and neutron are opposite to those in Fig. 1.

Figure 3

Collision process $\left(d,x\right)$ of two nucleons in a deuteron for $b=3\mathrm{fm}$ and $T_d=100\mathrm{MeV}$. The lines mean the same as in Fig. 1.

Figure 4

Neutron capture process $\left(d,p{}^{c}n\right)$ for $b=7.7\mathrm{fm}$ and $T_d=100\mathrm{MeV}$. The lines mean the same as in Fig. 1.

Figure 5

Proton capture process $\left(d,n{}^{c}p\right)$ for $b=7.5\mathrm{fm}$ and $T_d=100\mathrm{MeV}$. The lines mean the same as in Fig. 1.

Figure 6

Deuteron breakup process $\left(d,pn\right)$ for $b=8.3\mathrm{fm}$ and $T_d=100\mathrm{MeV}$. The lines mean the same as in Fig. 1.

Figure 7

Calculated deuteron-induced nonelastic cross sections for ${}^{12}\mathrm{C}, {}^{40}\mathrm{Ca}, {}^{58}\mathrm{Ni}$, and ${}^{208}\mathrm{Pb}$ below 200 MeV. The circles indicate experimental data, and in many cases the error bars are within the circles.

Figure 8

Incident-energy dependence of the contributions from the six processes for ${}^{12}\mathrm{C}$. The brown line represents $\left(d,x\right)$, the red line $\left(d,px\right)$, the blue line $\left(d,nx\right)$, the pink line $\left(d,p{}^{c}n\right)$, the light-blue line $\left(d,n{}^{c}p\right)$, and the green line is the deuteron breakup. The circles indicate experimental data, and the error bars are within the circles.

Figure 9

Incident-energy dependence of the contributions from the six processes for ${}^{40}\mathrm{Ca}$. The lines mean the same as in Fig. 8.

Figure 10

Incident-energy dependence of the contributions from the six processes for ${}^{58}\mathrm{Ni}$. The lines mean the same as in Fig. 8.

Figure 11

Incident-energy dependence of the contributions from the six processes for ${}^{208}\mathrm{Pb}$. The lines mean the same as in Fig. 8. The capture processes are almost zero for ${}^{208}\mathrm{Pb}$.

Figure 12

Incident-energy dependence of the contributions from the two effects in $d\text{−}{}^{12}\mathrm{C}$. Calculated results without Coulomb repulsion (red) and without DLC (green) are shown. The full calculation, accounting for both contributions, is shown by the black line, with the experimental data (circles).

Figure 13

Incident-energy dependence of the contributions from the two effects in $d\text{−}{}^{58}\mathrm{Ni}$. The colored lines mean the same as in Fig. 12.