Effects of nonlocality of nuclear potentials on direct capture reactions

Calculations of the direct radiative capture reactions are made for the ${}^{48}\mathrm{Ca}(n,\gamma ){}^{49}\mathrm{Ca}$, ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$, and ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ reactions with the Perey-Buck-type nonlocal potentials using a potential model. Our results reproduce the experimental data reasonably well. From comparisons to results obtained by using local potentials, it is found that the cross sections of direct capture reactions may change by around 25% due to the nonlocality of nuclear potentials.

Figure 1

$S$-wave phase shifts as functions of incident energies for neutron scattering from (a) ${}^{48}\mathrm{Ca}$, from (b) ${}^7\mathrm{Li}$, and for proton scattering from (c) ${}^{12}\mathrm{C}$ with the potentials listed in Table 1. Phase shifts obtained with nonlocal and local potentials are presented with solid and dashed curve, respectively. The $s$-wave phase shifts for the total spin $2^{+}$ of the $n+{}^7\mathrm{Li}$ system is shifted by $\pi$ for better visualization.

Figure 2

Upper panels: Comparisons between experimental data and results of theoretical calculations using local and nonlocal potentials for reactions ${}^{48}\mathrm{Ca}(\mathrm{n},\gamma ){}^{49}\mathrm{Ca}$ (a), ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ (b), and ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ (c). Contributions of transition to the ground (dashed curves) and the first excited sates (dotted curves) are shown explicitly for the ${}^{48}\mathrm{Ca}(\mathrm{n},\gamma ){}^{49}\mathrm{Ca}$ and ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ reactions and their summed cross sections (multiplied by a factor of 5) are represented by solid curves. Results obtained with local and nonlocal potentials are discriminated by thin and thick curves, with labels “nlp” and “lp,” respectively. Similarly, contributions of direct and resonant terms and their coherent sums are plotted for the ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ reaction. The symbols represents the experimental data for the ${}^{48}\mathrm{Ca}(\mathrm{n},\gamma ){}^{49}\mathrm{Ca}$ reaction from Ref. [31], for the ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ reaction from Ref. [39], and for the ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ reaction from Refs. [32] (asterisk) and [34] (solid circles). Lower panels: Comparisons of cross sections with potential nonlocality treated in both bound and scattering states (the same as in the upper panels) with those treated in the bound states only (solid curves) and in the scattering states only (double-dotted curves) for reactions ${}^{48}\mathrm{Ca}(\mathrm{n},\gamma ){}^{49}\mathrm{Ca}$ (d), ${}^7\mathrm{Li}(n,\gamma ){}^8\mathrm{Li}$ (e), and ${}^{12}\mathrm{C}(p,\gamma ){}^{13}\mathrm{N}$ (f). See the text for details.