Optical model potential of $A=3$ projectiles for $1p$-shell nuclei

A set of global optical potential parameters describing the $A=3$ particles (${}^3\mathrm{He}$ and ${}^3\mathrm{H}$) elastic scattering from $1p$-shell nuclei, $\mathrm{HT}1p$, is obtained by simultaneously fitting 118 sets of experimental data of ${}^3\mathrm{He}$ and ${}^3\mathrm{H}$ elastic scattering from ${}^9\mathrm{Be},{}^{10}\mathrm{B},{}^{11}\mathrm{B},{}^{12}\mathrm{C},{}^{13}\mathrm{C},{}^{14}\mathrm{C},{}^{14}\mathrm{N},{}^{15}\mathrm{N},{}^{16}\mathrm{O},{}^{17}\mathrm{O}$, and ${}^{18}\mathrm{O}$ with incident energies from $4\le E\le 118.5$ MeV and 24 sets of elastic scattering data with the ${}^6\mathrm{Li}$ and ${}^7\mathrm{Li}$ targets from $3\le E\le 44$ MeV. $\mathrm{HT}1p$ is found to be superior to GDP08 [D. Y. Pang, P. Roussel-Chomaz, H. Savajols, R. L. Varner, and R. Wolski, Phys. Rev. C 79, 024615 (2009)], which is a systematic potential designed for the heavy-target region, in the reproduction of the angular distributions of elastic scattering cross sections of ${}^3\mathrm{He}$ and ${}^3\mathrm{H}$ from $1p$-shell nuclei at energies below 100 MeV. At energies above 100 MeV, GDP08 is found to be better than HT1p.

Figure 1

Incident energy and target mass distributions covered by the database of the angular distributions of the differential cross sections collected for ${}^3\mathrm{He}$ elastic scattering from atomic nuclei. The squares represent those included in GDP08, the triangles are used for HT1p, and the circles are those unexplored by us.

Figure 2

Optical model calculations of the angular distributions and their comparisons with the experimental data for ${}^3\mathrm{He}$ elastic scattering from (a) ${}^9\mathrm{Be}$, (b) ${}^{10}\mathrm{B}$, (c) ${}^{11}\mathrm{B}$, and (d) ${}^{12}\mathrm{C}$. The cross sections are scaled by factors of ${10}^2$. The incident energies are indicated in the figures in unit of MeV. The solid and dashed curves are results of the optical model calculations with the systematic potential with $1p$-shell nuclei and that with GDP08 [16].

Figure 3

The same as in Fig. 2 but for ${}^3\mathrm{He}$ elastic scattering from targets (a) ${}^{13}\mathrm{C}$, (b) ${}^{14}\mathrm{C}$, (c) ${}^{14}\mathrm{N}$ (circles), and ${}^{15}\mathrm{N}$ (squares), (d) ${}^{16}\mathrm{O}$ (circles), ${}^{17}\mathrm{O}$ (squares), and ${}^{18}\mathrm{O}$ (triangles), and ${}^3\mathrm{H}$ elastic scattering from targets of (e) ${}^{12}\mathrm{C}$ (circles), ${}^{13}\mathrm{C}$ (asterisks), ${}^{14}\mathrm{C}$ (squares), and ${}^{16}\mathrm{O}$ (triangles).

Figure 4

The same as in Fig. 2 but for ${}^3\mathrm{He}$ elastic scattering from targets (a) ${}^6\mathrm{Li}$ (circles) and ${}^7\mathrm{Li}$ (squares), and (b) ${}^3\mathrm{H}$ elastic scattering from ${}^6\mathrm{Li}$.

Figure 5

Comparison of the optical model calculations for ${}^3\mathrm{He}$ elastic scattering from ${}^{12}\mathrm{C}$ at 118.5 and 217 MeV with HT1p (solid curve) and GDP08 (dotted curve). The experimental data are from Refs. [33, 88].

Figure 6

Volume integrals of the optical model potentials HT1p and GDP08 for ${}^3\mathrm{He}$ elastic scattering from ${}^{12}\mathrm{C}$ from 1 to 220 MeV. The vertical line divides the approximate energy regions in which HT1p and GDP08 are applicable for $1p$-shell nuclei. The solid and dashed curves in the upper part of this figure represent the volume integrals of the real potentials of HT1p and GDP08, respectively. The curves in the lower part are for the corresponding imaginary potentials.