Calculations of ${}^8\mathrm{He}+p$ elastic cross sections using a microscopic optical potential

An approach to calculate microscopic optical potential with the real part obtained by a folding procedure and with the imaginary part inherent in the high-energy approximation is applied to study the ${}^8\mathrm{He}+p$ elastic-scattering data at energies of tens of MeV/nucleon. The neutron and proton density distributions obtained in different models for ${}^8\mathrm{He}$ are used in the calculations of the differential cross sections. The role of the spin-orbit potential is studied. Comparison of the calculations with the available experimental data on the elastic-scattering differential cross sections at beam energies of 15.7, 26.25, 32, 66, and 73 MeV/nucleon is performed. The problem of the ambiguities of the depths of each component of the optical potential is considered by means of the imposed physical criterion related to the known behavior of the volume integrals as functions of the incident energy. It is shown also that the role of the surface absorption is rather important, in particular for the lowest incident energies (e.g., 15.7 and 26.25 MeV/nucleon).

Figure 1

Total [(a) and ($a^{\text{'}}$)], point-proton (b), and point-neutron (c) densities of ${}^8\mathrm{He}$ from the model of Tanihata [47], COSMA [20, 21], LSSM [44, 45], and JCM calculations [61, 62].

Figure 2

Microscopic real part ($V^F$) of OP [(a), (b), and (c)] and HEA imaginary part ($W^H$) [($a^{\text{'}}$), ($b^{\text{'}}$), and ($c^{\text{'}}$)] calculated using the LSSM, Tanihata, and JCM ($\beta =2.5\hspace{0.5em}{\mathrm{fm}}^{-1}$) densities of ${}^8\mathrm{He}$ for energies $E=15.7$ (solid lines), 32 (dashed lines), and 73 MeV/nucleon (dotted lines).

Figure 3

The ${}^8\mathrm{He}+p$ elastic-scattering cross sections at different energies calculated using $U_{\mathrm{opt}}$ [Eq. (18)] for values of the parameters $N_R=N_I=1$ and $N_R^{\mathrm{SO}}=N_I^{\mathrm{SO}}=0$. The used densities of ${}^8\mathrm{He}$ are LSSM (solid line), Tanihata (dash-dotted line), and JCM ($\beta =2.5\hspace{0.5em}{\mathrm{fm}}^{-1}$) (dashed line). Experimental data are taken for 15.7 [12], 26 [3], 32 [10, 11], 66 [10, 11], and 73 MeV/nucleon [10, 11, 13].

Figure 4

Point-neutron density of ${}^8\mathrm{He}$ (a), $V^F$ and $W^H$ of OP [(b) and ($b^{\text{'}}$)] for energy $E=32$ MeV/nucleon, and ${}^8\mathrm{He}+p$ elastic-scattering cross sections (c) at energies $E=15.7,32$, and 73 MeV/nucleon calculated using JCM densities of ${}^8\mathrm{He}$ for three values of the correlation parameter $\beta$.

Figure 5

The ${}^8\mathrm{He}+p$ elastic-scattering cross sections at different energies calculated using $U_{\mathrm{opt}}$ [Eq. (18)] for various values of the renormalization parameters $N_R$, $N_I$, $N_R^{\mathrm{SO}}$, and $N_I^{\mathrm{SO}}$ (presented in Table ) giving the best agreement with the data. The used density of ${}^8\mathrm{He}$ is LSSM. Experimental data are taken for 15.7 [12], 26 [3], 32 [10, 11], 66 [10, 11], and 73 MeV/nucleon [10, 11, 13].

Figure 6

The ${}^8\mathrm{He}+p$ elastic-scattering cross sections (a) at different energies using LSSM density of ${}^8\mathrm{He}$ and parameters from Table . Experimental data are taken for 15.7 [12], 26 [3], 32 [10, 11], 66 [10, 11], and 73 MeV/nucleon [10, 11, 13]. The obtained values of the volume integrals $J_V$ (b) and $J_W$ (c) (given by points) are shown as functions of the incident energy, while the dashed lines give the trend of this dependence.

Figure 7

(a) Volume (dashed line) and total (solid line) imaginary parts of the OP $U_{\mathrm{opt}}^{\text{'}}(r)$ [Eq. (21)] calculated using the LSSM density of ${}^8\mathrm{He}$ for energy $E=15.7$ MeV/nucleon; (b) The ${}^8\mathrm{He}+p$ elastic-scattering cross section at energy $E=15.7$ MeV/nucleon using LSSM density of ${}^8\mathrm{He}$ with fitted values of $N_R$, $N_I$, $N_R^{\mathrm{SO}}$, $N_I^{\mathrm{SO}}$, and $N_S$ given in the text. Experimental data are taken from Ref. [12].