Energy density functional forαclustering and scattering of lightA=4mnuclei

Abstract

The energy density functional (EDF) is applied to study $\ensuremath{\alpha}$ clustering and $\ensuremath{\alpha}$ scattering in light $A=4m$ nuclei. Our goal is to study the success of the EDF in predicting the ground-state $\ensuremath{\alpha}$ clustering in $4m$-conjugate nuclei. The $\ensuremath{\alpha}$-cluster density is obtained by optimizing the EDF with the help of the convolution theorem. The obtained cluster density reproduced the experimental binding energy of the considered nuclei. The obtained $\ensuremath{\alpha}$-cluster densities are investigated through the elastic scattering of $\ensuremath{\alpha}$ particles from $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{24}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{32}\mathrm{S}$, and $^{40}\mathrm{Ca}$ in the framework of the optical model. The real part of the optical model potential is calculated using $\ensuremath{\alpha}$-cluster single folding or the conventional double folding models based on the obtained densities. The obtained potentials are used to analyze the elastic scattering of $\ensuremath{\alpha}$-particle from (1) $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{24}\mathrm{Ne}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, $^{32}\mathrm{S}$, and $^{40}\mathrm{Ca}$ at 104 MeV, (2) $^{12}\mathrm{C}$, $^{24}\mathrm{Mg}$, and $^{28}\mathrm{Si}$ at 120 MeV, (3) $^{12}\mathrm{C}$, $^{16}\mathrm{O}$, $^{24}\mathrm{Mg}$, $^{28}\mathrm{Si}$, and $^{40}\mathrm{Ca}$ at 130 MeV. The obtained results are very satisfactory and in agreement with experimental data. This success indicates the validity and applicability of the EDF in $\ensuremath{\alpha}$-cluster calculation for $A=4m$ nuclei.