Microscopic calculation of the interaction cross section for stable and unstable nuclei based on the nonrelativistic nucleon-nucleontmatrix

Abstract

Fully quantal calculations of the total reaction cross sections ${\ensuremath{\sigma}}_{\mathrm{R}}$ and interaction cross sections ${\ensuremath{\sigma}}_{\mathrm{I}}$, induced by stable and unstable He, Li, C, and O isotopes on $^{12}\mathrm{C}$ target at ${E}_{\text{lab}}\ensuremath{\approx}0.8$ and $1\phantom{\rule{0.3em}{0ex}}\text{GeV}∕\text{nucleon}$ have been performed, for the first time, in the distorted wave impulse approximation (DWIA) using the microscopic complex optical potential and inelastic form factors given by the folding model. Realistic nuclear densities for the projectiles and $^{12}\mathrm{C}$ target as well as the complex $t$-matrix parametrization of free nucleon-nucleon interaction by Franey and Love were used as inputs of the folding calculation. Our parameter-free folding + DWIA approach has been shown to give a very good account (within $1--2\phantom{\rule{0.1em}{0ex}}%$) of the experimental ${\ensuremath{\sigma}}_{\mathrm{I}}$ measured at these energies for the stable, strongly bound isotopes. With the antisymmetrization of the dinuclear system properly taken into account, this microscopic approach is shown to be more accurate than the simple optical limit of Glauber model that was widely used to infer the nuclear radii from the measured ${\ensuremath{\sigma}}_{\mathrm{I}}$. Therefore, the results obtained for the nuclear radii of neutron-rich isotopes under study can be of interest for further nuclear structure studies.