Abstract
In this paper the results of measurements of the total cross sections for the $^{11}\mathrm{Li}+^{28}\mathrm{Si}$ reaction in the beam energy range $7A$--$25A$ MeV are presented. The experimental cross sections were obtained by registration of the prompt gamma and neutron radiation accompanying the interaction of $^{11}\mathrm{Li}$ nuclei with $^{28}\mathrm{Si}$ nuclei. The total cross sections for the $^{11}\mathrm{Li}+^{28}\mathrm{Si}$ reaction are calculated based on a numerical solution of the time-dependent Schr\odinger equation for the external weakly bound neutrons of the projectile nucleus $^{11}\mathrm{Li}$. The calculated total reaction cross sections are in good agreement with the experimental data.
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