Total cross sections for the reactions $^{10,11,12}$Be+$^{28}$Si and $^{14}$B+$^{28}$Si

In this paper, the results of measurements of the total cross sections for the reactions $^{10,11,12}$Be+$^{28}$Si and $^{14}$B+$^{28}$Si in the beam energy range $13A$--$47A$ MeV are presented. The experimental cross sections were obtained by detection of the gamma quanta and neutrons accompanying the interaction of the isotopes of Be and B with $^{28}$Si. It was found that the cross sections for $^{11,12}$Be are similar, but significantly exceed those for $^{10}$Be. A significant increase in the cross sections for $^{12}$Be with decreasing energy is observed in the entire measured energy range. A theoretical explanation of the obtained experimental data is given based on the microscopic model of deformed nuclei and the numerical solution of the time-dependent Schr\"{o}dinger equation for the outer weakly bound neutrons of the projectile nuclei. The calculated total reaction cross sections are in good agreement with the experimental data.