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

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