Speaker
Description
The isotopic spin in light and medium nuclei is a quantum number that serves to identify the ground and excited states and it is conserved in various nuclear processes. To verify this statement, we considered nucleon decays in the odd nuclei of the 1$p$-shell with isospin $T = 3/2$. By the magnitude of the widths $\Gamma$ of the decaying states, they can be classified into 2 groups. In $^7$Li, $^{11}$B, $^{15}$N nuclei, as a result of the decay of levels with $T = 3/2$, the direct transitions to daughter nuclei levels with $T = 1$ are possible. These are “allowed” transitions. In $^9$Be and $^{13}$C ($^{13}$N) nuclei, direct nucleon decay into levels with $T = 1$ of the formed even-even $^8$Be and $^{12}$C nuclei is not possible by energy. Decays to levels with $T = 0$ are possible only due to Coulomb mixing of the levels $T = 3/2$ and $T = 1/2$. These are “forbidden” transitions. Within the multi-particle shell model, we calculated the nucleon widths $\Gamma$ for $^7$Li, $^{11}$B, and $^{13}$C nuclei, as well as for nuclei mirror to them. The Coulomb mixing of the $T = 3/2$ and $1/2$ levels in $^9$Be and $^{13}$C ($^{13}$N) nuclei was calculated using perturbation theory. A similar situation arises for the $^{12}$C nucleus level with $(J^\pi, T)$ = (1$^+$, 1) at 15.11 $MeV$. Alpha decay of this level into $^8$Be nucleus levels is possible only due to Coulomb mixing of the $T = 1$ and $T = 0$ levels in initial nucleus.
The calculation results show that the $\Gamma$-widths for all “forbidden” transitions are several orders of magnitude smaller than the widths of “allowed” transitions, which indicates a high isospin level of light nuclei.
