Analysis of Angular $\boldsymbol{t{-}\gamma}$ Correlations in the Reaction ${}^{\boldsymbol{27}}$Al$\boldsymbol{(\alpha,t)^{28}}$Si(2${}^{\boldsymbol{+}}$)

Abstract

Angular $t$–$\gamma$ correlations measured earlier in the reaction ${}^{27}$Al$(\alpha,t)^{28}$Si(2${}^{+}$) occurring at $E_{\alpha}=30.3$ MeV and leading to the formation of the final nucleus in the lowest excited state are analyzed theoretically. The experimental results being considered are compared with their counterparts calculated by the coupled-channel method for the proton-stripping mechanism and in the statistical limit of the compound-nucleus model. The spectroscopic amplitudes for the ${}^{28}\textrm{Si}\to^{27}\textrm{Al}+p$ vertex function are calculated on the basis of the Nilsson model. The differential cross sections calculated within the aforementioned theoretical approach for the reaction ${}^{27}$Al$(\alpha,t)^{28}$Si leading to the formation of ${}^{28}$Si in the lowest three states are in satisfactory agreement with experimental data. The same applies to a large part of the orientation features of the ${}^{28}$Si(2${}^{+}$) nucleus.