T=2andT=3Analog States,28≤A≤40

Abstract

The simultaneous observation of ($p, t$) and ($p$, ${}_{}{}^3{}_{}{}^{}\mathrm{He}$) reactions has led to the location and identification of the lowest-energy ($0^{+}$) $T=2\mathrm{}$ states in ${}_{}{}^{28}{}_{}{}^{}\mathrm{Al}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{P}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Cl}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{40}{}_{}{}^{}\mathrm{K}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, as well as the ($0^{+}$) $T=3\mathrm{}$ states in ${}_{}{}^{38}{}_{}{}^{}\mathrm{Cl}$ and ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ar}$. The energies of these states are used to predict the masses of six neutron-deficient nuclei: ${}_{}{}^{28}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{Ar}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ca}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Sc}$, ${}_{}{}^{38}{}_{}{}^{}\mathrm{Ti}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ti}$. In addition, the ($p, t$) cross section for production of each analog state relative to the cross section for producing the ground state in the same nucleus is compared with calculations which assume a simple shell model. Good agreement is obtained.