(p,d) Reaction onN=ZNuclei in the2s−1dShell

An investigation of the ($p,d$) reaction on $N=Z$ nuclei in the $2s-1d$ shell has been made to obtain spectroscopic information and to study the $l_n=2\mathrm{}$ $J$-dependence for the ($p,d$) reaction. The experiments were performed with ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{32}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$, and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ as target nuclei, and virtually all of the $2s-1d$ shell hole strength was observed. Deuteron angular distributions for strongly excited levels in ${}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$, ${}_{}{}^{27}{}_{}{}^{}\mathrm{Si}$, ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Ar}$, and ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ca}$ were measured for laboratory angles from 10° to 155°, and spectroscopic factors were obtained using distorted-wave Born-approximation (DWBA) calculations. The $J$ dependence for the pickup of an $l_n=2\mathrm{}$ neutron appears mostly in the forward angles of the angular distributions and seems to follow systematic trends through the $2s-1d$ shell, thus suggesting spin assignments for levels in ${}_{}{}^{31}{}_{}{}^{}\mathrm{S}$, ${}_{}{}^{35}{}_{}{}^{}\mathrm{Ar}$, and ${}_{}{}^{39}{}_{}{}^{}\mathrm{Ca}$. Appreciable configuration mixing is found to exist in the ground-state wave functions of all the nuclei investigated. Of particular interest are the $l_n=1\mathrm{}$ levels excited in the ${}_{}{}^{24}{}_{}{}^{}\mathrm{Mg}\mathrm{}(p,d)\mathrm{}{}_{}{}^{23}{}_{}{}^{}\mathrm{Mg}$ and ${}_{}{}^{28}{}_{}{}^{}\mathrm{Si}\mathrm{}(p,d)\mathrm{}{}_{}{}^{27}{}_{}{}^{}\mathrm{Si}$ reactions, which could arise from the removal of either $1p$- or $2p$-shell neutrons. The ground states of ${}_{}{}^{36}{}_{}{}^{}\mathrm{Ar}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are observed to contain appreciable mixing with the $f_{\frac{7}{2}}$ shell, and evidence exists for a small ${\mathrm{}\left[2p\right]\mathrm{}}^2$ admixture in the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ ground state. The level orders of the residual nuclei and the DWBA spectroscopic factors are discussed in terms of the strong-coupling rotational model and Nilsson-model wave functions. Evidence for strong rotational band mixing is apparent in many cases.