Ca40(d,He3)K39reaction at 76 MeV

The differential cross sections of the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ groups emitted in the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}(d,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ reaction have been measured at a bombarding energy of 76 MeV. The ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ particles were measured with an energy resolution of 55 keV. Differential cross sections were fitted using a distorted wave program and spectroscopic factors were deduced for several proton hole states of ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$. The single hole final states essentially exhaust the sum rule for the $1d_{\frac{3}{2}}$, $2s_{\frac{1}{2}}$, and $1d_{\frac{5}{2}}$ subshells. Because of the strong absorption of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ particles in nuclear matter, this reaction is a surface reaction, and as such populates only the outer shells. By contrast, the ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,2p)\mathrm{}$ reaction is able to populate all proton hole states, including those of the $1p$ and $1s$ shells. The population of the quartet of odd parity states, which from a nuclear structure point of view consist of a ${1d}_{\frac{3}{2}}$ hole coupled to the $3^{-}$ state of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, was observed. The differential cross sections for the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ groups populating those states were calculated using a coupled channels program and these calculations are in satisfactory agreement with the experimental results.