Excitation of the32+, 2.02-MeV State inCa41by the (t,d) Reaction

The ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ ($t,d$) reaction, with 20-MeV tritons, was used to excite the ground and first two excited states of ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$. The measured differential cross sections were analyzed using the distorted-wave method, assuming the usual first-order stripping mechanism. The triton optical potential was obtained by fitting measurements of the elastic scattering. The spectroscopic factor $C^{2}S$ for $d_{\frac{3}{2}}$ capture into the 2.02-MeV state was found to be about 0.06 times that for $f_{\frac{7}{2}}$ capture into the ground state when the usual well-depth prescription was used for the neutron wave function. More realistic $d_{\frac{3}{2}}$ neutron form factors based upon simple model wave functions for ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ and ${}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}$ were also used. They led to spectroscopic factors which are at least twice as large and are found to be very sensitive to the type of nucleon-nucleon interaction assumed. The implications for the amount of particle-hole excitation in the ground state of ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are discussed.