ReactionCa42(p,t)Ca40and the structure ofCa40

The reaction ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}\mathrm{}(p,t)\mathrm{}{}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ was studied at 41.7 MeV; angular distributions were obtained over the range from 10 to 60°. The lowest $T=1,0^{+}$ state was identified at 9.386 ± 0.012 MeV by comparison with the analog reaction ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}(p,{}_{}{}^3{}_{}{}^{}\mathrm{He}){}_{}{}^{40}{}_{}{}^{}\mathrm{K}$ (1.639 MeV). The weak population of these states is attributed to destructive interference between $d_{\frac{3}{2}}^{}{}_{}{}^2$ pickup from the two-particle component of ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ and $f_{\frac{7}{2}}^{}{}_{}{}^2$ pickup from the four-particle two-hole component of ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$. The excitation energy of these states cannot be accounted for by the $f_{\frac{7}{2}}-d_{\frac{3}{2}}$ effective interaction. Spectroscopic amplitudes for the Gerace-Green wave functions are calculated in a shell-model basis. Distorted-wave Born-approximation (DWBA) calculations for the lowest $T=0\mathrm{}$ and $T=1,3^{-}, \mathrm{and} 5^{-}$ states are in qualitative agreement with the data. The DAWA calculations for the positive-parity states show greater pickup strength to the two-particle two-hole $0^{+}$ and $2^{+}$ states than to the four-particle four-hole $0^{+}$ and $2^{+}$ states. The experimental results are the opposite: the four-particle four-hole states are populated more strongly than the two-particle two-hole states. Although there are uncertainties in the DWBA calculations, it is suggested that the inability to account for the observed two-nucleon pickup demonstrates a deficiency in the Gerace-Green model.