Failure of the Coexistence Model to Account for Observed Two-Neutron Pickup Cross Sections

We have studied the ($p,t$) reaction on ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{42}{}_{}{}^{}\mathrm{Ca}$ at $E_p=41.7\mathrm{}$ MeV. The observed yields to the $0^{+}$, $T=0\mathrm{}$ states in ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are at variance with distorted-wave Born-approximation predictions using the coexistence model to describe the initial and final states of the targets. By use of wave functions which employ a more extensive set of configurations, satisfactory agreement with the observed yields is achieved for the reaction ${}_{}{}^{18}{}_{}{}^{}\mathrm{O}\mathrm{}(p,t)\mathrm{}{}_{}{}^{16}{}_{}{}^{}\mathrm{O}$.