Extended Shell-Model Description of Nucleon-Transfer Form Factors

A flexible microscopic model is introduced in an attempt to illuminate problems associated with the calculation of single-nucleon-transfer form factors. The model employs a truncated shell-model basis augmented by a set of single-nucleon channels. It can be used even when the residual nucleus is unbound, but ignores contributions from many-particle breakup channels. The model wave function is fully antisymmetric, and it is shown that all quantities which appear in the model are calculable. An approximate single-channel calculation of form factors for the reactions ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}\mathrm{}(d,p)\mathrm{}{}_{}{}^{41}{}_{}{}^{}\mathrm{Ca}\left(2.01\mathrm{} \mathrm{MeV}\right)$ and ${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}({}_{}{}^3{}_{}{}^{}\mathrm{He},d){}_{}{}^{41}{}_{}{}^{}\mathrm{Sc}\left(2.10\mathrm{} \mathrm{MeV}\right)$ is used to illustrate some of the features of the model.