One-nucleon overlap functions required for various nucleon-removal calculations must be solutions of the inhomogeneous equation with a source term whose shape and strength are determined by nuclear wave functions and the effective interaction of the removed nucleon with the nucleons in the remainder nucleus. A number of previous works has reported calculations of the source term and the overlap functions for a range of $A⩽16$ nuclei. It was shown that the source-term approach gives reasonable results for spectroscopic factors and asymptotic normalization coefficients and, in particular, it explains the phenomenon of reduction of spectroscopic factors observed in knockout reactions. In the present article, the source-term approach has been extended to $A⩾16$ nuclei. To achieve this, a new technique has been developed which excludes the spurious center-of-mass motion within the translation-invariant oscillator shell model. Applications using this technique are performed for double-closed-shell nuclei, both stable and away from $\beta$ stability, such as ${}^{16,24}$O, ${}^{40,48,60}$Ca, ${}^{56,78}$Ni, ${}^{100,132}$Sn, and ${}^{208}$Pb. The spectroscopic factors and asymptotic normalization coefficients for one-nucleon removal and addition have been calculated. They are compared to experimental values and results from other microscopic models when available.

• Received 25 July 2011

DOI:https://doi.org/10.1103/PhysRevC.84.054313