Overlap functions, spectroscopic factors, and asymptotic normalization coefficients generated by a shell-model source term

Abstract

Overlap functions for one-nucleon removal are calculated as solutions of the inhomogeneous equation. The source term for this equation is generated by the $0\ensuremath{\hbar}\ensuremath{\omega}$ no-core shell-model wave functions and the effective nucleon-nucleon ($\mathit{NN}$) interactions that fit oscillator matrix elements derived from the $\mathit{NN}$ scattering data. For the lightest $A\ensuremath{\leqslant}4$ nuclei this method gives reasonable agreement with exact ab initio calculations. For $4lA\ensuremath{\leqslant}16$, this method gives a fair agreement between the calculated and measured asymptotic normalization coefficients. The spectroscopic factors obtained show systematic deviation from the corresponding shell-model values. This deviation correlates with nucleon separation energies and follows a similar trend seen in the reduction factor of the nucleon knockout cross sections. Comparison with the overlap functions and spectroscopic factors obtained in the variational Monte Carlo method is presented and discussed.