Spectroscopic factors in the N=20 island of inversion: The Nilsson strong-coupling limit

Abstract

Spectroscopic factors, extracted from one-neutron knockout and Coulomb dissociation reactions, for transitions from the ground state of $^{33}\mathrm{Mg}$ to the ground-state rotational band in $^{32}\mathrm{Mg}$, and from $^{32}\mathrm{Mg}$ to low-lying negative-parity states in $^{31}\mathrm{Mg}$, are interpreted within the rotational model. Associating the ground state of $^{33}\mathrm{Mg}$ and the negative-parity states in $^{31}\mathrm{Mg}$ with the $\frac{3}{2}[321]$ Nilsson level, the strong coupling limit gives simple expressions that relate the amplitudes (${C}_{j\ensuremath{\ell}}$) of this wave function with the measured cross sections and derived spectroscopic factors (${S}_{j\ensuremath{\ell}}$). To obtain a consistent agreement with the data within this framework, we find that one requires a modified $\frac{3}{2}[321]$ wave function with an increased contribution from the spherical $2{p}_{3/2}$ orbit as compared to a standard Nilsson calculation. This is consistent with the findings of large-scale shell model calculations and can be traced to weak binding effects that lower the energy of low-$\ensuremath{\ell}$ orbitals.