Unexpected distribution of $\nu 1f_{7/2}$ strength in ${}^{49}\mathbf{Ca}$

The calcium isotopes have emerged as a critical testing ground for new microscopically derived shell-model interactions, and a great deal of experimental and theoretical focus has been directed toward this region. We investigate the relative spectroscopic strengths associated with $1f_{7/2}$ neutron hole states in ${}^{47,49}\mathrm{Ca}$ following one-neutron knockout reactions from ${}^{48,50}\mathrm{Ca}$. The observed reduction of strength populating the $7/2_1^{-}$ state in ${}^{49}\mathrm{Ca}$, as compared to ${}^{47}\mathrm{Ca}$, is inconsistent with shell-model calculations using both phenomenological interactions such as GXPF1, and interactions derived from microscopically based two- and three-nucleon forces. The result suggests a fragmentation of the $l=3$ strength to higher-lying states as suggested by the microscopic calculations, but the observed magnitude of the reduction is not reproduced in any shell-model description.

Figure 1

Experimentally observed $\gamma$-ray spectra (left) and populated level schemes (right) of (a) ${}^{47}\mathrm{Ca}$ from ${}^{48}\mathrm{Ca}(-1n)$, and (b) ${}^{49}\mathrm{Ca}$ from ${}^{50}\mathrm{Ca}(-1n)$ reactions. Experimental spectra are marked with the observed transitions in keV. In (c) and (d) the assigned spins and parities come from the literature, while the width of the arrows corresponds to the (efficiency-corrected) relative intensity of the $\gamma$-ray transitions. For reference, $S_n\left({}^{47}\mathrm{Ca}\right)=7.3$ MeV and $S_n\left({}^{49}\mathrm{Ca}\right)=5.1$ MeV. (e) and (f) show the parallel momentum distributions for the $7/2_1^{-}$ and $3/2_1^{-}$ states in ${}^{49}\mathrm{Ca}$ respectively, showing direct contributions and tails to low momentum resulting from indirect reaction processes.

Figure 2

Ratio of the spectroscopic factor for the population of the first $7/2^{-}$ state in one-neutron knockout from ${}^{50}\mathrm{Ca}\to {}^{49}\mathrm{Ca}$ vs ${}^{48}\mathrm{Ca}\to {}^{47}\mathrm{Ca}$, as predicted by the shell model calculations using the GXPF1A phenomenological interaction (left), NN+3N interaction in the $pf$ (center right) and $pf{g}_{9/2}$ (center left) model spaces, and measured (blue column, right).