\textit{Ab initio} study of spectroscopic factors in $^{48}$K and neighboring $N=28$ isotones

Abstract

A recent \(^{47}\text{K}(d,pγ)^{48}\text{K}\) transfer reaction measurement has identified new excited states in \(^{48}\text{K}\) and extracted the corresponding spectroscopic factors (SFs)[\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.134.162504}{C. J. Paxman, \textit{et al.} PhysRevLett.134.162504 (2025)}], but they exposed sizeable discrepancies with large-scale shell-model (LSSM) calculations-especially for the low-lying states-suggesting shortcomings in the proton-neutron interaction employed by the LSSM. In this work, we revisit the low-lying states and SFs of \(^{48}\text{K}\) using the \textit{ab initio} valence-space in-medium similarity renormalization group (VS-IMSRG) approach based on the chiral two- and three-nucleon forces. The calculated excitation energies reproduce the experimental data for \(^{48}\text{K}\), whereas computed SFs systematically exceed experimental values. We trace this overestimation to missing reduction factors that account for non-idealities of the transfer reaction. After introducing a phenomenological reduction factor, our VS-IMSRG results and the LSSM calculations achieve agreement with experiment. We also perform the same analysis for the neutron SFs of $^{47}$Ar. Furthermore, we extend the \textit{ab initio} calculations across the $N=28$ isotones, computing excitation energies and single-neutron transfer SFs from $N=29$ isotones ranging from $^{48}$K to $^{45}$S. By systematically removing protons from \(^{48}\text{K}\) to \(^{45}\text{S}\), we trace the evolution of the \(N=28\) shell strength via theoretical SFs values. Our results provide a microscopic pathway to quantify the weakening of the \(N=28\) shell closure.