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

P. Y. Wang, M. R. Xie, Q. Yuan, W. J. Huang, J. G. Li

TL;DR

This work uses ab initio VS-IMSRG calculations based on chiral NN+$3N$ forces to revisit the low-lying states and neutron SFs of $^{48}$K, comparing with recent transfer-reaction data. While the calculated energy spectra reproduce the observed level ordering (with one interaction correctly predicting the ground-state sequence), the SFs are consistently overestimated unless a phenomenological reduction factor (≈0.6) is applied, aligning theory with experiment for $^{48}$K and $^{47}$Ar. Extending the framework across the $N=28$ isotones from $^{48}$K to $^{45}$S reveals erosion of the $N=28$ shell gap, evidenced by evolving neutron ESPEs and changing orbital occupancies, indicating a microscopic weakening of the shell closure. The results underscore the need for a unified ab initio treatment of reaction mechanisms and structure to fully capture quenching effects and shell evolution in neutron-rich systems.

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.

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

TL;DR

This work uses ab initio VS-IMSRG calculations based on chiral NN+ forces to revisit the low-lying states and neutron SFs of K, comparing with recent transfer-reaction data. While the calculated energy spectra reproduce the observed level ordering (with one interaction correctly predicting the ground-state sequence), the SFs are consistently overestimated unless a phenomenological reduction factor (≈0.6) is applied, aligning theory with experiment for K and Ar. Extending the framework across the isotones from K to S reveals erosion of the shell gap, evidenced by evolving neutron ESPEs and changing orbital occupancies, indicating a microscopic weakening of the shell closure. The results underscore the need for a unified ab initio treatment of reaction mechanisms and structure to fully capture quenching effects and shell evolution in neutron-rich systems.

Abstract

A recent \(^{47}\text{K}(d,pγ)^{48}\text{K}\) transfer reaction measurement has identified new excited states in 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 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 , 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 Ar. Furthermore, we extend the \textit{ab initio} calculations across the isotones, computing excitation energies and single-neutron transfer SFs from isotones ranging from K to S. By systematically removing protons from to , we trace the evolution of the shell strength via theoretical SFs values. Our results provide a microscopic pathway to quantify the weakening of the shell closure.
Paper Structure (4 sections, 3 equations, 5 figures, 4 tables)

This paper contains 4 sections, 3 equations, 5 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Method
  3. Result
  4. Summary

Figures (5)

  • Figure 1: Spectra of $^{48}$K calculated by using VS-IMSRG with two chiral effective interactions, NN N$^3$LO + 3N(lnl) and EM1.8/2.0. The results predicted by LSSM using the phenomenological interactions SDPF-MU and SDPF-U are presented PhysRevLett.134.162504, as well as experimental data PhysRevLett.134.162504.
  • Figure 2: The $^{48}$K SFs calculated by using the NN + 3N(lnl) chiral interaction (above) and the SDPF-MU interaction (below) compared with the experimental results. The red diamonds represent the SFs directly calculated by the VS-IMSRG and LSSM, while the pink diamonds represent the SFs multiplied by the reduction factor. The experimental results are taken from Ref. PhysRevLett.134.162504.
  • Figure 3: The difference between the experimental SFs and the calculated results multiplied by the reduction factor 0.6.
  • Figure 4: Low-lying spectra of $^{47}$Ar and the corresponding neutron SFs. Theoretical results are from LSSM (SDPF-MU) and VS-IMSRG (NN N$^3$LO + 3N(lnl)) calculations. Experimental spectra are taken from Ref. PhysRevLett.101.032501, and the experimental SFs (Expt1, Expt2) from Refs. Gaudefroy2006 and BRADT2018155. Red annotations indicate the orbital and spin-parity associated with each SF. Theoretical SFs include quenching via an empirical reduction factor.
  • Figure 5: Low‑lying spectra of the $N=28$ isotones ($^{47}$K, $^{46}$Ar, $^{45}$Cl) and corresponding neutron SFs, calculated with VS‑IMSRG using the NN N$^3$LO + 3N(lnl) interaction. Experimental excitation energies for $^{47}$K, $^{46}$Ar, and $^{45}$Cl are taken from Refs. PhysRevLett.134.162504nndctghm-sszh. SFs for the neutron partial waves $0f_{7/2}$, $0f_{5/2}$, $1p_{3/2}$, and $1p_{1/2}$ are normalization by their degeneracy factors $(2j+1)$.