Direct transfer to $^{46,48}$K as a survey of the $π(s_{1/2})$$-ν(sdpf)$ interaction

TL;DR

This work probes the evolution of shell structure near the $N=28$ island of inversion by directly transferring a neutron with reactions that selectively couple the $π s_{1/2}$ proton orbital to a broad set of neutron orbitals across the $sd$-$pf$ shells. By performing simultaneous $^{47}$K(d,t)$^{46}$K and $^{47}$K(d,p)$^{48}$K measurements with VAMOS++, MUGAST, and AGATA, the authors map state-by-state occupancies and extract spectroscopic factors, highlighting both well-defined single-particle strengths and complex, mixed configurations. They compare experimental results to shell-model predictions (notably with the ZBM2* interaction) and find good energy/spin-parity reproduction but significant discrepancies in spectroscopic factors, pointing to inadequate proton configuration mixing in current interactions as a key limitation. The findings underscore the need for improved treatment of proton structure in near-degeneracy regions and establish a benchmark for understanding the microscopic origins of the island of inversion, with implications for predicting single-particle behavior across major shells.

Abstract

The collapse of the canonical $N=28$ magic number in nuclei with $Z<20$ has drawn significant interest as it relates to the emergence of an island of inversion centered on $^{42}$Si and $^{44}$S. In particular, interactions between the $πs_{1/2}$ orbital -- empty in $^{42}$Si and full in $^{44}$S -- and the neutron orbitals just above and below the $N=28$ gap are expected to be critical in this region, but remain relatively unexplored. In this paper, we expand upon the results of our previous study of the direct transfer reaction $^{47}$K(d,p$γ$)$^{48}$K [C.\,J.~Paxman \textit{et al.}, Phys. Rev. Lett. 134, 162504 (2025)] with the results of the complementary $^{47}$K(d,t$γ$)$^{46}$K reaction. Through this study, we present a comprehensive scan of the interaction between the critical $πs_{1/2}$ orbital and a broad range of neutron orbitals spanning nearly two full shells. We identify several discrepancies between the experimental results and state-of-the-art shell model calculations, which suggest a deficiency of the shell model to fully capture the complex proton configuration mixing in this region, highlighting a significant challenge for single-particle descriptions of the island of inversion.

Figures (18)

• Figure 1: Simplified schematic of the proton (neutron) orbitals and their occupation, shown in red (blue). As the ground state of $^{47}$K is dominated by $\pi(s_{1/2}^1 d_{3/2}^4)$, all states populated in $^{46}$K (a) and $^{48}$K (b) will be accessed via this component. The spin-parities of states that can be produced by coupling this proton to each of the accessible neutron orbitals is shown. Notably, $\nu p_{3/2}$ and $\nu f_{7/2}$ are accessible in both reactions due to the diffuse neutron occupation probabilities across $N=28$.
• Figure 2: Differential cross sections of experimental elastic scattering data, compared to various optical model calculations. The $^{47}$K(d,d) calculations are shown in blue, and $^{47}$K(p,p) calculations are shown in red. The range of experimental data used in the normalisation is indicated by green and purple dashed lines. Letter codes correspond to the optical model and the computational code. Optical models are from Ref. Optical_DCV (D), Ref. Optical_HanShiShen (H), Ref Optical_ChapHill (C), Ref. OpticalModel_BecchettiGreenlees1969 (B), Ref. Optical_Perey (P) and Ref. OpticalModel_KoningDelaroche2003 (K). Calculations were performed in FRESCO (F) fresco and DWUCK4 (W) dwuck.
• Figure 3: Comparison of the uncorrected (a,b) and corrected (c,d) reconstructed $^{48}$K excitation spectra, when adjusting the beam spot position and target thickness. Spectra in (a,c) are from each of the six upstream detectors. Notably, the corrected spectra show consistent agreement between detectors covering different $\phi_{lab}$ ranges -- see improvement from (a) to (c) -- and different $\theta_{lab}$ ranges -- see improvement from (b) to (d). The lowest-energy peak contains the ground state and 0.143 MeV state, and a such is not centered on 0 MeV.
• Figure 4: Energy of the detected light ejectiles, E$_{lab}$, versus detected angle in the laboratory frame, for $^{47}$K(d,t)$^{46}$K ($\theta_{lab}=4^\circ-22^\circ$) and $^{47}$K(d,p)$^{48}$K ($\theta_{lab}=104^\circ-156^\circ$). The position of the ground state and the neutron separation energy for each nucleus is marked, and the experimental E$_{lab}$ threshold of 1.4 MeV is visible. Note that the $^{48}$K events shown here only require a timing coincidence from the focal plane of VAMOS++, whereas the $^{46}$K events have additional particle identification requirements to reduce background.
• Figure 5: Level scheme of $^{46}$K, as determined through $^{47}$K(d,t) in this work, compared to $^{48}$Ca(d,$\alpha$) Paul1971_48Ca-da-46K_NormKineDaehnick1974_48Ca-da-46K_NormKine and $^{48}$Ca(p,$^{3}$He) Dupont1970_48Ca-p3He-46K_NormKineDupont1973_48Ca-p3He-46K_NormKineDaehnick1973_48Ca-p3He-46K_NormKine as compiled in Ref. NuclearDataSheets_Mass46. Letter labels relate to the subsection of Section \ref{['anal46K']} in which the states(s) are discussed. Four new $\gamma$-ray transitions and a new excited state have been identified in this work, marked in red. The two states marked with an asterisk, labeled (f), are unresolved in particle spectroscopy; the total peak contains $\ell=0$ and $\ell=2$ character, and shell model comparisons would suggest that one state is $0^+$ and the other is $1^+$, but this work is unable to assign these spin-parities to specific states.