Shell structure of potassium isotopes deduced from their magnetic moments

TL;DR

This study investigates the nuclear structure of potassium isotopes beyond the N=28 shell gap by measuring their magnetic moments and spins, comparing results with shell-model calculations to understand wave function compositions.

Contribution

It provides new experimental data on ground-state spins and magnetic moments of K isotopes from N=19 to N=32, and analyzes the evolution of shell gaps using both shell-model and ab initio frameworks.

Findings

Dominant wave function component for odd-A isotopes up to 45K is a π 1d3/2^{-1} hole.

For 47K and 49K, the main component is a π 2s1/2^{-1} hole, reverting to π 1d3/2^{-1} in 51K.

Ground state of 48K is significantly mixed, leading to a 1− state; 50K has a 0− ground state with specific proton-neutron configurations.

Abstract

\item[Background] Ground-state spins and magnetic moments are sensitive to the nuclear wave function, thus they are powerful probes to study the nuclear structure of isotopes far from stability. \item[Purpose] Extend our knowledge about the evolution of the $1/2^+$ and $3/2^+$ states for K isotopes beyond the $N = 28$ shell gap. \item[Method] High-resolution collinear laser spectroscopy on bunched atomic beams. \item[Results] From measured hyperfine structure spectra of K isotopes, nuclear spins and magnetic moments of the ground states were obtained for isotopes from $N = 19$ up to $N = 32$. In order to draw conclusions about the composition of the wave functions and the occupation of the levels, the experimental data were compared to shell-model calculations using SDPF-NR and SDPF-U effective interactions. In addition, a detailed discussion about the evolution of the gap between proton $1d_{3/2}$ and $2s_{1/2}$ in the shell model and {\it{ab initio}} framework is also presented. \item[Conclusions] The dominant component of the wave function for the odd-$A$ isotopes up to $^{45}$K is a $\pi 1d_{3/2}^{-1}$ hole. For $^{47,49}$K, the main component originates from a $\pi 2s_{1/2}^{-1}$ hole configuration and it inverts back to the $\pi 1d_{3/2}^{-1}$ in $^{51}$K. For all even-$A$ isotopes, the dominant configuration arises from a $\pi 1d_{3/2}^{-1}$ hole coupled to a neutron in the $\nu 1f_{7/2}$ or $\nu 2p_{3/2}$ orbitals. Only for $^{48}$K, a significant amount of mixing with $\pi 2s_{1/2}^{-1} \otimes \nu (pf)$ is observed leading to a $I^{\pi}=1^{-}$ ground state. For $^{50}$K, the ground-state spin-parity is $0^-$ with leading configuration $\pi 1d_{3/2}^{-1} \otimes \nu 2p_{3/2}^{-1}$.