Shell structure of potassium isotopes deduced from their magnetic moments

Abstract

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.Purpose: Extend our knowledge about the evolution of the $1/{2}^{+}$ and $3/{2}^{+}$ states for K isotopes beyond the $N=28$ shell gap.Method: High-resolution collinear laser spectroscopy on bunched atomic beams.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 $1{d}_{3/2}$ and $2{s}_{1/2}$ in the shell model and ab initio framework is also presented.Conclusions: The dominant component of the wave function for the odd-$A$ isotopes up to $^{45}\mathrm{K}$ is a $\ensuremath{\pi}1{d}_{3/2}^{\ensuremath{-}1}$ hole. For $^{47,49}\mathrm{K}$, the main component originates from a $\ensuremath{\pi}2{s}_{1/2}^{\ensuremath{-}1}$ hole configuration and it inverts back to the $\ensuremath{\pi}1{d}_{3/2}^{\ensuremath{-}1}$ in $^{51}\mathrm{K}$. For all even-$A$ isotopes, the dominant configuration arises from a $\ensuremath{\pi}1{d}_{3/2}^{\ensuremath{-}1}$ hole coupled to a neutron in the $\ensuremath{\nu}1{f}_{7/2}$ or $\ensuremath{\nu}2{p}_{3/2}$ orbitals. Only for $^{48}\mathrm{K}$, a significant amount of mixing with $\ensuremath{\pi}2{s}_{1/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}(pf)$ is observed leading to a ${I}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}$ ground state. For $^{50}\mathrm{K}$, the ground-state spin-parity is ${0}^{\ensuremath{-}}$ with leading configuration $\ensuremath{\pi}1{d}_{3/2}^{\ensuremath{-}1}\ensuremath{\bigotimes}\ensuremath{\nu}2{p}_{3/2}^{\ensuremath{-}1}$.