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 o
f 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 $ u 1f_{7/2}$ or $ u 2p_{3/2}$ orbitals. Only for $^{48}$K, a significant amount of mixing with $pi 2s_{1/2}^{-1} otimes u (pf)$ is observed leading to a $I^{pi}=1^{-}$ ground state. For $^{50}$K, the ground-state spin-parity is $0^-$ with leading configuration $pi 1d_{3/2}^{-1} otimes u 2p_{3/2}^{-1}$.
We report on the measurement of optical isotope shifts for $^{38,39,42,44,46text{-}51}$K relative to $^{47}$K from which changes in the nuclear mean square charge radii across the N=28 shell closure are deduced. The investigation was carried out by b
unched-beam collinear laser spectroscopy at the CERN-ISOLDE radioactive ion-beam facility. Mean square charge radii are now known from $^{37}$K to $^{51}$K, covering all $ u f_{7/2}$-shell as well as all $ u p_{3/2}$-shell nuclei. These measurements, in conjunction with those of Ca, Cr, Mn and Fe, provide a first insight into the $Z$ dependence of the evolution of nuclear size above the shell closure at N=28.
The ground-state spins and magnetic moments of $^{49,51}$K have been measured using bunched-beam high-resolution collinear laser spectroscopy at ISOLDE-CERN. For $^{49}$K a ground-state spin $I = 1/2$ was firmly established. The observed hyperfine st
ructure of $^{51}$K requires a spin $I > 1/2$ and from its magnetic moment $mu(^{51}text{K})= +0.5129(22), mu_N$ a spin/parity $I^pi=3/2^+$ with a dominant $pi 1d_{3/2}^{-1}$ hole configuration was deduced. This establishes for the first time the re-inversion of the single-particle levels and illustrates the prominent role of the residual monopole interaction for single-particle levels and shell evolution.
