Charge radii of neutron-deficientK36andK37

Background: The systematic trend in mean-square charge radii as a function of proton or neutron number exhibits a discontinuity at the nucleon-shell closures. While the established $N=28$ shell closure is evident in the charge radii of the isotopic chains of K through Mn, a similar signature of the $N=20$ shell closure is absent in the Ca region.Purpose: The isotope shift between neutron-deficient $^{36}\mathrm{K}$ and $^{37}\mathrm{K}$ was determined to investigate the change of the mean-square charge radii across $N=20$ in the K isotopic chain.Methods: The $D1$ atomic hyperfine spectra of $^{36}\mathrm{K}$ and $^{37}\mathrm{K}$ were measured using an optical pumping and subsequent $\ensuremath{\beta}$-decay asymmetry detection technique. Atomic rate equations were solved to fit the resonant line shape. The result was compared to Skyrme energy-density functional and shell-model calculations.Results: The isotope shift was obtained as $\ensuremath{\delta}{\ensuremath{\nu}}^{37,36}=\ensuremath{-}139(4)(3)$ MHz. Using a re-evaluated isotope shift, $\ensuremath{\delta}{\ensuremath{\nu}}^{39,37}=\ensuremath{-}264(2)(3)$ MHz, the isotope shift relative to $^{39}\mathrm{K}$ was determined to be $\ensuremath{\delta}{\ensuremath{\nu}}^{39,36}=\ensuremath{-}403(5)(4)$ MHz. The differential mean-square charge radius was then deduced as $\ensuremath{\delta}{\ensuremath{\langle}{r}^{2}\ensuremath{\rangle}}^{39,36}=\ensuremath{-}0.16(5)(8)\phantom{\rule{4pt}{0ex}}{\mathrm{fm}}^{2}$. The Skyrme energy-density functional and shell-model calculations overpredict the experimental values below $N=20$ and underpredict them above $N=20$, and their agreement is marginal.Conclusions: The absence of the shell-closure signature at $N=20$ in the K isotopic chain is understood as a balance between the monopole and the quadrupole proton-core polarizations below and above $N=20$, respectively.