Charge radii of neutron-deficient K 36 and K 37

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 K-36 and K-37 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 K-36 and K-37 were measured using an optical pumping and subsequent 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 delta nu(37,36) = -139(4)(3) MHz. Using a re-evaluated isotope shift, delta nu(39,37) = -264(2)(3) MHz, the isotope shift relative to K-39 was determined to be delta nu(39,36) = -403(5)(4) MHz. The differential mean-square charge radius was then deduced as delta < r(2)>(39,36) = -0.16(5)(8) 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.