Charge radii of potassium isotopes in the RMF(BCS)* approach

We apply the recently proposed RMF(BCS)* ansatz to study the charge radii of the potassium isotopic chain up to $^{52}$K. It is shown that the experimental data can be reproduced rather well, qualitatively similar to the Fayans nuclear density functional theory, but with a slightly better description of the odd-even staggerings (OES). Nonetheless, both methods fail for $^{50}$K and to a lesser extent for $^{48,52}$K. It is shown that if these nuclei are deformed with a $\beta_{20}\approx-0.2$, then one can obtain results consistent with experiments for both charge radii and spin-parities. We argue that beyond mean field studies are needed to properly describe the charge radii of these three nuclei, particularly for $^{50}$K.