Isotope shifts in the nuclear charge radius of even and odd calcium isotopes are calculated within the nuclear shell model. The model space includes all configurations of nucleons in the $2s, 1d_{ 3/2}, 1f_{ 7/2}, { \rm and} ~2p_{ 3/2}$ orbits. The shell model describes well the energies of the intruder states in Sc and Ca, as well as the energies of the low-lying $2^+$ and $3^-$ states in the even Ca isotopes. The characteristic features of the isotope shifts, the parabolic dependence on $A$ and the prominent odd-even staggering, are well reproduced by the model. These features are related to the partial breakdown of the $Z = 20$ shell closure caused by promotion, due to the neutron-proton interaction, of the $ds$ shell protons into the $fp$ shell.
Categories: nucl-th