The odd even scattering of the nuclear charge radii. A mirror for pairing correlations

As cause for the normal odd-even staggering of the nuclear charge radii the blocking of neutron pair correlations at its back-effect on the proton distribution is presumed. This effect is studied in the framework of the HFB theory which is because of the unification of the concept of the mean single-particle potential and pairing just offerred for this reason. Calculated are mean charge radii, realtively to a reference isotope, for spherical nuclei. It is shown proton pairing, are not able to reproduce the normal staggering. An immediate coupling of the neutron pairing to the mean HFB one-particle potential can result via many-particle interactions. This mechanism is studied by application of a proton-neutron separable many-particle interaction. Calculations for the isotope series lead, mercury, barium, tin, cadmium, and molybdenum give a normal scattering of the correct order of magnitude with often quantitative agreement between theory and experiment, so that the immediate influence of the mean proton single-particle potential by the neutron pair correlations can be considered as the cause for the normal staggering. This is a many-particle effect. Each many-particle interaction can in principle yield this mechanism. A tentative calculation for calcium isotopes shows that this model is also able to describe the extreme behaviour of the mean-square charge radius of the calcium isotopes. In order to study the effects of the particle-number violation on the mean-square charge radii instead of a HFB vacuum a particle-number projected vacuum was applied as variational approach to the nuclear ground state. Vacuum was applied as variational approach to the nuclear ground state. It was shown that the results of both calculations are very similar. (orig./HSI)