Calculation of double mass differences for near-magic nuclei on the basis of a semimicroscopic model

Double mass differences between nuclei having a magic number of protons (neutrons) and their neighbors differing by one or two protons (neutrons) have been calculated on the basis of a semimicroscopic model that has been proposed recently for the problem of nuclear pairing. A dominant term of the effective nucleonnucleon interaction has been calculated on the basis of the realistic Argonne nucleon-nucleon potential $v_{18}$. It has been supplemented with a moderately small phenomenological term that contains one universal parameter common to protons and neutrons. Double mass differences have been calculated for proton neighbors of the lead-isotope chain ($Z = 82$) and for neutron neighbors of $N = 82$ isotones. Corrections to the model that are caused by the contribution of low-lying surface vibrations (phonons) have been estimated.