ISOSPIN DEPENDENT OSCILLATOR SPACING FOR NEUTRONS AND PROTONS IN NUCLEI USING HF-BCS RADII

The oscillator spacing for neutrons ((h) over bar omega(n)) and proton s ((h) over bar omega(p)) is calculated as a function of the neutron n umber N and the proton number Z. The dependence of (h) over bar omega( n), ((h) over bar omega p) on N and Z is established employing a param etrization for the mean square nuclear radius obtained from HF-BCS cal culations. It turns out that the difference (h) over bar omega(n) - (h ) over bar omega(p) is appreciable, because (h) over bar omega amplifi es small differences of root mean square radii. It is also seen that t he correction due to valence nucleons is important for relatively ligh t and medium heavy nuclei. Satisfactory and simple approximate asympto tic formulas for (h) over bar omega(n)(N, Z) and (h) over bar omega(p) (N, Z) are also derived, which can be used in practice. Finally, the v alidity of our various approaches is checked and a possible applicatio n is also discussed.