The P-Factor and Atomic Mass Systematics: Application to Medium Mass Nuclei

Abstract

Recently it has been shownl that a measure of the average number of interactions of each valence nucleon with those of the other type given by the parameter P = NpNn/(Np+Nn) [where Np(Nn) are the number of valence protons (neutrons)] provides a general and physically meaningful explanation for the development of collectivity and the onset of deformation in medium and heavy nuclei. For example, as shown in Fig. 1, the energy ratio \({E_{{4^+}_1}}/{E_{{2^+}_1}}\) plotted versus P exhibits remarkedly similar behavior independent of mass region and, in all cases indicates a transition to deformation \(({E_{{4^+}_1}}/{E_{{2^+}_1}}\approx 3.0)\) when P ≈ 4–5. This rule provides a necessary condition for deformation that the nuclear ground state cannot be deformed for medium or heavy nuclei if the number of valence nucleons of either type is less than 4. Furthermore, this result was seen as a manifestation of the competition between the like nucleon pairing and p-n quadrupole interactions since the pairing strength, which is about 1 MeV and which supports sphericity, is approximately off-set by the quadrupole deformation-driving term when 4–5 valence p-n interactions (each with strength ≈ 200 keV) are present.