Valence p-n interactions and the development of collectivity in heavy nuclei

A universal, physically intuitive description of collectivity in heavy nuclei is obtained in terms of the parameter P=$N_p$$N_n$/($N_p$+$N_n$) which gives the average number of interactions of each valence nucleon with those of the other type. Regardless of mass region, deformation sets in when P=$P_{\mathrm{crit}\mathrm{\approxeq }4–}$5. This, in turn, gives a rule that medium-mass and heavy nuclei with effective $N_p$ or $N_n$≤4 cannot be deformed. An interpretation in terms of the monopole and quadrupole p-n interactions is discussed.