Theory of rapid (nonadiabatic) rotation of nonspherical nuclei

On the basis of the concept of the growing role of nonadiabatic effects of the non-conservation of the quantum number $K,$ a theory has been developed of the phenomenon which has been given the name of backbending. Above the transition point, for $J\geq J_c$, all the values $-J\leq K\leq J$ are equally probable. An investigation is made of the singularities possessed by the ordering parameter (proportional to the spectroscopic quadrupole moment of a nonspherical nucleus), the rotational angular velocity and the moment of inertia of a nucleus at the Curie point. Formulas have been derived for the intensity of quadrupole radiation in the more symmetric $n$-phase $J> J_c$. By analyzing the experimental values of the moments of inertia belonging to the $n$-phase, the radius of the mass distribution in the nucleus was determined. It agrees with the radius of the proton distribution derived from data on the scattering of electrons by nuclei. On the basis of the simplest form of the singularity of the parametric derivative of the Hamiltonian of the system a general theory of zero-temperature second-order phase transitions is developed in the Appendix.