Nuclear rotational anomaly and the HFB equations

Abstract

We show that the S-shape of the plot of moment of inertia versus square of the angular frequency observed experimentally for the rotational spectrum of rare-earth nuclei follows naturally from the solution of the Hartree-Fock-Bogoliubov equations. We consider the case of eight particles in the 1 h 11 2 level outside a closed shell and use the Sussex interaction for the nucleon-nucleon potential. Some properties of the upper, middle and lower branches are looked into and it is established that the transition indeed occurs due to reduction in the strength of the pairing part of the interaction due to the Coriolis force. Methods for calculating the moment of inertia and other nuclear properties in the transitional region, i.e. the middle branch, are suggested and it is found that the properties there are intermediate between the upper and lower branch. We also suggest the importance of higher (> 0) particle-particle channel coupled angular momentum of the nucleon force for the rotational spectrum of deformed nuclei at high angular momentum. A comment is also made on misleading results that can be obtained for e.g. moment of inertia, by projecting only even integral values of angular momentum in Hartree-Fock type solutions and thereby ignoring finer details.