Simple model for the quenching of the moments of inertia due to pairing correlations in rigidly deformed rotational bands
Résumé
Using Chandrasekhar's S-type coupling between rotational and intrinsic vortical modes one may simply reproduce the Hartree-Fock-Bogoliubov (HFB) dynamical properties of rotating nuclei within Routhian HF calculations free of pairing correlations yet constrained on the relevant so-called Kelvin circulation operator. From the analogy between magnetic and rotating systems, one derives a model for the quenching of pairing correlations with rotation, introducing a critical angular velocity—analogous to the critical field in supraconductors—above which pairing vanishes. Taking stock of this usual model, it is then shown that the characteristic behavior of the vortical mode angular velocity as a function of the global rotation angular velocity can be modelized by a simple two parameter formula, both parameters being completely determined from properties of the band-head (zero-spin) HFB solution. From calculation in five nuclei, the validity of this modelized Routhian approach is tested. It is clearly shown to be very good in cases where the evolution of rotational properties is only governed by the coupling between the global rotation and the pairing-induced intrinsic vortical currents, otherwise it fails. It therefore provides a sound ground base for evaluating the importance of coupling of rotation with other modes (shape distortions, quasiparticle degrees of freedom).