Pairing forces and nuclear collective motion

The influence of pairing forces on the collective vibrations in nuclei is studied using a perturbation expansion. The result is found to agree with that given by Belyaev using the superconductivity approximation except that here the number of particles is conserved. A general discussion is given of the collective quadrupole energy surface. In particular the anharmonic terms in the expansion about zero deformation and the general character of the stability of axially symmetric deformed systems are discussed.