Boson expansion theory description of anharmonic gamma vibrations in well deformed nuclei

The boson expansion theory, which has been used extensively in the past in describing anharmonic vibrations in spherical nuclei, is used here to describe anharmonic gamma vibrations in well deformed nuclei, notably in 168Er. By using this theory we go beyond simple one-phonon calculations such as in the Random Phase Approximation. This must be done since, by the nature of the anharmonicities, it is not possible to simply take linear superpositions of one-phonon states to predict higher energy vibrational states. Starting from the Nilsson single particle deformed states, the fermion form of the problem is presented by using either the Tamm-Dancoff Approximation or the Random Phase Approximation as a basis. The interactions chosen are of a collective quadrupole type including both particle hole and pairing interactions. Also, similar to our previous boson expansion works, we consider the effects of noncollective terms on our collective interactions. This is treated in a perturbative fashion within the framework of the Feshbach formalism. In addition, we include some higher order interactions recently developed. Both the fermion and corresponding boson forms of these terms are developed here. Finally, based on some recent advances, the interaction strengths are now calculated instead of being used as free parameters. Numerical results of our theory are presented. As predicted from other works the potential energy surface exhibits a nonzero minimum. The energy states calculated agree well with the experimental values