Removal of Redundancy from Backward Coupling in the Equation of Motion Method for Odd-Mass Nuclei.

The equation of motion method has had many successful applications, but when it is used in systems where collections of fermions are treated as bosons a complete treatment of the dynamical interaction and Pauli Principle constraints necessitate backward coupling. This, however, leads to an overcomplete and thus redundant representation. After general discussion of the problem and how it has manifested itself in nuclear structure theory, we present a general method for including backward coupling without redundancy by diagonalizing both the normalization matrix and the Hamiltonian of the overcomplete representation. The specific problems of a transformation between representations of different dimensions is discussed, and quantitative checks on the assumptions necessary to make such a transformation are given. The method, making assumptions consistent with the quasiparticle random phase approximation, is applied to two regions of odd mass nuclei where forward coupling by itself has not been successful. Energy levels and spectroscopic factors calculated with the present technique are compared with the cases of forward coupling only and that of backward coupling without removal of redundancy. It is shown that qualitative effects of backward coupling previously reported are not spurious effects of double counting, though they are significantly modified. Further refinements of the theory necessary to make an accurate comparison with experiment are discussed, as is the role of this method as a groundwork for a self -consistent microscopic theory linking even-even and odd -mass nuclei.