Algebraic solution of a general quadrupole Hamiltonian in the interacting boson model

A method based on an eigenmode condition and projection techniques is presented for solution of a general quadrupole Hamiltonian in the interacting boson model. It is shown that the intrinsic states obtained from the eigenmode condition provide a zeroth order solution to the diagonalization of the corresponding quadrupole Hamiltonian. The method is in effect a 1/N expansion, where N is the boson number, ideally suited for the deformed nuclei for which N≊12–16. Because of certain cancellations with the normalization, zeroth order solutions of the intrinsic states are sufficient to obtain matrix elements to order O(1/$N^2$).