Validity of an algebraic-variational approach to the theory of collective motion for an exactly soluble shell model with R(5) symmetry

An algebraic-variational approach to the theory of collective motion previously applied in variant forms to pairing and monopole interaction models is here developed for an exactly soluble shell model Hamiltonian with R(5) symmetry. The spectrum of this class of Hamiltonian operators has previously been shown to represent a two-dimensional vibrator-rotator. The approximation scheme developed yields almost exact results up to the two-phonon level in the spherical region and goes over smoothly into a theory of the lowest states of the ground state rotational band in the deformed regime.