An intrinsic state generating the ground state rotational band of a deformed nucleus and its approximate equivalence to an algebraic-variational treatment: Illustration by an exactly soluble model

We construct a class of intrinsic or trial states to generate the ground state band of a rotating nucleus in a highly schematized shell model possessing R(5) symmetry. This model is described in the preceding paper. The exponential form of the state links this work to a line of recent developments tracing back ultimately to the work of Jancovici and Schiff on the generator coordinate method. For the present case the state is a product of BCS states and is seen to contain more general (four-particle) correlations than a single deformed BCS state. A technique for the construction of the states is described. The major result of this paper is the proof that the cranking variational principle associated with the trial state is essentially equivalent (exactly equivalent in the thermodynamic or large system limit) to the algebraic-variational method described in the preceding paper, when the latter is restricted to the oneband approximation. The existence of sharp phase transitions in the model is then investigated analytically. A spherical to deformed transition is thus confirmed, as well as an anti-pairing transition. As explained, this is unrelated to the Coriolis anti-pairing phenomena.