  In this article, we derive a quantal self-consistent time-reversal invariant
parameter-free cranking model for isoscalar monopole excitation coupled to
intrinsic motion in even-even light nuclei. The model uses a wavefunction that
is a product of monopole and intrinsic wavefunctions and a constrained
variational method to derive, from a many-particle Schrodinger equation, a pair
of coupled self-consistent cranking-type Schrodinger equations for the monopole
and intrinsic systems. The monopole co-ordinate used is the trace of the
quadrupole tensor and hence describes the overall deformation of the nucleus.
The monopole and intrinsic wavefunctions are coupled to each other by the two
cranking equations and their associated parameters and by two constraints
imposed on the intrinsic system. For an isotropic Nilsson shell model and an
effective residual two-body interaction, the two coupled cranking equations are
solved in the Tamm Dancoff approximation. The strength of the interaction is
determined from a Hartree-Fock self-consistency argument. The excitation energy
of the first excited state is determined and found to agree closely with those
observed in the nuclei He-4, Be-8, C-12, O-16 , Ne-20, Mg-24, and Si-28. The
variation of the model parameters are explained. In particular, it is found
that the monopole excitation energy as a function of the mass number undergoes
an increase whenever the nucleons begin to occupy a new sub-shell state with
non-zero orbital angular momentum as a consequence of suppressing or
constraining the resulting spurious monopole excitation in the intrinsic
system.
