Quantum corrections to the potential energy for large amplitude collective motion

We discuss the problem of inclusion of quantum corrections in the semiclassical theory of adiabatic large amplitude collective motion for many-fermion systems. We concentrate on deriving a formula for the leading quantum correction to the classical collective potential energy function in this theory. This is an extension of the usual calculation of the quantum corrections to the static Hartree-Fock energy using the random phase approximation. The answer can be expressed in terms of those solutions of a local random phase approximation that describe oscillations orthogonal to the collective surface. Because of the strict enforcement of the Pauli principle, however, the answer differs from the usual quasiboson approximation, yielding the correct ground-state corrrelation energy for a static solution to the Hartree-Fock equations. The result is applied, approximately, to help improve a previous treatment of the low energy spectrum of {sup 28}Si.