Collective Hamiltonians in the generator coordinate method: Isoscalar monopole vibrations in light spherical nuclei

A procedure for constructing a collective Hamiltonian for a given nuclear collective motion is developed from the generator coordinate method. The procedure is based on the construction of a collective subspace of the many-body Hilbert space, and this is achieved by the generator coordinate method diagonalization of the overlap kernel. The Weyl transformation makes the connection between nonlocal phase space Hamiltonian kernels, obtained from the generator coordinate method, and operators in the collective space. The Gaussian overlap approximation and monopole vibrations in light spherical nuclei are studied in this formalism