The use of coherent states in the variational treatment of proton-neutron interactions

Coherent states are used as trial states to determine, variationally, the structure of the eigenvectors belonging to a schematic Hamiltonian consisting of single-particle, pairing and residual proton-neutron interaction terms. It is shown that the standard proton-neutron quasiparticle random-phase approximation (pn-QRPA) is recovered, as a variational theory, by replacing quasiparticle pair creation and annihilation operators by bosons. It is also shown that an exact, algebra preserving, mapping of the Hamiltonian is needed to describe the spectrum beyond the QRPA phase transition. The role of the spurious components of the trial wave functions is discussed. Received: 19 February 2002 / Accepted: 3 May 2002