PN-QRPA AND HIGHER-ORDER APPROXIMATIONS

The proton-neutron Quasi-particle Random Phase Approximation (pn-QRPA) is reviewed and higher-order approximations discussed with reference to the beta decay physics. The approach is fully developed in a boson formalism. Working within a schematic model, we first illustrate a fer mion-boson mapping procedure and apply it to construct boson images of the fermion Hamiltonian at different levels of approximation. The qua lity of these images is tested through a comparison between approximat e and exact spectra. Standard QRPA equations are derived in correspond ence with the quasi-boson limit of the boson Hamiltonian. The use of h igher-order Hamiltonians is seen to improve considerably the stability of the approximate solutions. The mapping procedure is also applied t o Fermi beta operators and transition amplitudes are discussed. The ra nge of applicabilty of the QRPA formalism is examined.