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 fermion-boson mapping procedure and apply it to construct boson images of the fermion Hamiltonian at different levels of approximation. The quality of these images is tested through a comparison between approximate and exact spectra. Standard QRPA equations are derived in correspondence with the quasi-boson limit of the boson Hamiltonian. The use of higher-order Hamiltonians is seen to improve considerably the stability of the approximate solutions. The mapping procedure is also applied to Fermi beta operators and transition amplitudes are discussed. The range of applicabilty of the QRPA formalism is examined.