Quasiparticle random-phase approximation andβ-decay physics: Higher-order approximations in a boson formalism

The quasiparticle random-phase approximation (QRPA) is reviewed and higher-order approximations are discussed with reference to β-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 first-order 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 β operators: exact and approximate transition amplitudes are discussed together with the Ikeda sum rule. The range of applicabilty of the QRPA formalism is analyzed.