Calculation of β-decay rates in a relativistic model with momentum-dependent self-energies

Abstract

The relativistic proton-neutron quasiparticle random phase approximation (PN-RQRPA) is applied in the calculation of \ensuremath{\beta}-decay half-lives of neutron-rich nuclei in the $Z\ensuremath{\approx}28$ and $Z\ensuremath{\approx}50$ regions. The study is based on the relativistic Hartree-Bogoliubov calculation of nuclear ground states, using effective Lagrangians with density-dependent meson-nucleon couplings, and also extended by the inclusion of couplings between the isoscalar meson fields and the derivatives of the nucleon fields. This leads to a linear momentum dependence of the scalar and vector nucleon self-energies. The residual QRPA interaction in the particle-hole channel includes the $\ensuremath{\pi}+\ensuremath{\rho}$ exchange plus a Landau-Migdal term. The finite-range Gogny interaction is employed in the $T=1$ pairing channel, and the model also includes a proton-neutron particle-particle interaction. The results are compared with available data, and it is shown that an extension of the standard relativistic mean-field framework to include momentum-dependent nucleon self-energies naturally leads to an enhancement of the effective (Landau) nucleon mass, and thus to an improved PN-QRPA description of ${\ensuremath{\beta}}^{\ensuremath{-}}$-decay rates.