Symmetry restoration in the axially deformed proton-neutron quasiparticle random-phase approximation for nuclear <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> decay: The effect of angular-momentum projection

We examine the effects of symmetry restoration on nuclear beta decay within the axially deformed proton-neutron quasiparticle random phase approximation (QRPA). We employ the proton-neutron finite-amplitude method (pnFAM) to compute transition amplitudes, and perform angular-momentum projection both after variation and after the QRPA to restore rotational symmetry. Exact projection reduces the calculated beta decay half-lives from those that use the needle approximation by up to 60%, and even more when taking the effects of projection on the ground-state energy into account.