Axially deformed relativistic quasiparticle random-phase approximation based on point-coupling interactions

Collective nuclear excitations, like giant resonances, are sensitive to nuclear deformation, as evidenced by alterations in their excitation energies and transition strength distributions. A common theoretical framework to study these collective modes, the random-phase approximation (RPA), has to deal with large dimensions spanned by all possible particle-hole configurations satisfying certain symmetries. It is the aim of this work to establish a new theoretical framework to study the impact of deformation on spin-isospin excitations, that is able to provide fast and reliable solutions of the RPA equations. The nuclear ground state is determined with the axially deformed relativistic Hartree-Bogoliubov (RHB) model based on relativistic point-coupling energy density functionals (EDFs). To study the excitations in the charge-exchange channel, an axially deformed proton-neutron relativistic quasiparticle RPA (pnRQRPA) is developed in the linear response approach. After benchmarking the axially deformed pnRQRPA in the spherical limit, a study of spin-isospin excitations including Fermi, Gamow-Teller (GT), and spin-dipole (SD) is performed for selected $pf$-shell nuclei. For GT transitions, it is demonstrated that deformation leads to a considerable fragmentation of the strength function. A mechanism inducing the fragmentation is studied by decomposing the total strength to different projections of total angular momentum $K$ and constraining the nuclear shape to either spherical, prolate, or oblate. A similar fragmentation is also observed for SD transitions, although somewhat moderated by the complex structure of these transitions, while, as expected, the Fermi strength is almost shape independent. The axially deformed pnRQRPA introduced in this work open perspectives for the future studies of deformation effects on astrophysically relevant weak interaction processes, in particular beta decay and electron capture.