The quasiparticle finite amplitude method is extended to describe charge-exchange transitions based on the relativistic Hartree-Bogoliubov model, adopting the point-coupling energy density functional DD-PC1 and a finite-range separable pairing force. After validation through comparison with relativistic quasiparticle random-phase approximation results in spherical nuclei, the deformation effects on isobaric analog resonances and Gamow-Teller (GT) transitions in Zn isotopes are investigated. The GT strength exhibits significant fragmentation in deformed nuclei. The analysis of summed strengths and centroid energies in GT resonance region between the $K=0$ and $K=1$ components reveals that prolate configurations exhibit stronger $K=1$ strength and lower $K=1$ centroid energy, while oblate shapes show an opposite behavior, with stronger $K=0$ strength and lower $K=0$ energy. The effects of isoscalar pairing on GT strength distributions for different shape configurations are also examined.

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• Charge-exchange reactions
• Nuclear structure & decays
• Nuclear density functional theory