Effect of deformation on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> clustering from a pocket-type dynamical double-folding potential

The ongoing quest for the boundaries of the chart of nuclides has led to the discovery of many new heavy nuclei near the drip line, which generally exhibit large shape deformation. To explore the impact of nuclear deformation on ground-state $\ensuremath{\alpha}$-decay properties, particularly $\ensuremath{\alpha}$ clustering, we develop a deformed version of the pocket-type dynamical double-folding potential (DDFP) model. By analyzing the geometry of the pocket potential and the systematics of extracted $\ensuremath{\alpha}$-preformation factors, we find that the effect of deformation on ${P}_{\ensuremath{\alpha}}$ can be described by a simple linear correlation with the square of quadrupole-deformation parameter. Based on this finding, we propose an empirical formula for ${P}_{\ensuremath{\alpha}}$ that accounts for both shell and deformation effects. Using the deformed pocket-type DDFP and the proposed formula, we predict the $\ensuremath{\alpha}$-decay half-lives for neutron-deficient Pu, Cm, and Cf isotopes near the proton drip line.