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Proton radioactivity half-lives with nuclear asymmetry factor

The dependence of proton emission half-lives on the nuclear asymmetry parameter is investigated using the WKB method and two types of empirical formula. Using the single-folding formalism with asymmetry-dependent nuclear radius and surface diffuseness of nuclear matter, the nuclear potential and consequently the half-life are functions of the asymmetry factor. Despite small values of asymmetry in neutron-deficient proton emitters, noticeable changes in the half-lives are observed. The addition of an asymmetry parameter term to the two forms of empirical formulas leads to a reduction in the rms error for ground state and isomeric transitions. A noticeable reduction of about 43% is obtained for isomeric transitions in the second form of the empirical formula. Considering ground state transitions in two categories, odd-even and odd-odd emitters, and adopting deformation and asymmetry-dependent empirical formulas, the rms decreases remarkably. The lowest values of rms errors, viz. 0.1492, 0.2312, and 0.1999, are obtained for the aforementioned empirical formulas for ground state transitions of odd-even and odd-odd emitters and for all isomeric transitions, respectively.