Shell correction dependence of potential depth in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math>-decay cluster model

The depth of nuclear potential for $\ensuremath{\alpha}$ decay is systematically investigated using 178 measured $\ensuremath{\alpha}$-decay half-lives of even-even nuclei. We find that, by considering the shell effect in the depth of the potential, the results can be significantly improved. The root-mean-square deviation across the 178 data points is reduced from 0.278 to 0.188 by introducing a new formula that accounts for the shell correction dependence of potential depth. The $\ensuremath{\alpha}$-decay half-lives for unknown nuclei with charge numbers $Z=118$ and 120 are predicted with the proposed formula.