Systematic calculations of $\alpha$-decay half-lives with an improved empirical formula

Based on the recent data in NUBASE2012, an improved empirical formula for evaluating the $\alpha$-decay half-lives is presented, in which the hindrance effect resulted from the change of the ground state spins and parities of parent and daughter nuclei is included, together with a new correction factor for nuclei near the shell closures. The calculated $\alpha$-decay half-lives are found to be in better agreements with the experimental data, and the corresponding root-mean-square (rms) deviation is reduced to $0.433$ when the experimental $Q$-values are employed. Furthermore, the $Q$-values derived from different nuclear mass models are used to predict $\alpha$-decay half-lives with this improved formula. It is found that the calculated half-lives are very sensitive to the $Q$-values. Remarkably, when mass predictions are improved with the radial basis function (RBF), the resulting rms deviations can be significantly reduced. With the mass prediction from the latest version of Weizs\"{a}cker-Skyrme (WS4) model, the rms deviation of $\alpha$-decay half-lives with respect to the known data falls to $0.697$.