The empirical systematics of long-range $\alpha$-particle emission probabilities $P_{\mathrm{LRA}}$ are investigated in spontaneous and thermal-neutron-induced fission of heavy and superheavy nuclei. The correlations between $P_{\mathrm{LRA}}$ and various parameters, including the fissility $Z^2/A$, the linear combination of proton and mass numbers $4Z-A$, and the release energy $Q_{\alpha }$ of $\alpha$ decay are studied. A new semiempirical formula for $P_{\mathrm{LRA}}$, expressing it as a linear function of $Q_{\alpha }$, is proposed and its predictive power is compared with existing empirical and semiempirical formulas. The influence of experimental data uncertainties on the fitting results is shown. The values of $P_{\mathrm{LRA}}$ are predicted for neutron-deficient nuclei and superheavy nuclei. The approach was extended to describe the emission of light charged particles and clusters in both spontaneous and thermal-neutron-induced fission of heavy and superheavy nuclei.

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• Alpha decay
• Fission
• Nuclear reactions