Unified Royer law revision for alpha-decay half-lives: shell corrections, pairing,and orbital-angular-momentum

TL;DR

This work introduces a unified four-parameter revision of the Royer law for alpha-decay half-lives by incorporating shell-correction energy, a pairing term, and an angular-momentum term. The model reduces the parameter count from 12 to 4 and achieves a substantial improvement in predictive accuracy, with the RMSD dropping from 0.520 to 0.279 across 550 data points. The shell term mitigates discrepancies near the N=126 shell closure, while the l(l+1) term captures centrifugal hindrance, enabling accurate treatment of both favored and unfavored decays within a single framework. The approach also demonstrates extrapolation capability to superheavy nuclei (Z=117–120) and suggests possible neutron subshell structures at N_d = 178, 184, 196, supporting broader applications in nuclear-structure predictions.

Abstract

The Royer law is a widely used empirical relation for calculating alpha-decay half-lives; however, it requires 12 parity-dependent parameters.It exhibits systematic deviations near the shell closure. We propose an improved Royer law by adding a shell-correction term, an odd-even pairing indicator, and an orbital-angular-momentum contribution. This unified framework reduces the number of free parameters to just four, leading to significant improvements in accuracy. The root-mean-square deviation across 550 experimental data points decreases from 0.520 to 0.279, corresponding to a 66.7% reduction in parameters and 46.3% improvement in accuracy. Using this refined formalism, we predict alpha-decay half-lives for superheavy nuclei with atomic numbers.

Figures (5)

• Figure 1: (a) The discrepancy between experimental and calculated logarithmic $\alpha$-decay half-lives using Eq. (\ref{['Eq1']}) for even-even polonium isotopes is plotted against the neutron number $N$. (b) Similar to (a), except that the ordinate represents the variation of shell-correction energy ${E}_{\rm sh}$ with the neutron number, with calculated values taken from Eq. (\ref{['Eq3']}). The dashed line indicates the neutron number $N = 126$. The variation trends and structural features of the two are highly similar.
• Figure 2: (Color online) Comparison of the differences between experimental and theoretical $\alpha$-decay half-lives calculated by Eq. (\ref{['Eq1']}) and Eq. (\ref{['Eq2']}) for four categories of $l=0$ nuclei: (a) even-even (190 nuclei), (b) even-odd (88 nuclei), (c) odd-even (71 nuclei), and (d) odd-odd (57 nuclei), plotted against neutron number $N$. The RMSD $\sigma$ is indicated in parentheses after each formula.
• Figure 3: (Color online) Comparison of deviations between experimental and calculated $\alpha$-decay half-lives: (a) 406 favored $\alpha$-decays with angular-momentum $l = 0$; (b) 144 unfavored $\alpha$-decays with $l \neq 0$; (c) Full dataset of 550 nuclei.
• Figure 4: Systematic behavior of $\log_{10}\gamma^2$ as a function of the fragmentation potential $V_c - Q$. Panels (a) to (d) correspond to the neutron-number regions: (a) $N \leq 82$, (b) $82 < N \leq 126$, (c) $126 < N \leq 152$, and (d) $N > 152$. Black squares represent values derived from experimental half-lives, and red circles denote results calculated using the improved Royer law in Eq. (\ref{['Eq2']}). The blue lines indicate the linear fitting of the experimental data.
• Figure 5: (Color online) The $\log_{10} T_{1/2}$ values of $Z=117-120$ isotopes versus neutron number of daughter nucleus $N_d$. The open circles, stars, and the solid squares denote the prediction results with the improved Royer law (Eq. (\ref{['Eq2']})), the original revision (Eq. (\ref{['Eq1']})), and the DZR model (Ref. 2020gyy). Experimental data (solid circles) for $^{293,294}\mathrm{Ts}$ and $^{294}\mathrm{Og}$ are included for comparison. The vertical dashed lines indicate the possible existence of magic numbers or neutron subshell structures at neutron numbers $N_d = 178$, 184, and 196.