The nuclear surface diffuseness effects on the alpha decay of heavy and super heavy nuclei

TL;DR

The study investigates how nuclear surface diffuseness (NSD) influences alpha-decay in heavy and super-heavy nuclei by modifying the proximity-potential framework with NSD through the reduced radius $ar{C}$ and central radii $C_i$. Using the WKB formalism, the total interaction potential $V_{ m tot}=V_C+V_ ext{4}+V_N$ is evaluated with NSD-adjusted nuclear terms from Zhang 2013 and Guo 2013 forms, leading to changes in barrier height and transmission probability. Across 300 nuclei with $Z=64$–$106$, NSD improves agreement with experimental half-lives, notably when both the curvature-radius and universal-function adjustments are included. In the SHN region, the Guo 2013 (C form) model provides reliable predictions, aligning with semi-empirical Royer and UDL estimates for $Z=120$–$126$, underscoring the practical utility of incorporating NSD in alpha-decay modeling for heavy systems.

Abstract

We select 300 different parent nuclei in the range Z from 64 to 106. The proximity potentials Zhang 2013 and Guo 2013 are employed to calculate the nuclear potential. The influence of the nuclear surface diffuseness is applied in the calculations of interaction potential between the emitted alpha particle and daughter nucleus through the reduced radius parameter. The systematic analysis of the radial behavior of interaction potential with and without the surface diffuseness effect reveals that these effects play decisive role in the calculation of nucleus-nucleus potential at the touching radius of the two interacting nuclei. We indicate that its influence decreases outside the touching configuration. In addition, our results reveal that the barrier penetration probability of the alpha particle through the barrier decreases by imposing the mentioned physical effects. It is worth noting that the calculated alpha-decay half-lives using the Zhang 2013 and Guo 2013 proximity potentials accompanied by the surface effects agree very well with the available experimental data. The theoretical halflives are calculated for 50 super-heavy nuclei using the modified forms of the Zhang 2013 and Guo 2013 models. The comparison with available experimental data and also with different empirical formulas demonstrates that the Guo 2013 model is suitable to deal with the alpha decay half-lives of SHN. Then the predictions of alpha decay half-lives for 65 SHN with Z from 120 to 126 are made by using Guo 2013 model with the surface effects. We found that there is a good agreement between our predicted half-lives and those obtained from semi-empirical formulas such as Royer and UDL.

Figures (9)

• Figure 1: (Colored online) The ratio $\frac{\bar{C}}{\bar{R}}$ (the central and sharp radii) as a function of the mass number of the $^4$He, $^8$Be, $^{12}$C, and $^{14}$C clusters of the $^{122}$294.
• Figure 2: (Colored online) The behavior of $\frac{V_{\rm tot}^{\bar{R}}}{V_{\rm tot}^{\bar{C}}}$ ratio as a function of radial distance $r$ (in fm) for $^4$He cluster ($^{199}$Rn decay). The touching point and saturation radius values are $R_T= 8.50$ fm and $R_S= 13.57$ fm, respectively, which are indicated by vertical dashed lines. The horizontal dashed line refers to the saturation value $\frac{V_{\rm tot}^{\bar{R}}}{V_{\rm tot}^{\bar{C}}}=1$.
• Figure 3: (Colored online) The extracted values of the saturation radius $R_S$ (fm) in terms of $A_d^{1/3}+A_{\alpha}^{1/3}$ for 300 alpha decays based on the Zhang 2013 potential model. The linear fit is shown by the red line.
• Figure 4: (Colored online) The total interaction potential $V_{\rm tot} (r)$ (in MeV) as a function of the radial distance $r$ (in fm) for alpha-decay of $^{219}$Fr$\rightarrow^{215}$At+$^{4}$He using (a) Zhang 2013 and (b) Guo 2013 potential models with and without the NSD effects. The black dashed line indicates the $Q_{\alpha}$-value. The black short dotted lines show the $R_S$ and $R_T$ values.
• Figure 5: (Colored online) Variation of the decimal logarithm of the alpha-decay half-life with the neutron number of the daughter nuclei $N_d$ for (a) Pu, (b) Rn and (c) Fr isotopic groups using Zhang 2013 (C form) (star) and Zhang 2013 (R form) (triangle) models. Experimental half-life data are shown with black circles. Also, the magic number $N=126$ is marked with a dashed line.