Influence of the Pauli exclusion principle on $\alpha$ decay

In this study, the effects of repulsive nucleon-nucleon interactions arising from the Pauli exclusion principle were examined regarding the half-lives of heavy even-even nuclei with $84\le Z\le 92$. The Pauli exclusion principle is applied to our investigations by renormalizing the nucleon-nucleon interactions according to the Bohr-Sommerfeld quantization condition. It is also applied to the double-folding (DF) formalism as a modification term by investigating the kinetic energy variation at the overlapping regions between the densities of the alpha and daughter nuclei. The standard deviation for the calculated half-lives from their corresponded experimental data is 0.340 for the renormalized DF formalism. Its value reduces to 0.309 for the DF formalism modified with the kinetic-energy contribution estimated by the extended Thomas-Fermi approach. The calculated $\alpha$-decay half-lives are more consistent with experimental data if the kinetic-energy contribution is associated with the DF formalism.

Figure 1

(a) The calculated $V_C\left(R\right), V_N\left(R\right)$, and kinetic energy, $K_E\left(R\right)$, typically for $\alpha$ and ${}^{208}\mathrm{Pb}$. (b) The dashed line is the M3Y total potential and the dotted line is the total potential with added kinetic energy. The solid horizontal line indicates the $Q_{\alpha }$ value for the ${}^{212}\mathrm{Po}$.

Figure 2

The solid line is the kinetic energy estimated by the ETF approach and the dashed line is the simulated double-folded integral with a $\delta$ function, typically for the overlapping of $\alpha$ and ${}^{208}\mathrm{Pb}$.

Figure 3

The kinetic-energy values for the overleaping $\alpha$ and daughter nuclei examined at $R=0$ with respect to the daughter neutron number.

Figure 4

The strength of the simulated double-folded integral with a $\delta$ function for the overleaping $\alpha$ and daughter nuclei adjusted at $R=0$ due to the kinetic energy.