Improved double-folding $\alpha$-nucleus potential by including nuclear medium effects

The nuclear medium effect in $\alpha$ decay is introduced into the microscopic double-folding model to construct an improved $\alpha$-nucleus potential. Under the local density approximation, the $\alpha$-cluster density distribution is considered to vary with the surrounding matter density as a result of the medium effect. The density-dependence of the $\alpha$ cluster is incorporated by the width parameter of the Gaussian function and constrained by the critical features derived from previous microscopic studies. The influence of the medium effect to the geometry of the $\alpha$-nucleus potential is studied by comparing with the conventional double-folding potential. To examine the improved potential, the $\alpha$-decay half-lives and preformation factors of even-even spherical nuclei are calculated and compared with experimental data. With the $\alpha$-decay data being well explained, it is concluded that the inclusion of the nuclear medium effect contributes to an improved double-folding $\alpha$-nucleus potential, which incorporates more details of the $\alpha$-decay process.

Figure 1

The variation of the $\alpha$-cluster density distribution with increasing overlap of the $\alpha$ and daughter clusters. The horizontal axis $R$ represents the center-of-mass position of the $\alpha$ cluster. The blue dashed line and the black dot-dashed line are the density distributions of the $\alpha$ and the daughter clusters, respectively. The red solid line shows the variation of $\beta \left(R\right)$.

Figure 1

The variation of the $\alpha$-cluster density distribution with increasing overlap of the $\alpha$ and daughter clusters. The horizontal axis $R$ represents the center-of-mass position of the $\alpha$ cluster. The blue dashed line and the black dot-dashed line are the density distributions of the $\alpha$ and the daughter clusters, respectively. The red solid line shows the variation of $\beta \left(R\right)$.

Figure 2

The effect of the width parameter $\beta$ on the peak density ${\rho }_{2,s}$ of the $\alpha$-cluster density distribution. The legend shows the parameters $(a_1,a_2)$ in the Eq. (13). Both $\beta$ and ${\rho }_{2,s}$ smoothly decrease with increasing matter density. The minimum values of $\beta$ and ${\rho }_{2,s}$ are reached at the saturation density which corresponds to the intercepts with the right border. The results indicates that the variation of ${\beta }_{min}$ only slightly affects the $\alpha$-cluster density distribution.

Figure 2

The effect of the width parameter $\beta$ on the peak density ${\rho }_{2,s}$ of the $\alpha$-cluster density distribution. The legend shows the parameters $(a_1,a_2)$ in the Eq. (13). Both $\beta$ and ${\rho }_{2,s}$ smoothly decrease with increasing matter density. The minimum values of $\beta$ and ${\rho }_{2,s}$ are reached at the saturation density which corresponds to the intercepts with the right border. The results indicates that the variation of ${\beta }_{min}$ only slightly affects the $\alpha$-cluster density distribution.

Figure 3

The double-folding $\alpha$-nucleus potential of the $\alpha +{}^{208}\mathrm{Pb}$ system for the $\alpha$ decay of ${}^{212}\mathrm{Po}$. The Coulomb potential $V_C$, the nuclear potential $V_N$, and the total potential $V$ are distinguished by different colors. The potentials with and without the medium effect are, respectively, denoted by the solid and dashed lines. The interior and the surface region of the $\alpha$-nucleus potentials are separated by the second turning point $R_2$.

Figure 3

The double-folding $\alpha$-nucleus potential of the $\alpha +{}^{208}\mathrm{Pb}$ system for the $\alpha$ decay of ${}^{212}\mathrm{Po}$. The Coulomb potential $V_C$, the nuclear potential $V_N$, and the total potential $V$ are distinguished by different colors. The potentials with and without the medium effect are, respectively, denoted by the solid and dashed lines. The interior and the surface region of the $\alpha$-nucleus potentials are separated by the second turning point $R_2$.

Figure 4

(a) Comparison of the calculated half-lives with experimental data. (b) Variation of the $\alpha$-preformation factors with mass number. The medium effect mainly leads to a general decrease in the magnitude of $P_{\alpha }$ factors, while a reasonable trend of the variation is maintained.

Figure 4

(a) Comparison of the calculated half-lives with experimental data. (b) Variation of the $\alpha$-preformation factors with mass number. The medium effect mainly leads to a general decrease in the magnitude of $P_{\alpha }$ factors, while a reasonable trend of the variation is maintained.