α-nucleus potential for α-decay and sub-barrier fusion

The set of parameters for α-nucleus potential is derived by using the data for both the α-decay half-lives and the fusion cross sections around the barrier for reactions $\alpha +$${}^{40}\mathrm{Ca}$, $\alpha +$${}^{59}\mathrm{Co}$, and $\alpha +$${}^{208}\mathrm{Pb}$. The α-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated α-decay half-lives and the fusion cross sections agreed well with the data. Fusion reactions between α particles and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.

Figure 1

(Color online) (Left panels) The experimental (circles) [13, 14, 18] and theoretical (crosses) values of $\log {}_{10}(T_{1/2})$ for α decays in even-even (e-e), even-odd (e-o), odd-even (o-e), and odd-odd (o-o) parent nuclei. (Right panels) Dots represent the difference between the experimental and theoretical values of $\log {}_{10}(T_{1/2})$ for α decays in even-even (e-e), even-odd (e-o), odd-even (o-e), and odd-odd (o-o) parent nuclei.

Figure 2

(Color online) The experimental and theoretical values of $\log {}_{10}(T_{1/2})$ for superheavy region. Squares with error bars are data from Refs. 13, 18, circles are theoretical values obtained by using Eqs. (1, 2, 3, 4, 5, 6, 7, 8, 9) and (11, 12, 13, 14, 15, 16, 17), plus and cross signs are the values obtained by using empirical relations from Refs. 7 and [28] respectively, and stars are the results of calculations from Ref. 18.

Figure 3

(Color online) The experimental and theoretical values of fusion cross sections for reactions $\alpha +$${}^{40}\mathrm{Ca}$, $\alpha +$${}^{59}\mathrm{Co}$, and $\alpha +$${}^{208}\mathrm{Pb}$. Squares are the data for the reaction $\alpha +$${}^{208}\mathrm{Pb}$ from Ref. 41, circles are the data for the reaction $\alpha +$${}^{59}\mathrm{Co}$ from Ref. 40, up- and down-pointing triangles are the data for the reaction $\alpha +$${}^{40}\mathrm{Ca}$ from Refs. 39 and [38], respectively. Lines are results of calculations obtained by using Eqs. (5, 6, 7, 8, 9, 10, 11) and (14, 15, 16, 17, 18, 19), and stars are the result of calculations using CCFULL code [35].

Figure 4

(Color online) The nuclear part of potentials between α particles and ${}^{40}\mathrm{Ca}$ or ${}^{208}\mathrm{Pb}$. The solid, dash, dots, dash-dot, and dash-dot-dot lines are evaluation results using our model and parametrizations from Refs. 2, 5, 7, 9, respectively.

Figure 5

(Color online) The fusion cross section for $\alpha +$${}^{252}\mathrm{Cf}={}^{256}\mathrm{Fm}$ reactions. The solid and dashed lines are fusion cross sections in the cases of deformed and spherical shape of ${}^{252}\mathrm{Cf}$ respectively. The square marks the collision energy at which ${}^{256}\mathrm{Fm}$ is formed in the ground state. The triangle and diamond are threshold energies for one- and two- neutron emissions from ${}^{256}\mathrm{Fm}$, respectively.