Systematic study of the isotopic behavior of the fusion cross section at energies near and below the fusion barrier using the proximity formalism

The isotopic behavior of the fusion cross sections and barrier curvature at energies near and below the barrier are explored using the proximity formalism. For this purpose, various versions of the proximity potentials are used to calculate the nuclear part of the interaction potential. Our study has been restricted to the isotopic systems which obey the condition of $0.5\le N/Z\le 1.6$ for their compound nuclei. The obtained results show that the barrier curvature and the fusion cross section follow a similar behavior at near- and below-barrier energies. In fact, these quantities decrease nonlinearly (second order) with the addition of a neutron. In the present study, the energy dependence of the fusion cross sections is also discussed for the considered isotopic systems.

Figure 1

Variation trend of $\hslash \omega$ as a function of $(N/Z-1)$ based on the selected potentials (a) AW 95, (b) Bass 80, (c) Denisov DP, and (d) Prox.2010. In each panel, the dotted and dash-dotted lines are related to $\Delta \hslash \omega (\%)$ values in $0.5\le N/Z\le 1$ and $1\le N/Z\le 1.6$ regions, respectively. The solid curves show a nonlinear fitting of the calculated values in the whole range of $0.5\le N/Z\le 1.6$.

Figure 2

Percentage difference of the fusion cross section $\Delta {\sigma }_{\mathrm{fus}}(\%)$ as a function of $(N/Z-1)$ based on the potentials (a) AW 95, (b) Bass 80, (c) Denisov DP, and (d) Prox.2010 for $E_{\mathrm{c}.\mathrm{m}.}=0.95V_b$. The dotted and dash-dotted lines show a linear fitting of the function $\Delta {\sigma }_{\mathrm{fus}}(\%)$ in $0.5\le N/Z\le 1$ and $1\le N/Z\le 1.6$ regions, respectively. The solid curves show a non-linear fitting of the calculated values in the whole range of $0.5\le N/Z\le 1.6$.

Figure 3

Same as Fig. 2, but for $E_{\mathrm{c}.\mathrm{m}.}=0.9V_b$.

Figure 4

Behaviors of the constant coefficients (a) ${\beta }_1$, (b) ${\beta }_2$, (c) ${\beta }_1^{*}$, and (d) ${\beta }_2^{*}$ as a function of the center-of-mass energy $E_{\mathrm{c}.\mathrm{m}.}$. The center of mass energy is shown in units of $V_b$ (barrier height).