Fusion cross section for Ni-based reactions within the relativistic mean-field formalism

In this theoretical study, we establish an interrelationship between the nucleon-nucleon potential and the nuclear fusion reaction cross sections at low energies. The axially deformed self-consistent relativistic mean field with nonlinear $\mathrm{NL}{3}^{*}$ and TM1 force parameters is used to calculate the density distributions of the projectile and target nuclei, which are further used in the double-folding approach to obtain the nucleus-nucleus interaction potentials. The Wong formula is used to estimate the fusion cross section and barrier distributions from the nucleus-nucleus optical potential for Ni-based systems, which are known for fusion hindrance phenomena. The results of the application of the so-obtained nucleus-nucleus potential for the fusion cross section from the recently developed relativistic effective NN interactions (R3Y) are compared with the well-known, phenomenological M3Y potential. The effect of the nucleon-nucleon interaction potential on the fusion cross section, in terms of the nuclear interaction potential, is included in the present analysis. We found relatively good results from R3Y interactions below the barrier energies as compared to the M3Y potential concerning the experimental data.

Figure 1

The relativistic (R3Y) NN-interaction potential for NL-HS (linear), $\mathrm{NL}{3}^{*}$ (nonlinear $\sigma$ field), and TM1 (nonlinear $\sigma$ and $\omega$ fields) force parameters along with the phenomenological M3Y potential. See the text for details.

Figure 2

The RMF ($\mathrm{NL}{3}^{*}$ and TM1), proton (${\rho }_Z$), neutron (${\rho }_N$), and total (${\rho }_T$) density distributions for ${}^{58,64}\mathrm{Ni}$ and ${}^{124,132}\mathrm{Sn}$ nuclei. See the text for details.

Figure 3

The total nucleus-nucleus optical potential $V_T\left(R\right)$ and the individual contributions [the nuclear $V_n\left(R\right)$ (M3Y) and $V_n\left(R\right)$ (R3Y) for $\mathrm{NL}{3}^{*}$ and TM1 parameter sets and the Coulomb $V_C\left(R\right)$ potential] as a function of radial separation $R$ for ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$. See the text for details.

Figure 4

Fusion-evaporation cross section as a function of center-of-mass energy $E_{\mathrm{c}.\mathrm{m}.}$, calculated by using the Wong formula for R3Y for $\mathrm{NL}{3}^{*}$ (solid line), TM1 (dotted line), M3Y (dashed line) NN interactions along with the corresponding cross section using the $\ell$-summed Wong formula and compared with experimental data for ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$ [40]. See the text for details.

Figure 5

Same as for Fig. 4, but for the reaction ${}^{58}\mathrm{Ni}+{}^{124}\mathrm{Sn}$. The experimental data are taken from Refs. [37, 41, 42]. See the text for details.

Figure 6

Same as for Fig. 4, but for the reaction ${}^{58}\mathrm{Ni}+{}^{132}\mathrm{Sn}$. The experimental data are taken from Refs. [43]. See the text for details.

Figure 7

Same as for Fig. 4, but for the reaction ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$. The experimental data are taken from Ref. [34]. See the text for details.

Figure 8

Same as for Fig. 4, but for the reaction ${}^{64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$. The experimental data are taken from Refs. [35, 36, 37]. See the text for details.

Figure 9

Same as for Fig. 4, but for the reaction ${}^{64}\mathrm{Ni}+{}^{132}\mathrm{Sn}$. The experimental data are taken from Refs. [38, 39]. See the text for details.

Figure 10

The barrier distributions for the reactions (a) ${}^{58}\mathrm{Ni}+{}^{58}\mathrm{Ni}$, (b) ${}^{58}\mathrm{Ni}+{}^{124}\mathrm{Sn}$, (c) ${}^{58}\mathrm{Ni}+{}^{132}\mathrm{Sn}$, (d) ${}^{64}\mathrm{Ni}+{}^{64}\mathrm{Ni}$, (e) ${}^{64}\mathrm{Ni}+{}^{124}\mathrm{Sn}$, and (c) ${}^{64}\mathrm{Ni}+{}^{132}\mathrm{Sn}$, as a function of the center-of-mass energy. The experimental data are taken from Refs. [34, 35, 36, 37, 38, 39, 40, 41, 42, 43]. See the text for details.