Implementation of a microscopic nuclear potential in the coupled-channels calculations to study the fusion dynamics of oxygen-based reactions

We incorporate a microscopic relativistic nuclear potential obtained from the recently developed relativistic R3Y $NN$ potential in the coupled-channels code ccfull to study fusion dynamics. The R3Y $NN$ potential and the densities of interacting nuclei are obtained for the relativistic mean-field approach for the $\mathrm{NL}{3}^{*}$ parameter set. Note that the R3Y $NN$ potential can be expressed in terms of masses of the mesons and their couplings by considering the meson degrees of freedom within the relativistic mean field, which has a form similar to the widely used M3Y potential. We focused on the fusion cross sections for oxygen-based reactions with targets from different mass regions of the periodic table, i.e., ${}^{16}\mathrm{O}+{}^{24}\mathrm{Mg}, {}^{18}\mathrm{O}+{}^{24}\mathrm{Mg}, {}^{16}\mathrm{O}+{}^{148}\mathrm{Sm}, {}^{16}\mathrm{O}+{}^{176}\mathrm{Hf}, {}^{16}\mathrm{O}+{}^{176}\mathrm{Yb}, {}^{16}\mathrm{O}+{}^{182}\mathrm{W}$, and ${}^{16}\mathrm{O}+{}^{186}\mathrm{W}$. A comparison is also made with the cross sections calculated using the nuclear potential obtained from the traditional Woods-Saxon potential and the widely used M3Y $NN$ potential within ccfull. The coupled-channels calculations are performed with shape and rotational degrees of freedom to examine the fusion enhancement at below-barrier energies. It is observed from the calculations that the fusion cross sections obtained using the R3Y $NN$ potential with rotational degrees of freedom are found to be more consistent with the experimental data than those for the M3Y and Woods-Saxon potentials, mainly at below barrier energies.

Figure 1

The total interaction potential as a function of radial separation $r$ for ${}^{16}\mathrm{O}+{}^{24}\mathrm{Mg}, {}^{18}\mathrm{O}+{}^{24}\mathrm{Mg}$, and ${}^{16}\mathrm{O}+{}^{148}\mathrm{Sm}$ reactions calculated using the M3Y (dashed red lines) and R3Y (dotted blue lines) $NN$ potentials. The microscopic nuclear potential is further compared with the traditional WS (solid black line) potential. See the text for details.

Figure 2

The fusion cross sections as a function of $E_{\mathrm{c}.\mathrm{m}.}$ (MeV) for the Woods-Saxon potential (solid black line) and R3Y (dotted blue line) and M3Y (dashed red line) $NN$ interactions with the $\mathrm{NL}{3}^{*}$ parameter set using coupled-channels code. The corresponding cross section for the $4^{+}$ excited state for R3Y (double-dotted–dashed grey line) and M3Y(dashed-dotted red line) potentials along with the inclusion of ${\beta }_2$ and ${\beta }_4$ deformations. The calculated results are compared with the experimental data [55, 57] for ${}^{16}\mathrm{O}+{}^{24}\mathrm{Mg}, {}^{18}\mathrm{O}+{}^{24}\mathrm{Mg}$, and ${}^{16}\mathrm{O}+{}^{148}\mathrm{Sm}$ reactions. See the text for details.

Figure 3

Same as Fig. 2, but for ${\beta }_4<0$, namely reactions ${}^{16}\mathrm{O}+{}^{176}\mathrm{Hf}, {}^{16}\mathrm{O}+{}^{176}\mathrm{Yb}, {}^{16}\mathrm{O}+{}^{182}\mathrm{W}$, and ${}^{16}\mathrm{O}+{}^{186}\mathrm{W}$. The experimental data are taken from Refs. [9, 56, 58]. See the text for details.