Role of microscopic temperature-dependent binding energies in the decay of ${}^{32}\mathrm{Si}^{*}$ formed in the ${}^{20}\mathrm{O}+{}^{12}\mathrm{C}$ reaction

The investigation of fusion reactions involving light neutron-rich exotic nuclei is of paramount significance to understand nucleosynthesis in astrophysical scenarios. It is also estimated as a possible heat source to ignite ${}^{12}\mathrm{C}+{}^{12}\mathrm{C}$ reaction and production of x-ray superbursts from accreting neutron star. Recently, the fusion of neutron-rich ${}^{20}\mathrm{O}$ with ${}^{12}\mathrm{C}$ target has been studied with measurement of fusion cross-section $\left({\sigma }_{\text{fus}}\right)$. Bass model under predicts the ${\sigma }_{\text{fus}}$ and time-dependent Hartree-Fock model also fails to explain the experimental data. To explicate the same, the investigation of ${}^{20}\mathrm{O}+{}^{12}\mathrm{C}$ reaction at near barrier energies has been made within quantum mechanical fragmentation-based dynamical cluster-decay model (DCM). Within DCM, the fragmentation potential comprises temperature-dependent Coulomb, nuclear and centrifugal potentials, along with temperature-dependent binding energies (T.B.E.) calculated within the macroscopic approach of Davidson mass formula. Recently, we have explored the temperature-dependence of different nuclear properties and nuclear symmetry energy within microscopic relativistic mean-field (RMF) theory [M. Kaur et al., Nucl. Phys. A 1000, 121871 (2020)]. In the present work, we inculcate the microscopic T.B.E. from RMF theory within DCM and investigate the structure of fragmentation potential for ${}^{32}\mathrm{Si}^{*}$ formed in ${}^{20}\mathrm{O}+{}^{12}\mathrm{C}$ reaction, comparatively for macroscopic (mac) and microscopic (mic) T.B.E. obtained from Davidson mass formula and RMF theory, respectively. The structure and magnitude of fragmentation potential are found to change drastically/notably along with a change in energetically favored/minimized fragments for both choices of T.B.E. The $\alpha$ particles $({}^4\mathrm{He}$, ${}^5\mathrm{He})$ are favored at lower angular momenta in fragmentation profile for mic T.B.E. case only, which is in the agreement with predictions of statistical model results. This change in the nuclear structure embodied via fragmentation potential energy carries its imprints in the preformation probability $P_0$ of different fragments and affects the contribution of individual light-charged particle (LCP) channel in the ${\sigma }_{\text{fus}}$. A comparison of the relative cross-section of different LCP channels toward ${\sigma }_{\text{fus}}$ is quite different for both cases of T.B.E. The cross-section of ${}^2\mathrm{H}$ and ${}^4\mathrm{He}$ LCP channels is relatively enhanced for mic T.B.E. compared to mac T.B.E. Among different LCP channels, the ${}^5\mathrm{He}$ channel is the major contributor in ${\sigma }_{\text{fus}}$, which is in line with the results of the statistical EVAPOR model. The DCM-calculated ${\sigma }_{\text{fus}}$ is in agreement with the experimental data.

Figure 1

Fragmentation potential V (MeV) in the decay of ${}^{32}\mathrm{Si}$ at $T=0$ MeV using (a) Davidson formula-based macroscopic (mac) B.E. and (b) RMF theory-based microscopic (mic) B.E.

Figure 2

Mass-dependence of fragmentation potential V (MeV) in the decay of ${}^{32}\mathrm{Si}^{*}$ formed at $T=3.09$ MeV at $\ell$ = 0 $\hslash$ (left panel) and ${\ell }_{\text{max}}$ value (right panel) using (a, c) Davidson formula-based macroscopic T.B.E. and (b, d) RMF theory-based microscopic T.B.E.

Figure 3

The macroscopic and microscopic binding energies (B.E.) for some isobars with mass number $A=10$, 14, 18, 22, 26, 30 at $T=0$ MeV and 3.09 MeV obtained using Davidson formula and RMF theory, respectively.

Figure 4

Preformation probability $P_0$ of different fragments in the decay of ${}^{32}\mathrm{Si}^{*}$ formed at $T=3.09$ MeV at $\ell$ = 0 $\hslash$ (left panel) and ${\ell }_{\text{max}}$ value (right panel) using (a, c) Davidson formula-based macroscopic T.B.E. and (b, d) RMF theory-based microscopic T.B.E.

Figure 5

Same as Fig. 4 but for replaced light-charged particles (LCP).

Figure 6

Angular momentum dependence of preformation probability $P_0$ of LCP for ${}^{32}\mathrm{Si}^{*}$ nuclear system formed at $T=3.09$ MeV for (a) mac T.B.E. and (b) mic T.B.E. case.

Figure 7

Scattering potential for the emission of ${}^3\mathrm{H}$, ${}^4\mathrm{He}$, ${}^5\mathrm{He}$ with complimentary ${}^{29}\mathrm{Al}$, ${}^{28}\mathrm{Mg}$, ${}^{27}\mathrm{Mg}$ channels, respectively, in the decay of ${}^{32}\mathrm{Si}^{*}$ nuclear system at $T=3.09$ MeV.

Figure 8

(a) Summed up preformation probability $\mathrm{\Sigma }{P}_0$ and (b) summed up cross-section $\mathrm{\Sigma }\sigma$ of different LCP channels in the decay of ${}^{32}\mathrm{Si}^{*}$ nuclear system formed at T = 3.09 using mac and mic T.B.E.