Two-body dissipation effect in nuclear fusion reactions

Friction coefficients for the fusion reaction ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}\to {}^{32}\mathrm{S}$ are extracted based on both the time-dependent Hartree-Fock and the time-dependent density matrix methods. The latter goes beyond the mean-field approximation by taking into account the effect of two-body correlations, but in practical simulations of fusion reactions we find that the total energy is not conserved. We analyze this problem and propose a solution that allows for a clear quantification of dissipative effects in the dynamics. Compared to mean-field simulations, friction coefficients in the density-matrix approach are enhanced by about $20\%$. An energy dependence of the dissipative mechanism is also demonstrated, indicating that two-body collisions are more efficient at generating friction at low incident energies.

Figure 1

Total energy of the fusion system ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}\to {}^{32}\mathrm{S}$ at incident $E_{\mathrm{c}.\mathrm{m}.}=40\mathrm{MeV}$ as a function of time $t$. The calculation is performed using the ${\mathrm{TDDM}}^{\mathrm{P}}$ model. The dashed blue line indicates the constant initial energy for reference. This figure is obtained with $N_{\text{max}}=60$.

Figure 2

Collective potential defined in Eq. (15) as a function of relative distance, $R$, for the fusion path in the reaction ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}\to {}^{32}\mathrm{S}$. The solid and dotted lines indicate the results of TDDM and TDHF, respectively. The blue (lower) and red (upper) lines indicate the results at incident energies of $E_{\mathrm{c}.\mathrm{m}.}=20\mathrm{MeV}$ and $E_{\mathrm{c}.\mathrm{m}.}=40\mathrm{MeV}$, respectively. The green (dashed) line shows the asymptotic Coulomb potential, $64e^2/R$, for reference.

Figure 3

Solid line: the total energy of ${}^{16}\mathrm{O}$ as it evolves from the Hartree-Fock state to the TDDM correlated state by switching on the residual interaction adiabatically. Dashed line: the mean-field energy in the same conditions. This figure is obtained with $N_{\text{max}}=30$.

Figure 4

(a) Friction coefficient $\gamma$ as a function of $R$ for the fusion reaction ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}\to {}^{32}\mathrm{S}$ at $E_{\mathrm{c}.\mathrm{m}.}=40\mathrm{MeV}$. Different line styles indicate results calculated with different $N_{\text{max}}$. (b) $\beta$ parameters in the same conditions.

Figure 5

Intrinsic energy as a function of $R$. The solid and dotted lines indicate the results of TDDM and TDHF simulations, respectively. The blue (upper) and red (lower) lines indicate the results at incident energies of $E_{\mathrm{c}.\mathrm{m}.}=20\mathrm{MeV}$ and $E_{\mathrm{c}.\mathrm{m}.}=40\mathrm{MeV}$, respectively.

Figure 6

(a) Friction coefficient $\gamma$ for ${\mathrm{TDDM}}^{\text{P}}$ (solid lines) and TDHF (dotted lines) simulations as a function of $R$. Blue (upper) and red (lower) lines indicate the results at incident energies of $E_{\mathrm{c}.\mathrm{m}.}=20\mathrm{MeV}$ and $E_{\mathrm{c}.\mathrm{m}.}=40\mathrm{MeV}$, respectively. (b) $\beta$ parameters in the same conditions.