Universal damping mechanism of quantum vibrations in deep sub-barrier fusion reactions

We demonstrate the damping of quantum octupole vibrations near the touching point when two colliding nuclei approach each other in the mass-asymmetric ${}^{16}\mathrm{O}$ + ${}^{208}\mathrm{Pb}$ system, for which the strong fusion hindrance was clearly observed. We, for the first time, apply the random-phase approximation method to the heavy-mass asymmetric dinuclear system to calculate the transition strength $B$($E3)$ as a function of the center-of-mass distance. The obtained $B(E3)$ strengths are substantially damped near the touching point, because the single-particle wave functions of the two nuclei strongly mix with each other and a neck is formed. The energy-weighted sums of $B(E3)$ are also strongly correlated with the damping factor, which is phenomenologically introduced in the standard coupled-channel calculations to reproduce the fusion hindrance. This strongly indicates that the damping of the quantum vibrations universally occurs in the deep sub-barrier fusion reactions.

Figure 1

Nilsson diagram for the ${}^{16}\mathrm{O}$ + ${}^{208}\mathrm{Pb}$ system as a function of $R$. The light gray (red) thick lines represent the occupied $p_{1/2}$ and $p_{3/2}$ states in ${}^{16}\mathrm{O}$. The dark gray (blue) thick solid lines show the occupied states in ${}^{208}\mathrm{Pb}$. The gray area indicates the overlap region of the colliding nuclei. The arrows represent the main particle-hole excitations constituting the RPA modes.

Figure 2

Contour maps of the proton transition densities and current distributions for the first excited $3^{-}$ states of ${}^{16}\mathrm{O}$ and ${}^{208}\mathrm{Pb}$ at $R=20$ and 10.73 fm. The contour lines correspond to multiples of 0.01 and $0.005 {\mathrm{fm}}^{-2}$ for ${}^{16}\mathrm{O}$ and ${}^{208}\mathrm{Pb}$, respectively. The arrows represent the current density. The currents and colors are normalized at $R=20$ fm in individual nuclei. The (red) thick solid circles indicate the half depth of the mean-field potential.

Figure 3

Energy-weighted sums of $B(E3)$ for (a) ${}^{16}\mathrm{O}$ and (b) ${}^{208}\mathrm{Pb}$ as functions of $R$. The solid circles show the results of the RPA calculations. The dashed curves represent the damping factor, which well reproduces the experimental data of the fusion cross section for ${}^{16}\mathrm{O}$ + ${}^{208}\mathrm{Pb}$ taken from Ref. [11]. The gray area indicates the overlap region of the colliding nuclei.

Figure 4

Density distributions of the $p_{1/2}$ and $d_{5/2}$ states originally belonging to ${}^{16}\mathrm{O}$ at $R=20$ fm and their evolutions at $R=11.65$ fm. The (red) thick solid circles indicate the half depth of the mean-field potential. The contour lines correspond to multiples of $0.0015 {\mathrm{fm}}^{-3}$. The colors are normalized at $0.01 {\mathrm{fm}}^{-3}$.