Investigating multichannel quantum tunneling in heavy-ion fusion reactions with Bayesian spectral deconvolution

Excitations of colliding nuclei during a nuclear reaction considerably affect fusion cross sections at energies around the Coulomb barrier. It has been demonstrated that such channel coupling effects can be represented in terms of a distribution of multiple fusion barriers. I here apply a Bayesian approach to analyze the so-called fusion barrier distributions. This method determines simultaneously the barrier parameters and the number of barriers. I particularly investigate the ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ and ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ systems in order to demonstrate the effectiveness of the method. The present analysis indicates that the fusion barrier distribution for the former system is most consistent with three fusion barriers, even though the experimental data show only two distinct peaks.

Figure 1

Test function defined by Eq. (12). It is obtained with $B=60$ MeV, $R=11$ fm, $\hslash \mathrm{\Omega }=4.5$ MeV, and $\mathrm{\Delta }E=1.8$ MeV.

Figure 2

Free energy $F\left(K\right)=-lnZ\left(K\right)$ as a function of the number of effective barriers $K$ for hypothetical data generated with $K=2$.

Figure 3

(a) Free energy $F\left(K\right)=-lnZ\left(K\right)$ as a function of the number of effective barriers $K$ for the ${}^{16}\mathrm{O}+{}^{144}\mathrm{Sm}$ system. (b) Fusion cross sections for the same system. The solid line was obtained with the Bayesian spectral deconvolution with $K=3$. (c) Corresponding barrier distribution defined by $d^2\left(E{\sigma }_{\mathrm{fus}}\right)/d{E}^2$. The contribution of each test function is also shown by the dashed lines. The experimental data are from Ref. [13].

Figure 4

Same as Fig. 3, but for the ${}^{16}\mathrm{O}+{}^{154}\mathrm{Sm}$ system. Panels (b) and (c) were obtained with $K=5$.