A hybrid model for fusion at deep sub-barrier energies

A hybrid model where the tunneling probability is estimated based on both sudden and adiabatic approaches has been proposed to understand the heavy ion fusion phenomena at deep sub-barrier energies. It is shown that under certain approximations, it amounts to tunneling through two barriers: one while overcoming the normal Coulomb barrier (which is of sudden nature) along the radial direction until the repulsive core is reached and thereafter through an adiabatic barrier along the neck degree of freedom while making transition from a di-nuclear to a mono-nuclear regime through shape relaxation. A general feature of this hybrid model is a steep fall-off of the fusion cross section, sharp increase of logarithmic derivative L(E) with decreasing energy and the astrophysical S-factor showing a maxima at deep sub-barrier energies particularly for near symmetric systems. The model can explain the experimental fusion measurements for several systems ranging from near symmetric systems like $^{58}Ni+^{64}Ni, ^{58}Ni+^{58}Ni$ and $^{58}Ni+^{69}Y$ to asymmetric one like $^{16}O+^{208}Pb$ where the experimental findings are very surprising. Since the second tunneling is along the neck co-ordinate, it is further conjectured that deep sub-barrier fusion supression may not be observed for the fusion of highly asymmetric projectile target combinations where adiabatic transition occurs automatically without any hindrance. The recent deep sub-barrier fusion cross section measurements of $^{6}Li+^{198}Pt$ system supports this conjecture.