Semiclassical Mean Field Theory of Quantum Tunneling in a Coupled System

Abstract

Heavy-ion fusion reactions at energies below the Coulomb barrier are typical examples of the quantum tunneling under influence of the intrinsic degrees of freedom. In order to calculate the barrier transmission probability it is necessary to have a framework which describes the classically allowed and the tunneling regions in a unified way. Another example which requires such a theory is the low energy nuclear reactions in laboratory experiments, where the bound electrons in the target nucleus yield screening effects on the potential barrier between the target and projectile nuclei. To this end, we develop a novel semiclassical theory of quantum tunneling under influence of other degrees of free-dom. The method relies upon the mean field variational principle to handle the coupling between the tunneling and the other degrees of freedom, and consistently describes the classically allowed and the tunneling regions. Also, the method can be applied to a wide range of problems with various degree of adiabaticity.