Semiclassical theory of quantum tunneling in multidimensional systems

Abstract

classical method. Providing the coupling has a physically reasonable form factor, the coupling produces an enhancement in the tunneling rate. The enhancement becomes larger when the tunneling degree of freedom couples with a harmonic oscillator with lower frequency. The semiclassical method is found to be quite useful in situations where the coupled channel method becomes numerically difficult. The effect on quantum tunneling of the internal degrees of freedom has been much discussed recently' ' in connection with the large enhancement of subbarrier fusion cross sections found in heavy ion collisions. ' ' An interesting question in this respect is the relative roles of high- and low-frequency collective excitations of the individual nuclei. The problem is quite difficult to study by the numerical coupled channel methods, when many degrees of freedom are involved simultaneously and one deals with energies much below the barrier. We shall examine the problem using the influence functional formalism of Feynman's path integral method. This method conveniently clarifies the importance of the potential renormalization, and the decisive role of the functional form of the coupling to the internal motion. We compare the results of the path integral method with those of coupled channel calculations to verify the accuracy of the path integral method.