Role of mass renormalization in adiabatic quantum tunneling

We introduce an adiabatic expansion to derive a formula for a macroscopic quantum tunneling probability that takes the mass renormalization due to the coupling to fast environmental degrees of freedom into account. The formula is applied to studying the effects of nuclear vibrational excitations on the fusion cross section in heavy-ion collisions at energies below the Coulomb barrier. It is shown that mass renormalization plays an important and useful role to discuss the effects of vibrational excitations of moderate energy. Also a general proof is given to show that the renormalized part of the effective mass appearing in our formula is the cranking mass.