Abstract
The inverse Kramers problem, i.e., a particle passing over the barrier of a metastable potential and then escaping from the potential well, can be applied to model many subjects such as nuclear and atom cluster fusions, molecular collision. We consider the metastable potential to be a parabolic potential linking smoothly with a harmonic potential, thus the staying dynamics of a particle in the metastable potential well is investigated semi-analytically. The analytical expression of time-dependent staying probability is obtained through a coarse graining scheme for the particle multi-passing process over the joint point of potentials. A combination of the Kramers rate formula for intermediate to long times with our theoretical results is in well agreement with the Langevin simulations. The staying probability at the crossover between our result and the Kramers formula may be used to improve the calculation of the fusion probability in superheavy nuclei synthesis.
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