Quantum effect in the diffusion along a potential barrier: Comments on the synthesis of superheavy elements

Abstract

We discuss a quantum effect in the diffusion process by developing a theory, which takes the finite curvature of the potential field into account. The transport coefficients of our theory satisfy the well-known fluctuation-dissipation theorem in the limit of Markovian approximation in the cases of diffusion in a flat potential and in a potential well. For the diffusion along a potential barrier, the diffusion coefficient can be related to the friction coefficient by an analytic continuation of the fluctuation-dissipation theorem for the case of diffusion along a potential well in the asymptotic time, but contains strong non-Markovian effects at short times. By applying our theory to the case of realistic values of the temperature, the barrier curvature, and the friction coefficient, we show that the quantum effects will play significant roles in describing the synthesis of superheavy elements, i.e., the evolution from the fusion barrier to the conditional saddle, in terms of a diffusion process. We especially point out the importance of the memory effect, which increases at lower temperatures. It makes the net quantum effects enhance the probability of crossing the conditional saddle.

12 pages, 3 figures, accepted for publication in Phys. Rev. C

References in corpus (4)

• Two-Step Model of Fusion for Synthesis of Superheavy Elements
• Diffusion over a saddle with a Langevin equation
• Influence of microscopic transport coefficients on the formation probabilities for super-heavy elements
• Dynamics of barrier penetration in thermal medium: exact result for inverted harmonic oscillator

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• Transient and quasi-stationary dissipative effects in the fission flux across the barrier in 1 A GeV 238U on deuterium reactions
• Sub-barrier capture with quantum diffusion approach: actinide-based reactions
• Quantum Statistical Effects on Fusion Dynamics of Heavy-Ions
• Quantum Monte-Carlo method applied to Non-Markovian barrier transmission
• Neutron pair transfer in sub-barrier capture process
• Non-Markovian diffusion over a parabolic potential barrier: influence of the friction-memory function
• Threshold energy for sub-barrier fusion hindrance phenomenon
• Optimal path of diffusion over the saddle point and fusion of massive nuclei
• Quasifission at extreme sub-barrier energies