Improved WKB approximation for quantum tunneling: Application to heavy ion fusion

Abstract

In this paper we revisit the one-dimensional tunneling problem. We consider Kemble's approximation for the transmission coefficient. We show how this approximation can be extended to above-barrier energies by performing the analytical continuation of the radial coordinate to the complex plane. We investigate the validity of this approximation by comparing their predictions for the cross section and for the barrier distribution with the corresponding quantum mechanical results. We find that the extended Kemble's approximation reproduces the results of quantum mechanics with great accuracy.

arXiv comment8 pages, 6 figures, in press, in European. Phys. Journal A (2017)

References in corpus (4)

• A program for coupled-channels calculations with all order couplings for heavy-ion fusion reactions
• Subbarrier fusion reactions and many-particle quantum tunneling
• Large-angle scattering and quasi-elastic barrier distributions
• Reaction Cross Section in Heavy-Ion Collisions

Cited by in corpus (7)

• Coupled-channels calculations for nuclear reactions: from exotic nuclei to superheavy elements
• The total reaction cross section of heavy-ion reactions induced by stable and unstable exotic beams: The low-energy regime
• Approximate transmission coefficients in heavy ion fusion
• Theoretical considerations about heavy-ion fusion in potential scattering
• Applicability of the Wong formula for fusion cross sections from light to heavy systems
• Generalizing Fowler-Nordheim Tunneling Theory for an Arbitrary Power Law Barrier
• Study of Cluster Structures in Nuclei through the Ratio Method. A Tribute to Mahir Hussein