Tunneling near the peaks of potential barriers: Consequences of higher-order Wentzel-Kramers-Brillouin corrections

Journal Article · Sun May 15 04:00:00 EDT 1988 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.37.3674· OSTI ID:5223648

Will, C M; Guinn, J W

We derive the quantum-mechanical tunneling transmission coefficient for energies near the peak of a general potential barrier, to fourth order in the Wentzel-Kramers-Brillouin (WKB) approximation, using a method based on an eighth-order Taylor expansion of the potential near the peak. The result agrees with contour-integral formulations of WKB tunneling. For the Poeschl-Teller potential the WKB series converges rapidly to the known exact transmission coefficient. Higher-order WKB corrections may be important in attempts to determine the internuclear potential by inversion using low-energy fusion cross-section data.

• Research Organization: McDonnell Center for the Space Sciences and Department of Physics, Washington University, St. Louis, Missouri 63130
• OSTI ID: 5223648
• Journal Information: Phys. Rev. A; (United States), Journal Name: Phys. Rev. A; (United States) Vol. 37:10; ISSN PLRAA
• Country of Publication: United States
• Language: English

Related Subjects

653003 -- Nuclear Theory-- Nuclear Reactions & Scattering
657002* -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
CORRECTIONS
HEAVY ION FUSION REACTIONS
MECHANICS
NUCLEAR REACTIONS
POTENTIALS
QUANTUM MECHANICS
TUNNEL EFFECT
WKB APPROXIMATION