Eur. Phys. J. A (2017) 53: 34
https://doi.org/10.1140/epja/i2017-12225-6

Regular Article - Theoretical Physics

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

¹ Departamento de Engenharia Nuclear, Escola Politécnica, Universidade Federal do Rio de Janeiro, C.P. 68529, 21941-909, Rio de Janeiro, RJ, Brazil
² École CentraleSupélec, Plateau de Moulon, 3 rue Joliot-Curie, 91192, Gif-sur-Yvette, France
³ Paris Saclay, Espace Technologique, Bat. Discovery - RD 128 - 2e t., 91190, Saint-Aubin, France
⁴ Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, Rio de Janeiro, Brazil
⁵ Instituto de Física, Universidade Federal Fluminense, Av. Litoranea s/n, Gragoatá, 24210-340, Niterói, RJ, Brazil
⁶ Instituto de Estudos Avançados, Universidade de São Paulo, C.P. 72012, 05508-970, São Paulo, SP, Brazil
⁷ Instituto de Física, Universidade de São Paulo, C.P. 66318, 05314-970, São Paulo, SP, Brazil
⁸ Departamento de Física, Instituto Tecnológico de Aeronáutica, CTA, São José dos Campos, São Paulo, SP, Brazil

^* e-mail: hussein@if.usp.br

Received: 9 December 2016
Accepted: 6 February 2017
Published online: 24 February 2017

Abstract

In this paper we revisit the one-dimensional tunnelling 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.