Approximate Transmission Coefficients in Heavy Ion Fusion

In this paper, we revisit the one-dimensional tunneling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the barrier shape by functional forms where the transmission co...

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Bibliographic Details
Published inBrazilian journal of physics Vol. 47; no. 3; pp. 321 - 332
Main Authors Toubiana, A. J., Canto, L. F., Hussein, M. S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2017
Springer Nature B.V
Subjects
Cross-sections
General and Applied Physics
Physics
Physics and Astronomy
Heavy ion reactions
Quantum tunneling
Transmission coefficients
Fusion
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Summary:In this paper, we revisit the one-dimensional tunneling problem. We consider different approximations for the transmission through the Coulomb barrier in heavy ion collisions at near-barrier energies. First, we discuss approximations of the barrier shape by functional forms where the transmission coefficient is known analytically. Then, 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 the different approximations considered in this paper by comparing their predictions for transmission coefficients and cross sections of three heavy ion systems with the corresponding quantum mechanical results.
ISSN:0103-9733
1678-4448
DOI:10.1007/s13538-017-0499-7