Approximate Transmission Coefficients in Heavy Ion Fusion
- 66 Downloads
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.
KeywordsHeavy ion reactions Fusion Quantum tunneling Transmission coefficients
We are grateful to Raul Donangelo for critically reading the manuscript. Partial support from the Brazilian funding agencies, CNPq, FAPESP, and FAPERJ, is acknowledged. M. S. H. acknowledges support from the CAPES/ITA Senior Visiting Professor Fellowship Program.
- 11.L. F. Canto, M. S Hussein, Scattering theory of molecules, atoms and nuclei. World Scientific Publishing Co. Pte. Ltd. (2013)Google Scholar
- 13.R. A Broglia, A Winther, Heavy ion reactions. Westview Press (2004)Google Scholar
- 14.E. Merzbacher, Quantum mechanics, 3rd ed. Wiley (1998)Google Scholar
- 15.C. J Joachain, Quantum collision theory. North Holland (1983)Google Scholar
- 17.N. Fröman, P. Fröman, JWKB Approximation: contributions to the theory, 1st ed. North-Holland (1965)Google Scholar