Approximate Transmission Coefficients in Heavy Ion Fusion |
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| Authors: | A J Toubiana L F Canto M S Hussein |
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| Institution: | 1.Departamento de Engenharia Nuclear, Escola Politécnica,Universidade Federal do Rio de Janeiro,Rio de Janeiro,Brazil;2.école CentraleSupélec,Plateau de Moulon,Gif-sur-Yvette,France;3.Instituto de Física,Universidade Federal do Rio de Janeiro,Rio de Janeiro,Brazil;4.Instituto de Física,Universidade Federal Fluminense,Niterói,Brazil;5.Departamento de Física Matemática, Instituto de Física,Universidade de S?o Paulo,S?o Paulo,Brazil;6.Instituto de Estudos Avan?ados,Universidade de S?o Paulo,S?o Paulo,Brazil;7.Departamento de Física, Instituto Tecnológico de Aeronáutica,CTA,S?o Paulo,Brazil |
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| Abstract: | 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. |
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