Approximate quantum transmission coefficients in fusion cross sections: A simplified analytical model

Using different forms of analytic Using different forms of analytic approximate transmission coefficients, Hill-Wheeler, Morse, Eckart, and WKB the fusion cross section of three reactions were calculated and compared with the exact transmission coefficient deduced from IWBC model. Using different forms of analytic approximate transmission coefficients, Hill-Wheeler, Morse, Eckart, and WKB the fusion cross section of three reactions were calculated and compared with the exact transmission coefficient deduced from IWBC model. By considering two different forms of angular dependence of the barrier height: i) direct determination at each l ii) approximate determination using S-wave barrier height and centrifugal term, two sets of Hill-Wheeler (Wong), Morse and Eckart transmission coefficient and consequently cross sections were obtained. The comparison was showed that for sub-barrier energies WKB coincides with IWBC, for near barrier energies all forms, except WKB because of its domain of applicability, are in accordance with IWBC, and for well-above barrier the first set of cross sections are close to the IWBC.