Heavy-ion fusion cross section formula and barrier height distribution
C. L. Jiang, B. P. Kay
Abstract
Methods for obtaining fusion cross section formulas are discussed, especially for those that take on an empirical form. A new expression starting with $\ensuremath{\sigma}(E)=\frac{1}{E}{\ensuremath{\int}}_{{E}_{0}}^{E}\left({\ensuremath{\int}}_{{E}_{0}}^{{E}^{\ensuremath{'}}}B({E}^{\ensuremath{''}})d{E}^{\ensuremath{''}}\right)d{E}^{\ensuremath{'}}$ has been explored. Here, $B(E)$ is a reasonable, assumed function of the barrier height distribution, $\frac{{d}^{2}(\ensuremath{\sigma}E)}{d{E}^{2}}$. The resulting analytic cross section formula reproduces very well the excitation functions for many light and heavy fusion systems across wide energy ranges, when $B(E)$ is assumed to be a multi-Gaussian function. This study offers an improved determination of the fusion barrier height distribution over other numerical techniques.