<i>S</i>-matrix analysis of heavy-ion elastic scattering

Abstract

A procedure to minimize ${\mathrm{\ensuremath{\chi}}}^{2}$ is described which explores the fact that the ${\mathrm{\ensuremath{\chi}}}^{2}$ distribution is of the fourth degree in the S-matrix elements. The fact that all three roots of the scale parameter for the minimum of ${\mathrm{\ensuremath{\chi}}}^{2}$ in its gradient direction are algebraically determined gives the present procedure some global features that previous methods did not contemplate. The automatic search procedure also preserves the unitary bound constraint of the S-matrix at every step. When the search in the gradient direction slows down, the procedure reverts to the traditional quadratic approximation with zero-order regularization. The method is applied to the elastic scattering of the $^{12}\mathrm{C}$${+}^{16}$O reaction near the Coulomb barrier. \textcopyright{} 1996 The American Physical Society.