Excitation cross sections of theH2(XΣg+1→bΣu+3) by the combined close-coupling—R-matrix method

We have calculated the excitation cross sections of ${\mathrm{H}}_2$ ($X{}_{}{}^1{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}\to b{}_{}{}^3{}_{}{}^{}\Sigma _u^{+}{}_{}{}^{}$) by combining the advantageous features of the close-coupling and $R$-matrix methods. In this work approximate close-coupling solutions are used as basis functions to calculate the $R$ matrix inside a sphere of radius $a$. The $R$-matrix boundary condition then provides the starting solutions at $r=a$ with which the coupled differential equations are integrated outward by the Numerov method into the asymptotic region with the electron-exchange terms neglected. Comparison with the standard close-coupling calculation shows an agreement typically within 5%, while the computing time is reduced by a factor of about 5. The basis set employed in constructing the $R$ matrix consists of two or three functions per channel, which is a markedly smaller set than usually included in $R$-matrix calculations for similar processes.