Cross sections for excitation of theb3Σu+, aΣg+3, andc3Πustates ofH2by low-energy electrons

We used a multichannel extension of the Schwinger variational principle [K. Takatsuka and V. McKoy, Phys. Rev. A 24, 2473 (1981)] to study the cross sections for excitation of the X ${}_{}{}^1{}_{}{}^{}$ ${\mathrm{\Sigma }}_{\mathrm{g}}^{+}$→b ${}_{}{}^3{}_{}{}^{}\mathrm{\Sigma }_{\mathrm{u}}^{+}{}_{}{}^{}$, a ${}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$, and $c^3$ ${\Pi }_u$ transitions in ${\mathrm{H}}_2$ by low-energy electrons. These cross sections were obtained with two open channels for each transition and for energies near threshold to 30 eV. The results for the $b^3$ ${\Sigma }_u^{+}$ and a ${}_{}{}^3{}_{}{}^{}\Sigma _g^{+}{}_{}{}^{}$ states agree quite well with available experimental data. However, the cross sections for excitation of the c ${}_{}{}^3{}_{}{}^{}\Pi _u^{}{}_{}{}^{}$ state differ significantly from the measured values at the two energies, 20 and 30 eV, where data are available.