Equations of motion method: Inelastic electron scattering for helium and CO2 in the Born approximation

We have applied the equations of motion method to the computation of generalized oscillator strengths in helium and CO₂. The equations of motion approach yields excitation energies without the computation of separate ground and excited state wavefunctions and is ideally suited for computing matrix elements of the operator used in the Born approximation. Our results for helium agree well with more extensive calculations [Y. Kim and M. Inokuti, Phys. Rev. 175, 176 (1968)]. We compare our generalized oscillator strengths for CO₂ with experiment, and discuss assignments including the peaks at 8.61 and 9.16 eV in the experimental energy loss spectrum. We also compute a valencelike ${}^1{\Sigma }_u^{+}$ state below the first ionization potential with a large oscillator strength (f=0.64), which may be responsible for the proposed continuum absorption between 11–14 eV in CO₂.