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For the inelastic electron scattering of atoms and molecules, a consensus has been reached that the first Born approximation is easily approached by decreasing the momentum transfer at the same impact electron energy or increasing the impact electron energy at the same momentum transfer. Although this consensus is applicable for the elastic electron scattering of most atoms and molecules, it is violated for helium where the experimental differential cross sections deviate from the first Born approximation prediction gradually with the decrease of squared momentum transfer at the same impact electron energy. Since this anomalous phenomenon was observed more than 40 years ago, the intrinsic mechanism is not explicit. In the present work, using the high-resolution x-ray scattering, we isolate the scattering contribution from the nucleus and directly obtain the pure electronic structure of helium. Then, the anomalous asymptotic behavior of the elastic electron scattering of helium has been elucidated, i.e., in the small squared momentum transfer region, the scattering contribution from the target's electrons is counteracted by the one from the atomic nucleus, which results in the residual contribution beyond the first Born approximation being drastically enlarged. [ABSTRACT FROM AUTHOR]

The generalized oscillator strengths of the low-lying valence-shell excitations of N2, O2, and C2H2 have been studied by the high-energy electron scattering, the high-resolution inelastic X-ray scattering, and the multireference single- and double-excitation configuration-interaction methods. Good agreement between the present electron-scattering results and the X-ray-scattering ones for the a ′ ′ 1 Σ g + v ′ = 0 and a ′ ′ 1 Σ g + v ′ = 1 + b 1 Π u v ′ = 0 excitations of N2 and the A ′ 3 Δ u excitation of O2 is achieved in the small squared momentum transfer region, while obvious discrepancies among them are observed in the large squared momentum transfer region. This phenomenon indicates that the first Born approximation is satisfied in the small squared momentum transfer region, while it does not hold in the large squared momentum transfer region at an incident electron energy of 1500 eV, in view of the fact that the first Born approximation is satisfied in the X-ray scattering. In addition, the present calculation for the a ′ ′ 1 Σ g + excitation shows that the traditional assigned v′ = 0 and 1 of the a ″ 1 Σ g + excitation correspond to v′ = 9 and 13 of the 2 1 Σ g + excitation and reproduces the X-ray-scattering results of the a ′ ′ 1 Σ g + v ′ = 0 excitation very well except the ones in the small squared momentum transfer region. We also report the generalized oscillator strengths of the A ̃ + B ̃ excitations of C2H2, and its profile shows that the bending geometry has great influence on the transition feature. [ABSTRACT FROM AUTHOR]

The generalized oscillator strengths of the low-lying valence-shell excitations of N 2 , O 2 , and C 2 H 2 have been studied by the high-energy electron scattering, the high-resolution inelastic X-ray scattering, and the multireference single- and double-excitation configuration-interaction methods. Good agreement between the present electron-scattering results and the X-ray-scattering ones for the a ''1 Σ g + v ' =0 and a ''1 Σ g + v ' =1+b 1 Π u v ' =0 excitations of N 2 and the A '3 Δ u excitation of O 2 is achieved in the small squared momentum transfer region, while obvious discrepancies among them are observed in the large squared momentum transfer region. This phenomenon indicates that the first Born approximation is satisfied in the small squared momentum transfer region, while it does not hold in the large squared momentum transfer region at an incident electron energy of 1500 eV, in view of the fact that the first Born approximation is satisfied in the X-ray scattering. In addition, the present calculation for the a ''1 Σ g + excitation shows that the traditional assigned v' = 0 and 1 of the a ″1 Σ g + excitation correspond to v' = 9 and 13 of the 2 1 Σ g + excitation and reproduces the X-ray-scattering results of the a ''1 Σ g + v ' =0 excitation very well except the ones in the small squared momentum transfer region. We also report the generalized oscillator strengths of the à + B̃ excitations of C 2 H 2 , and its profile shows that the bending geometry has great influence on the transition feature.