Angular Dependence of Differential Cross Sections for Electron Excitation of Singlet→Triplet Transitions

Abstract

Articles you may be interested in Energies and relative cross sections of singlet-triplet transitions in methylsubstituted 1,3butadienes by ionimpact spectroscopyThe failure of previous calculations to predict the correct "forward-peaking" angular dependence of the electron-impact differential cross section for the helium 1'S->2 3 S transition is shown to be due to the neglect of the core contribution. Even a simple approximation to the jull Born-Oppenheimer transition amplitude based on an expansion in inverse powers of the incident electron momentum predicts the correct angular dependence of this transition for electron energies to within 40 eV of threshold. For electron-impact excitation of the lowest singlet->triplet transition in molecular hydrogen, the peaking of the differential cross section away from zero scattering angle is due mainly to a molecular diffraction effect, and the success of Ochkur's approximation in predicting this dependence is shown to be merely a consequence of the relatively small contribution made by the core terms for this particular transition and cannot be generalized. For higher singlet->triplet transitions in H2, the angular dependence of the differential cross section and the magnitude of the core contribution are shown to depend importantly on the separated atom state with which the molecular wavefunction correlates at infinite separation.

Second Born Zero Angle Differential Cross Sections in the High Energy Limit for the Electron Impact Excitation of He: The 23S ← 11S and 23P ← 11S Transitions

“…The energy dependence of the first Born term is basically of the order of l/k 2 but is reduced to l/k4 or Ilk 3 , depending on the symmetry properties of the wavefunctions involved. The leading second Born terms are shown here to be of order 1/k 3 for both transitions and hence of order 11k smaller than the first Born dependence (1/k 2 ) in the absence of restrictions on the nature of target wavefunctions.…”

“…The exchange amplitude can be written as (2) where R=Hro+ro'), x=ro-ro', KOn=k-kn, tOn= Hk+k n ) =k-!CKan), and the prime on fo indicates that it is the position coordinate of the incident electron that is to be acted on by the antisymmetrizer. The prime on the total Hamiltonian indicates the presence of the additional terms k2-2t'k· Vo which result from commuting exp(t'k·ro) through the inverse operator.…”

“…7 The total differential cross section for a singlet-triplet excitation is related to the exchange amplitude gOnCO) by (du/dfJ) =3(kn/k) \ gOnCO) \2, where the factor 3 results from carrying out the spin averages. Equation (2) can best be simplified by choosing KOn as the Z direction and expanding the exponential depending on Kan in a powers series so that…”

Electron-Impact Excitation of the He 1 1S → 2 3S, 1 1S → 2 3P, and 1 1S → 2 1P Transitions

“…Downloaded to IP: inverse powers of the incident momentum, ko• Since contribution to the exchange amplitude from interaction of the incident electron with the target electron with which it exchanges has the weakest dependence on l/ko at high energy, this approximation ignores contributions from other interactions. In a previous publication 3 we showed that a more consistent and equally tractable approximation to the first Born exchange amplitude is to retain leading terms in both rearrangement and core contributions. Additionally it was shown that the relative magnitude of these contributions depended importantly on the nature of the transition.…”