The Bethe theory for dissociative excitations and ionisation of H₂⁺(1sσ_g) by electron impact

Abstract

The revised Bethe theory due to Inokuti et al for the inelastic scattering of charged particles by atoms and molecules is applied to Hl(lsog). In the 'reflection' approximation, the cross sections for the sum of all the discrete excitations oex, ionisation ui and total excitations o,,, given in an asymptotic expression with three constants (the so-called Born asymptote) instead of two constants (the so-called Bethe asymptote) are accurately calculated. The Bethe asymptotes are given for comparison with the less accurate ones reported by Peek. It is shown that the ionisation cross sections given by the Born asymptote including the free-electron exchange correction are most compatible with the experimental data, but the ones given by the Bethe asymptote are only valid at high incident energies. The calculated o,, and uto, are also shown to be in excellent agreement with the experimental data at incident energies above 50 eV. This work also points out that the obtained cross sections (oto,+o,), vex and o,,,, are very sensitively dependent on the accuracy of the rotational-vibrational ( R V ) state distribution of Hl(lsog) used to take the vibrational average. The calculated cross sections (olor+u,), including an error of 5% due to the vibrational average over the measured distribution, are also shown to be in agreement with two sets of experimental data. In general, the agreement between theory and experiment is consistent with that reported for one-electron atomic targets. Thus it is concluded that the assumptions made to account for the nuclear vibrational and rotation motions, such as the Born-Oppenheimer (BO) approximation, the reflection approximation and the closure argument, are valid for H: by electron impact.

The exact Born-Oppenheimer oscillator strength distribution moments of H2+(1sσg) for the excitation to all the continua

“…where Note that Lex(p, R ) is the contribution due to all discrete excitations. The value of L(-1, 2.0) given here is in excellent agreement with that calculated from the five given moments S ( p , 2.0) using the moment theory (Langhoff and Yates 1972) reported in an early work (Liu 1974) and it is also in good agreement with the value reported by Peek (1974). Furthermore the values of L t ( p , a) for p = 0, *l, *2 are also in excellent agreement with those for the H atom reported by Inokuti (1963).…”

Calculations of electron scattering from H2+

“…The dependence on the initial vibrational level distribution (FC or BD) is minor and only visible at the cross-section peak. Although not shown, the vibrationally weighted CCC results are in good agreement with the first-order Bethe weighted reflection method of Liu [19] at energies above 1 keV. Vibrationally weighted FC and BD results are in excellent agreement with the experiment of Peart and Dolder [9] across the entire energy range.…”

“…Born-Oppenheimer calculations of the electron-H 2 + system within the first Born [17,18] and Bethe-Born [18] approximations found that the DE cross sections have a strong dependence on v and increase dramatically as v becomes larger. Liu [19] used the Bethe theory combined with the reflection approximation to calculate PP, DI, and DE cross sections assuming the BD and FC distribution. These methods compared well with experimental PP and DI data at high energies.…”

Effective oscillator strengths and transition energies for the hydrogen molecular ion

“…and for H~-is important in the computation of ionization cross-sections in the Bethe-Born theory of high-energy electron-Hf dissociative collisions [22,23]. Average logarithmic sums for H + have been given [22][23][24]; but not in the variationperturbation theory.…”

“…Average logarithmic sums for H + have been given [22][23][24]; but not in the variationperturbation theory. Peek [22] used a modified moment method and Liu [23,24] Effective dipole properties for H + 25 used a combination of explicit construction of the discrete spectrum and a subtraction/differentiation of fits to oscillator strength sums to obtain the continuum contribution. The most extensive tabulation is due to Liu [24], who gave average sums for p = -2,..., 2, with energies expressed in Rydbergs.…”