Differential cross sections for near-threshold electron impact dissociation of molecular hydrogen

Abstract

Electron impact dissociation of molecular hydrogen is considered to be a major route to molecular break-up in cool hydrogen plasmas. Such plasmas are found in a number of astrophysical environments and in the divertor region of tokamak fusion plasma.At low energies, the major pathway for the electron impact dissociation of H is throughdissociative excited electronic state. The purpose of this work is to develop a theoretical formulation for this process for an arbitrary diatomic molecule, and to derive the formal expressions that describe the differential and total cross sections, which involve three fragments in the exit channel, and to study the electron impact dissociation of molecular hydrogen and its isotopomers at near-threshold energies.Ab initio calculations of total cross sections, angular differential cross sections, energy differential cross sections and double differential cross sections are made for the § © vibrational level of H . The effect of nuclear motion is then included in such calculations, with the dissociation taking place from the electronic ground state at different initial vibrational levels, dissociating into continuum states.Studies of mixed isotopes are performed using the R-matrix method, and total cross sections, energy differential cross sections and rate coefficients for electron impact dissociation of H , D , T , HD, HT and DT as a function of the vibrational states are presented.Finally, a scaling rule that describes integral cross sections as a function of the initial vibrational state, the reduced mass of the target molecule and the energy of the projectile electron is developed and compared against cross sections calculated accurately for the H molecule and its isotopomers.2

Low-energy electron-impact dissociative excitation of molecular hydrogen and its isotopologues

“…We find that for triplet state excitations the partial wave convergence is readily established with M max = 5, not only at the low energies considered in this work, but across all energies [15]. This has also been observed in the Rmatrix calculations of Trevisan and Tennyson [16].…”

“…As with the FN calculations, these AN calculations are in significant disagreement with each other. The calculation of Trevisan and Tennyson [16] predicted a peak lower than both the Khakoo and Segura [7] and Nishimura and Danjo [6] measurements, and shifted to about 12.5 eV. The calculation of Celiberto et al [17] was in reasonable agreement with the R-matrix calculation below 9 eV, but in substantial disagreement at higher energies, particularly in predicting a peak closer to 15 eV.…”

“…In this energy regime the adiabatic nuclei (AN) approximation is a more accurate approach. The AN approximation has been previously applied to e − -H 2 excitation, for example, the calculations by Trevisan and Tennyson [16], Celiberto et al [17], and Rescigno and Schneider [18]. As with the FN calculations, these AN calculations are in significant disagreement with each other.…”

Complete Solution of Electronic Excitation and Ionization in Electron-Hydrogen Molecule Scattering

“…The CCC formalism provides a complete solution of the electronmolecular hydrogen scattering problem in the fixed-nuclei approximation, irrespective of the projectile energy or the electronic transition of interest. The fixed-nuclei approximation is the foundation on which techniques are built to describe vibrational and rotational excitations, resonance and dissociative processes in molecules [9,10,20,51] . This will allow us to model such processes and address some long standing problems, such as the controversy over the vibrational excitation cross sections for molecular hydrogen [3].…”

“…A large number of theoretical methods have been applied to calculate electron collisions with the H 2 molecule. Among the most advanced and general are calculations based on the Schwinger variational principle [5], Kohn variational method [6], R-matrix method [7][8][9][10][11], and time-dependent close-couplig method (TDCC) [12]. Agreement between theory and experiment for this most fundamental of all molecules is mixed at best.…”