Resonant contributions to dissociation of Hz by low - energy electron impact

A resonance theory of electron-impact vibrationd excitation of diatomic molecules is extended to the case where the final vibrational level of the molecule lies in the " h u m . 7he extended theory is applied to resonant dissoeiation of molecular hydrogen by low-energy electron impact. Theoretical moss sections for dissociation of ground-state H2 via the X '4 and B 2 C i resonance a ~ e presented and compared with thearetiad cmss sections obtained by other authors using non-resonant methods. An imponant aim of the present work is M study the effect of initial vibrational excitation on the dissociation cross section. It is found that fhe B 'E: resonance convibvles significantly M the total dissociation emss section for dI values of U,, for incidenl energies between 12 eV and 18 eV, while the effect of the X 22: m n m c e becomes appreciable only for larger values of vi. Dissociation of molecular hydrogen by electron impact is currently of interest in modelling electron transport in hydrogen plasmas (Cacciatore et a1 1989). Modelling of negative hydrogen ion discharges requires accurate knowledge of neutral hydrogen vibrational level populations, and dissociation by electron impact contributes to their depletion (Hiskes 1992). At normal laboratory temperatures, molecular hydrogen is mostly in the ui = 0 level, and its dissociation by lowenergy electron impact occurs mainly through excitation of the repulsive b 3Z: electronic state of neutral H2, which dissociates into two neutral H atoms. This process is generally considered to be a direct scattering process, and can be pictured schematically as e+ H*(X 'Zp', vi = 0) -+ e+ Hz(b 'E:) -r e+ H(ls) + H(ls). (1) The threshold energy for this process is approximately 8 eV (Hiskes 1992) and the cross section is of the order of IO-" cm2 (Hall and Andric 1984, Rescigno and Schneider 1988). Significant cross sections for dissociation at lower impact energies are not observed experimentally under normal laboratory conditions. This process, and dissociation at higher impact energies via excitation of higher-lying electronic states of H2. have been studied both theoretically (Fliflet and McKoy 1980. Rescigno and Schneider 1988) and experimentally (Hall and Andric 1984, Nishimura and Danjo 1986) in recent years. However, the possibility of a significant contribution to the dissociation cross section due to resonant scattering, i.e. of enhancement of dissociation caused by trapping of the electron in a temporary anion state, hasnot been considered, to our knowledge, in any previous calculation. This is especially surprising considering the fact that early observations of dissociation via the b state of Hz were attributed to the decay of resonant qstates (Ehrhardt and Weingartshofer 1969, Weingartshofer et a1 1970). The purpose of this letter is to report the results of our 0953-4075/93R10759+07$07.50 @ 1993 IOP Publishing Ltd L759 L760 Letter to the Editor Figure 1. Polential energy c w e s of the X '$ and b '2: electronic stateh of Hz. and of the X2E:andB2E: resonancesofH;. theoretical investigation of the contribution to the e-HZ dissociation cross section due to temporary excitation of the two lowest-lying reSonant anion states of H;. The two resonant states of H; that might contribute significantly to the production of ground-state neutral H atoms in low-energy e-Hz scattering are. the X *E: and the B 'E: resonances, whose potential energy C U N ~ S are plotted, together with those of the X I X$ and b states of neutral Hz. in figure 1. The X zE: resonance decays only to the ground electronic state of molecular hydrogen, while the B 'E: resonance lies above the b 3X: state of neutral HZ for internuclear separations smaller than about 5.2 00 and decays primarily to that state, though it can decay to ground state Hz as well. We have therefore the possibility of the following resonant channels, in addition to the direct channel described above: e+ Hz(X 'Ep'. v i ) + H;(B 'E:) + e+ Hdb 'E;) + e+ H( Is) + H(ls) (2) e-+H2(X'Ep', u ~ ) ~ H ; ( B ' E ~ ) ~ ~ + H z ( X ' C ~ ) * ~ + H ( I S ) + H ( I S ) (3) e-+Hz(X'E;, vi)+ H;(XZE:)-te-+H~(X'E:8+) +e-+H(ls )+H(ls ) . (4) We have examined the contributions of the above channels to the total cross section for the dissociation of ground-state neutral Hz by electron impact for incident electron energies below 18 eV. Special attention was given to the effect of initial vibrational excitation of the target cn the cross sections for dissociation. This effect has been studied by other investigators, although chiefly at higher energies, and in a non-resonant Context (Redmon er nl 1985, Rescigno and Schneider 1988, Celibetto and Rescigno 1993). In this paper we first outline briefly the theoretical description of the scattering process used in the present work, which has been given in detail by several authors (Fano 1961, O'Malley 1966, Bardsley 1968). Next we give the fonnula for calculating cross secljons for dissociation via resonance formation, which is a simple extension of the well known expression for the resonant vibrational excitation cross section. We also describe the potentials and widths, as well as the numerical techniques, used in our calculations. Finally we present cross sections Letter to the Editor L761 obtained from the theory, discuss their significance, and compare them with theoretical cross sections reported by other authors. The present treatment is based on the traditional resonant scattering theory. In this treatment, the motion of the nuclei in the X 2E: and B ' C l resonant anion states is described by wavefunctions and ea, respectively, which depend only on the relative nuclear position vector R. Each of these nuclear wavefunctions satisfies an integrodifferential equation with a complex, non-local kemel. Within the local approximation, the radial parts of these wavefunctions satisfy, in atomic units, the following ordinary differential equations: