The electron-ion recombination mechanisms of ${\mathrm{He}}_2^{+}$ are determined along with the rate coefficients of the important elementary processes which govern the relaxation of the helium afterglow, at room temperature. The experimental data (atomic- and molecular-ion currents to the walls, atomic and molecular metastable concentrations, electron concentration, elastic electron collision frequency, electron radiation temperature) obtained as a function of time under a wide range of experimental conditions are compared with the solutions of a system of five coupled partial differential equations which includes all the processes occurring in a helium afterglow. A unique set of rate coefficients and constants is found allowing the precise reproduction of all the experimental data obtained at seven pressures from 5 to 100 Torr. The electron energy balance and electron energy distribution function are calculated as a function of time and space. It is shown that the spatial distribution of the electron energy in our cylindrical experimental cell is not uniform and has to be taken into account, as well as the influence of the non-Maxwellian electrons. The recombination rate coefficient for ${\mathrm{He}}_2^{+}$, given under the form ${\alpha }_2=({\alpha }_{c2\mathrm{}}+k_{02}{n}_0){\left(\frac{T_e}{293°\mathrm{K}}\right)}^{-x_2}+k_{e2\mathrm{}}{n}_e{\left(\frac{T_e}{293°\mathrm{K}}\right)}^{{-y}_2}$, is found to be such that ${\alpha }_{c2\mathrm{}}<5<{10}^{-10\mathrm{}}$ ${\mathrm{cm}}^3$ / sec, $k_{02}=(5\mathrm{}\pm 1)\times {10}^{-27\mathrm{}}$ ${\mathrm{cm}}^6$ / sec, $k_{e2\mathrm{}}=(4.0\mathrm{}\pm 0.5)\times {10}^{-20\mathrm{}}$ ${\mathrm{cm}}^6$ / sec, $x_2=1\mathrm{}\pm 1$, $y_2=4.0\mathrm{}\pm 0.5$. These coefficients correspond to a collisional-radiative model for the recombination of ${\mathrm{He}}_2^{+}$ with electrons, which strongly depends on pressure, electron concentration, and electron temperature. 70% of the recombined molecular ions produce atomic metastables corresponding to a dissociation in the lower excited states of the molecule. The rate coefficients for ionizing collisions between metastables are found to be ${\beta }_{11}=(1.5\mathrm{}\pm 0.3)\times {10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ / sec, ${\beta }_{22}=(1.5\mathrm{}\pm 0.5)\times {10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ / sec, ${\beta }_{12}=(2.5\mathrm{}\pm 1.5)\times {10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ / sec. The superelastic electron-metastable rate coefficients are ${\gamma }_1=(4.2\mathrm{}\pm 0.6)\times {10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ / sec and ${\gamma }_2=(3.8\mathrm{}\pm 0.8)\times {10}^{-9\mathrm{}}$ ${\mathrm{cm}}^3$ / sec. All the rate coefficients compare very well with available theoretical data. The method used gives a complete solution of the helium afterglow at room temperature. It can be extended in pure helium to many other experimental conditions and applied to the study of afterglows in other pure gases or mixtures.

• Received 6 August 1975

DOI:https://doi.org/10.1103/PhysRevA.13.1140