Effects of excitation and ionization in meteor trains

In a previous paper we examined the problem of the determination of the ionization coefficient β, and we now extend our analysis to the luminous efficiency τ, relating this to an excitation coefficient ζ, essentially the number of times an atom is excited during the thermalization process. We discuss the scattering processes involved and develop integral equations expressing ζ in terms of the relevant scattering cross-sections. The data available in applying these equations are (i) direct measurements of β and ζ for iron particles moving through an ionization chamber, with velocities between 18 and 46 km s
⁻¹
; (ii) scattering cross-sections σ
i
and σ
e
, for ionization and excitation on collision between Fe atoms and air molecules, measured under controlled single-atom collision in the laboratory for relative velocities between 60 and 120 km s
⁻¹
; (iii) theoretical calculations of the diffusion cross-section σ
d
of iron atoms in air over the relevant velocity range. Employing an approximation in which the scattering is isotropic in the centre-of-mass frame (the random scattering approximation, RSA), we take the laboratory simulation results for the ionization and luminosity and invert the equations for β and ζ to obtain values of β
0
and ζ, the ionization and excitation probabilities at the first collision. We find that for velocities above 42 km s
⁻¹
the value of ζ
0
becomes greater than unity. As ζ
0
is a probability, this must be incorrect, leading to the conclusion that the contribution from subsequent collisions is underestimated. This is possible if small-angle scattering is underestimated in the RSA. To investigate this we have taken the extreme case in which the trajectories of atoms are supposed to undergo no deviation at all on ionization or excitation. This now enables us to derive the ratios σ
i
σ
d
and σ
e
σ
d
and hence, using the theoretical values of the diffusion cross-section, values of σ
i
and σ
e
. The values so obtained appear unacceptably high and inconsistent with the experimental cross-sections. A possible reason for the failure of the equations is the assumption that ionization permanently removes atoms available for excitation, which will not be true if charge transfer takes place. No cross-sections are available for this process, but we can evaluate ζ in the limiting case when the loss of velocity during transfer may be neglected. To compare our results for the ionization and excitation cross-sections with the experimental ones, we have extrapolated them to 60 km s
⁻¹
and find quite satisfactory agreement. We have accordingly extended the results for the excitation and ionization coefficients to velocities above 60 km s
⁻¹
utilizing the experimental cross-sections for this region. We consider the values of ζ and the corresponding luminous efficiencies to be the best available in the present circumstances.