**Effective Energetic Costs of Excitation of Electronic States of N _{2},
O_{2}, and O by Electrons**

**Introduction**

The effective energetic
costs are numerical quantities defined to simplify estimation of excitation
rates of electronic states of the Earth’s atmospheric gases by electron impact.
In was shown [1] that for energies >1 keV the energetic costs are typically
independent on initial electron energy and on the altitude in atmosphere. This
approach is mainly valid for aeronomic applications
(aurora). The constant energetic costs are usually enough for typical
applications to electron-excited aurora, but this approach cannot be
straightforwardly applied, for example, to secondary electrons produced by
other impact particles, and in case of some exceptions. The exceptions are: i) dependence on altitude
for states with low (<7 eV) thresholds; and ii)
strong dependence on initial electron energy in region of thresholds (<50
eV). Considerable density of thermal electrons is typical for ionospheric
altitudes, so the electron-electron interaction can also modify the energetic
costs at small energies.

So, in common case
the energetic cost *ε _{j}^{i}* of excitation of a
state

**Tables for N _{2} Tables for O_{2} Tables for O **

**How
it was obtained**

The energetic costs
have been calculated numerically. The numerical model used is the Monte-Carlo
code which simulates degradation of electron energy within
collision-by-collision scheme down to the lowest threshold energy. All
generations of secondary electrons are also taken into account sequentially.
The local degradation was assumed and the gas composition can be an arbitrary
mixture of 3 gases: molecular nitrogen, molecular oxygen, and atomic oxygen.
For illustration we have presented results for homogeneous gas and mixtures
which are typical at auroral altitudes 100 km, 120 km and 200 km.

The partial cross
sections used in the numerical model are mainly the same as in [1, 2]. The only
improvements based on [3-8] are: i) more careful
shapes for vibrational states (*v*=1,2,3,4)
of molecular nitrogen and molecular oxygen at small energies; ii) the rotation
states (*r*=1,2,3,4) of
molecular nitrogen are added.

The electron-electron
interaction is included to the simulation by effective loss function obtained by
[9]:

*L _{ee}*

Statistical discrepancy
of all calculated valued are less than 0.1%, therefore the main reason of possible
errors is the partial collisional cross sections which are typically known with
discrepancy >30%.

**How
to apply**** **

The excitation rate
of given state *j *of gas *i* can be calculated as:

,

Here *W _{i}* is the energy lost by
electron flux in collisions with gas

*W _{i}*

Here *n _{i}* is density of gas

More details see in [1] and [2, chapter
7].

**References**

1. Sergienko T.I., Ivanov V.E. A new approach to calculate
the excitation of atmospheric gases by auroral
electron impact, *Ann. Geophys.*
V.11, P.717, 1993.

2. Ivanov V.E.,
Kozelov B.V., Transport of electron and
proton-hydrogen atom fluxes in the Earth atmosphere. *Published by
KSC RAS*, Apatity, 2001 (book in Russian, pdf-file).

3. Allan M., Excitation
of vibrational levels up to *v*=17 in N_{2}
by electron in the 0-5 eV region, *J. Phys. B: At. Mol. Phys*. 18 (1985) 4511-4517.

4. Vicic M., Poparic G., Belic D.S., Large
vibrational excitation of N_{2} by low-energy electrons, *J. Phys. B: At. Mol. Opt. Phys*. 29 (1996) 1273–1281.

5. Brennan M. J., Alle D. T.,
Euripidest P., Buckman S. J.
and M. J. Brungert, Elastic
electron scattering and rovibrational excitation of N_{2}
at low incident energies, *J. Phys.
B: At. Mol. Opt. Phys*. 25 (1992)
2669-2682.

6. Gote M. and
H. Ehrhardt, Rotational
excitation of diatomic molecules at intermediate energies: absolute
differential state-to-state transition cross sections for electron scattering
from N_{2}, Cl_{2}, CO and HCl, *J. Phys. B: At. Mol. Opt. Phys*. 28
(1995) 3957-3986.

7. Kutz H.and
Meyer H-D, Rotational excitation of N_{2} and Cl_{2} molecules
by electron impact in the energy range 0.01-1000 eV:
Investigation of excitation mechanisms, *Physical
Rev. A*, V.51 (5), 3819-3830, 1995.

8. Campbell L., M.J. Brunger,
D.C. Cartwright, P.J.O. Teubner, Production of vibrationally excited N_{2} by electron impact, *Planet. Space Sci., 52 815-822, 2004.*

9. Schunk R.W., Hays P.B.
Photoelectron energy losses to thermal electrons, *Planet. Space Sci*. (1971) - V.19. - P.113-117.

Version 2013-08-03

(c) Boris Kozelov, PGI KSC RAS, E-mail: boris.kozelov@gmail.com