The Collision Frequency of O+ and O

The momentum transfer collision frequency of O+-O is a fundamental parameter describing the coupling of the ionosphere and thermosphere. Empirical values of the collision frequency for O+-O found by comparing ionospheric and thermospheric data are up to 1.7 times the theoretical value using resonance charge exchange as the only ion-neutral interaction. This is a summary timeline of the many contributions to this field.


W. Dean Pesnell
Nomad Research, Inc.

Year Significant development
1958 Dalgarno deduces the energy dependence of the diffusion cross section and gets the diffusion coefficient.
1964 Stebbings et al. measure the charge exchange cross section for O+-O. Knof et al. use an extrapolation of RKR potential energy curves to derive the collision integral. Dalgarno uses the Stebbings data to recalibrate the diffusion coefficient, increasing it by a factor of three. The RCE cross section was reduced by a factor of three at E = 1 eV, so that the A value became 9.43/31/2 = 5.44.
1966 Banks writes the collision frequencies, declaring the Knof results to be superior.
1968 Stubbe uses the Stebbings data to recalculate the collision integral, including polarization and high-speed correction. He claims that polarization increases the cross section by 35–22% over the temperature range 500–2000 K. A reanalysis of his numbers shows that the use of Stebbings data leads to an increase of 16% at 500 K, 12% at 1000 K, and 9.1% at 2000 K.
1971 Lo et al. report measurements of the charge exchange cross section at energies of 30 keV and higher. Their cross sections lie above those of Stebbings et al. (1968) in the energy region closest to the earlier measurements.
1973 Banks and Kockarts gives the nod to the Knof results. Schunk and Walker publish a widely used value of the collision frequency.
1974 Rutherford and Vroom measure the RCE cross section for O+-O and find good agreement with Stebbings.
1975 Roble finds that an increase in the collision frequency is necessary give agreement of the diurnal variations of the ionosphere with observations over Millstone Hill. Thomas and Williams analyze the ion drifts over Malvern and deduce that the collision frequency could be as much as four times the value of Dalgarno.
1976 Beebe et al. do a large calculation of the potential energy curves of O2+, but the data is not published, only graphs that are difficult to interpolate.
1977 Carlson and Harper use energy balance to deduce the collision frequency, agrees with Stubbe. Disagrees with the magnitude of the increase due to polarization in Stubbe [1968]. Either Stubbe or Carlson & Harper have misinterpreted the energy in Stebbings formula, calling it the kinetic energy of relative motion when it is the ion kinetic energy. Furthermore, Dalgarno and Stubbe do not get the same answers when polarization is ignored. Carlson & Harper should compare the increase of the collision frequency to a direct extrapolation of Stebbings data. Gentry and Giese show how the ion charge splits the degeneracy of the ground state levels of O, making the dominant ion-neutral interaction a charge-quadrupole potential.
1982 Marian et al. calculates the potential energy curves; they do not go far enough into the asymptotic region to be useful.
1983 Burnside et al. compares measured and derived diffusion velocities to find the F factor. Finds F = 1.3, with a range of 0.82 to 1.61.
1986 Coxon and Haley publish their RKR analysis of the A2ΠuX2Πg system. Partridge and Stallcop calculate the cross section using JWKB theory and their potential energy curves with polarization. They find that polarization increases the cross section by 25% over the RCE value.
1987 Burnside et al. reanalyzes the 1983 data using the variance minimization technique. Finds F = 1.7.
1988 Winser et al. finds that F = 0.3 - 0.5. Heavily criticized as having too much activity. Combines the energy conservation law with the momentum balance. Figueroa and Hernández analyze the affect of the high-speed correction on power-law potentials.
1990 Moffet et al. modeled the variation in hmF2 and NmF2 caused by variations in the collision frequency. Values of F of 4.2 and 0.5 cause unrealistic large variations in the predawn sector. Ion thermal diffusion is considered too small to be important.
1991 Sipler et al. find that F > 1.7 by a momentum balance technique. SPL redoes the potential energy curves, finds collision integrals that agree with Stubbe and Carlson and Harper. Charge-quadrupole is used in their asymptotic ion-neutral potential.
1992 Buonsanto et al. find that the derived value of N(O) agrees with the MSIS-86 value for 1.7 < F < 1.9. Their values are insensitive to F at mid to late night times. A value of F = 1.4 actually fits better at those times. Only early night data distinguishes between values of F.
1993 Pesnell et al. recalculate the collision cross sections and find agreement with SPL, Stubbe, and Carlson and Harper. Salah proposes and CEDAR accepts the standard value of F = 1.7.
1994 Pesnell et al. analyze the affect of the high-speed correction for the RCE potential and show that it is not responsible for the biases. Their results agree with those of Figueroa and Hernández (1988) for power-law potentials. Reddy, et al. show a bias in the variance technique.
1995 Pesnell analyzes the theoretical collision cross sections calculated from a variety of potential energy curves and casts doubts on the factor of two disagreement in the theoretical results. There is little room left to push the theory up to F = 1.7, we must be content with F = 1.3 - 1.4. Davis et al. reanalyzed the data of Winser et al.. Showed how systematic errors and vertical winds can contaminate the model used to interpret the results. Values of F range from 0.5 to 4.4 and >5. After eliminating data they considered unrepresentative, they derived F = 1.2-1.4.
1997 Buonsanto et al. calculate F for many points and determine the distribution of F. Showed that the median of the data is a better indicator of the true value of F. Rederived the empirical equations to explicitly show the parameters varied in the Monte Carlo simulations.
1998 Omidvar et al. show how various forms of linear least squares analysis change the value of F.
2001 Lindsay et al. remeasure the cross section and show an increase over the earlier values.
2001 Pesnell studies how varying the resonance charge exchange parameters can affect the theoretical cross sections. Uses a community computing model provided by Parabon Computing. See the computing story in NetworkWorldFusion.


Banks, P. M., Collision frequencies and energy transfer rates, Planet. Sp. Sci., 14, 1105–1122, 1966.

Banks, P. M., and G. Kockarts, Aeronomy (New York, Academic), Table 9.10, 1973.

Beebe, N. H. F., E. W. Thulstrup, and A. Andersen, Configuration interaction calculations of low-lying electronic states of O2, O2+, and O22+, J. Chem. Phys., 64, 2080–2093, 1976.

Buonsanto, M. J., Y.-K. Tung, and D. P. Sipler, Neutral atomic oxygen density from nighttime radar and optical wind measurements at Millstone Hill, J. Geophys. Res., 97, 8673–8679, 1992.

Buonsanto, M. J., D. P. Sipler, G. B. Davenport, and J. M. Holt, Estimation of the O+, O collision frequency from coincident radar and Fabry-Perot observations at Millstone Hill, J. Geophys. Res., 102, 17,267–17,274, 1997.

Burnside, R. G., R. A. Behnke, and J. C. G. Walker, Meridional neutral winds in the thermosphere at Arecibo, simultaneous incoherent scatter and airglow observations, J. Geophys. Res., 88, 3181–3189, 1983.

Burnside, R. G., C. A. Tepley, and V. B. Wickwar, The O+-O collision cross-section: Can it be inferred from aeronomical measurements?, Ann. Geophys., 5A, 343–350, 1987.

Carlson, H. C., and H. Harper, An experimental estimate of the O+-O resonant charge transfer cross-section, collision frequency, and energy transfer rate, J. Geophys. Res., 82, 8673–8680, 1977.

Coxon, J. A., and M. P. Haley, Rotational analysis of the A2ΠuX2Πg second negative band system of 16O2+, J. Molec. Spec., 108, 119–136, 1986.

Dalgarno, A., The mobilities of ions in their parent gases, Phil. Trans. Roy. Soc., A250, 426–439, 1958.

Dalgarno, A., Ambipolar diffusion in the F-region, J. Atmos. Terr. Phys., 26, 939, 1964.

Davis, C. J., A. D. Farmer, and A. Aruliah, An optimised method for calculating the O+-O collision parameter from aeronomical measurements, J. Atmos. Terr. Phys., 50, 369–377, 1995.

Figueroa, D. and R. Hernández, Collisional transfer rates for momentum and energy exchange in the case of relative drifts between moving ions and their parent neutral gas, J. Atmos. Terr. Phys., 50, 447–454, 1988.

Gentry, W. R., and C. F. Giese, Long-range interactions of ions with atoms having partially filled p subshells, J. Chem. Phys., 67, 2355–2361, 1977.

Hedin, A. E., MSIS-86 Thermospheric model, J. Geophys. Res., 92, 4649–4662, 1987.

Knof, H., E. A. Mason, and J. T. Vanderslice, Interaction energies, charge exchange cross sections, and diffusion cross sections for N+-N and O+-O collisions, J. Chem. Phys., 40, 3548–3553, 1964.

Lindsay, B. G., D. R. Sieglaff, K. A. Smith, and R. F. Stebbings, Charge transfer of keV O+ ions with atomic oxygen, J. Geophys. Res., 106, 8197–8204, 2001.

Lo, H. H., L. Kurzweg, R. T. Brackman, and W. L. Fite, Electron capture and loss in collisions of heavy ions with atomic oxygen, Phys. Rev. A., 4, 1462–1476, 1971.

Marian, C. M., R. Marian, S. D. Peyerimhoff, B. A. Hess, R. J. Buenker, and G. Seger, Ab initio CI calculation of 16O2+ predissociation phenomena induced by a spin-orbit coupling, Mol. Phys., 46, 779–810, 1982.

Moffet, R. J., R. Sellek, and G. J. Bailey, The influence of O+-O collision frequency on ionospheric F-region behavior, J. Atmos. Terr. Phys., 52, 125–132, 1990.

Omidvar, K., R. Menard, and M. J. Buonsanto, Empirical determination of the O+-O collision frequency, J. Atmos. Solar-Terr. Phys., 60, 1485–1496, 1998.

Partridge, H., and J. R. Stallcop, N+-N and O+-O interaction energies, dipole transition moments, and transport cross sections, in Thermophysical Aspects of Re-Entry Flow, ed. J. N. Moss and C. D. Scott (New York, AIAA), 243–260, 1986.

Pesnell, W. D., K. Omidvar, and W. R. Hoegy, Momentum transfer collision frequency of O+-O, Geophys. Res. Let., 20, 1343–1346, 1993.

Pesnell, W. D., K. Omidvar, W. R. Hoegy, and L. E. Wharton, O+-O collision frequency in high-speed flows, J. Geophys. Res., 99, 21,375–21,382, 1994.

Roble, R. G., The calculated and observed diurnal variation of the ionosphere over Millstone Hill on 23–24 March 1970, Planet. Sp. Sci., 23, 1017–1033, 1975.

Rutherford, J. A., and D. A. Vroom, The reaction of atomic oxygen with several atmospheric ions, J. Chem. Phys., 61, 2514–2519, 1974.

Salah, J. E., Interim standard for the atomic oxygen collision frequency, Geo. Res. Lett., 20, 1543–1546, 1993.

Schunk, R. W., and J. C. G. Walker, Theoretical ion densities in the lower ionosphere, Planet. Sp. Sci., 21, 1875–1896, 1973.

Sipler, D. P., M. E. Hagan, M. E. Zipf, and M. A. Biondi, Combined optical and radar wind measurements in the F region over Millstone Hill, J. Geophys. Res., 96, 21,255–21,262, 1991.

Stallcop, J. R., H. Partridge, and E. Levin, Resonance charge transfer, transport cross sections, and collision integrals for N+(3P)-N(4S0) and O+(4S0)-O(3P) interactions, J. Chem. Phys., 95, 6429–6439, 1991.

Stebbings, R.F., A.C.H. Smith, and H. Ehrhardt, Charge transfer between oxygen atoms and O+ and H+ ions, J. Geophys. Res., 69, 2349–2355, 1964.

Stubbe, P., Frictional forces and collision frequencies between moving ion and neutral gases, J. Atmos. Terr. Phys., 30, 1965–1985, 1968.

Thomas, D. P., and P. J. S. Williams, Measurements of ion-drag induced by plasma velocity in the F-region, J. Atmos. Terr. Phys., 37, 1271–1275, 1975.

Winser, K. J., A. D. Farmer, D. Rees, and A. Aruliah, Ion-neutral dynamics in the high latitude ionosphere: First results from the INDI experiment, J. Atmos. Terr. Phys., 50, 369–377, 1988.