VOL. 79, NO. 16 JOURNAL OF GEOPHYSICAL RESEARCH JUNE 1, 1974 Oxygen Recombination in the Tropical Nightglow P.S. JULIENNE AND J. DAVIS Naval ResearchLaboratory, Washington, D.C. 20375 E. ORAN Science Applications, Inc., Arlington, Virginia 22209 In order to explain O I lines in thetropical nightglow, complet[ andreasonably accurate recombina- tion and emission rate coefficients are used to construct a detailed radiative cascade model of a recom- bining oxygenplasma. Effectiverecombination coefficients are given for all low quantum number O I levels for the two limiting cases of zero and infiniteoptical depthof the resonance lines. The directrecom- bination coefficients for the S levels, and to a lesser extent the P levels, are significantly smaller than those previouslyquoted in the literature. The quantitative evaluation of radiative cascading in the optically thin limit predicts an order of magnitude lower intensity for the 1304-A line thanthat predicted by a recentlypublished optically thin model usingan estimate of the cascade contributions to the intensity. However,the opticallythick model,whichis more realistic for the F2region than the thin model,predicts a 1304-A intensity in goodagreement with observations of the 1304-A line. In recent years, UV emissions from atomic oxygen in the F region havebeenobserved near the peaks of the equatorial anomaly [Hicks andChubb, 1970; Barth andSchaffner, 1970]. The magnitude of the atomic oxygen line radiation in this tropical nightglow has recently beenexplained in termsof emission following the recombination of an electron with an O+(4S) ion [Hanson, 1969; Tinsley et al., 1973;Meier and Opal; 1973]. We have constructed a detailed theoretical model of radiative cascading in a recombinirrg oxygen plasma [Oran et al., 1972] and find some significant differences with the recombination rates discussed by Tinsleyet al. [1973]. One important effect not considered previously is the sensitivity of theintensity of the1304-A line (as well as certain other triplet lines) to the optical depth of the lines of the nd•D-2p • 8p series. This paper presents our calculated effective recombina- tion coefficients for the two limiting cases in which all tran- sitions to theground state areeither optically thin or infinitely thick.Our optically thin model with a quantitative calculation of radiative cascading predicts anintensity forthe1304-A line an order of magnitude lower than that predicted by the op- ticallythin model of Tinsley et al. on the basis of a plausible guess aboutthe branching of the cascading. A quantitatively evaluated optically thin modelof radiativecascading cannot explain the observed 1304-A intensity of the tropical nightglow. However, our optically thick model, which is much more realistic for the F• region than a thin model,does predicta 1304-A intensity comparable to that of the thin model of Tinsley et al. and in good agreement with obser- vations of the 1304-/[ linesas discussed by Meier and Opal [1973]. We will first describe the model and the atomic rate coefficients and then discuss the nature of radiative cascading in the two limits. The impact of theseimprovedrecombina- tion rateson the interpretation of the tropical nightglow will be discussed. MODEL The radiative cascade model we have used is described in detail elsewhere [Oran et al., 1972]. The method follows the Copyright (D 1974by the American Geophysical Union. cascade matrix technique discussed by Pengelly[1964]. The effective recombination coefficient a• for level k is = + k'>k where ag o is the direct recombination coefficient into level k and the second term represents the cascade contribution. The cascade matrix element C•,• gives the probabilityrhat forma- tion of level k' results in formation of level k, all possible cascade paths being considered. The determination of the cascade matrix C requires a knowledge of the Einstein A coefficients of all transitions in O I. The rate coefficient a•x for formation of a particular line X originating from level k is a•x = r•xa• (2) where r•x is the branchingratio into the line X. There are two limiting cases for which the effective recom- bination coefficient can be obtained simply. The first, called case A [Pengelly,1964], assumes all emission linesto be op- tically thin. The second, called caseB, assumes that all lines terminating on the groundstate have infiniteopticaldepthfor resonant scattering. This second case is more realisticfor the tropical nightglow,since the optical depth of the O I triplet resonance lines from the emitting F: region is large in com- parison with unity over distancesof the order of a scale height. Both cases A and B can be treated in the same cascade matrix formulation. In case B all transitions to the ground state are neglected in calculating the cascade matrix C; i.e., the EinsteinA coefficients of all such lines are set equal to zero. Our model explicitly included all O I triplet and quintet 2p80S)nl levels through principalquantum number n = 20 but neglectedhigher levels. The quantum defect method of Burgess and Seaton [1960] was used to calculate the direct recombination coefficients for each s,p, andd level[Davis and Lewis, 1973; Oran et al., 1972], and the analytic recombina- tion coefficients [Burgess, 1965] of atomic hydrogen wereused forthe essentially hydrogenic levels with I > 3. The Einstein A coefficients among the I > 3 levels were also taken to be hydrogenic. The A coefficients for transitions amongexcited s, p, and d levels were calculated by using the seminumerical 2540