JULY1969 A. DALGARNO, M. B. McELROY AND A. I. STEWART 753 Electron Impact Excitation of the Dayglow A. ~)ALGARNO Harvard College Observatory and Smithsonian Astrophysical Observatory, Cambridge, Mass. M. B. McELRoY Kitt Peak National Observatory, Tucson, Ariz. .~m) A. I. STEWART~ Dept. of Physics, The University of Pittsburgh (Manuscript received 2 December 1968, in revised form 6 March 1969) ABSTRACT Calculations are described of the equilibrium velocity distributions of the photoelectrons produced inthe F region by solar ionizing radiation. Detailed estimates are presented of the intensities and altitudeprofiles of emission features of atomic oxygen, molecular nitrogen, and molecular oxygen, appearing inthe dayglow as a result of photoelectron impacts.1. Introduction The fast photoelectrons, produced in the upper atmosphere by the absorption of solar ultraviolet radiationin ionizing transitions, lose energy in collision processesleading to ionization and excitation of the neutralparticles and to heating of the electron and ion gases.The excitation processes produce a substantial component of the dayglow luminosity of the upper atmosphere, the observation and interpretation of which canprovide detailed information on the distribution ofenergy sources in the daytime atmosphere. The prediction of the intensities of the dayglow emissionfeatures is similar to the calculation of electron heatingrates (Dalgarno et al., 1963, 1967) but involves a moredetailed description of the individual processes thatslow down the photoelectrons and a more precisecalculation of the apportionment of the available energyamong them.2. Production of photoelectrons The calculation of the initial energy spectrum of thephotoelectrons, which involves a choice of model atmospheres, of absorption and photoionization crosssections, and of solar ultraviolet intensities, has beendescribed in detail (Dalgarno et al., 1963, 1967). Thepredicted initial spectra at various altitudes for a solarzenith angle of 72- and a model atmosphere with anexospheric temperature of 750K are shown in Fig. 1. t Present affiliation: Laboratory for Atmospheric and SpacePhysics, University of Colorado, Boulder.3. Slowing down of photoelectrons The photoelectrons lose energy by exciting andionizing the neutral particle constituents of the atmosphere and by elastic collisions with the ambientelectrons (Dalgarno et al., 1963). Many processes contribute to the energy degradation but few of the crosssections are known with precision. For atomic oxygen, the ionization cross section hasbeen measured by Fite and Brackmann (1959) andRothe et al. (1962), the cross sections for populating theIOOC_~.FxO. 1. Production rate of photoelectrons with initial energygreater than E as a function of E for various altitudes.754 JOURNAL OF THE ATMOSPHERIC SCIENCES Vot. t~t~ 26upper levels of the green and red lines, i.e.,e+O -P) -~ e+O('$),e+O(aP) ~ eq-O(~D), (2) have been calculated by Smith et al. (1967), and the cross section for populating the 3s aS state has been calculated by Stauffer and McDowell (1966). For molecular oxygen, the ionization cross sectionhas been measured by Tare and Smith (1932), Craggset al. (1957), Lampe et al. (1957), Fire and Brackmann(1959), Rapp and Englander-Golden (1965) and Schramet al. (1965, 1966). The cross section for simultaneousionization into the b 42;~- state of 02+ has been measuredby Stewart and Gabathuler (1958), Nishimura (1966,1968), and Aarts and de Heer (1968). The cross sectionfor dissociative attachment has been measured by Rappand Briglia (1965), and some cross-section data for theinelastic scattering of electrons with energies between4.5 and 12.5 eV have been obtained by Schulz andI)owell (1962).(see also McGowan et al., 1964). Recently, Hake and Phelps (1967) have analyzed energyloss in O2 to derive a set of inelastic cross sections withthresholds at 4.4, 5.0, 8.0 and 9.7 eV. The inelasticscattering of electrons at energies in the region of 500 eVhas been investigated for O2 by Lassettre et al. (1964)and Silverman and Lassettre (1964). Suitably analyzed,the data can yield the Born .approximation to the crosssection at other impact energies, and the Born approximation for.the dissociation of O2 in the SchumannRunge continuum has been so derived by Silvermanand Lassettre. The ionization cross section for N2 has been measuredby Tare and Smith (1932), Lampe et al. (1957), Peterson(1964), Rapp and Englander-Golden (1965) andSchram et al. (1965, 1966). The excitation function forthe production of the first negative system has beenmeasured by Stewart (1956), Sheridan et al. (1961),Hayakawa and Nishimura (1964), Davidson and O'Neil(1965), McConkey and Latimer (1965), McConkeyet al. (1967), Holland (1967), Srivastava and Mirza(1968), Nishimura (1968) and Aarts et al. (1968). Theexcitation functions for populating the CalIu state ofN2, the upper level of the second positive system, arealso available (Thieme, 1932; Langstroth, 1933,;Herrmann, 1936; Stewart and Gabathuler, 1958;Kishko and Kuchinka, 1959; Zapesochnyi and Kishko,1959; Fink and Welge, 1964; Zapesochnyi and Skubenich, 1966; Jobe et al., 1967; Burns et al., 1969), as arethose for simultaneous excitation and ionization to theA 2110 state of N~+, the upper level of the infraredMeinel band system (Zapesochnyi and Skubenich, 1966;Srivastava and Mirza, 1968), for populating the B ~II,state of N2, the upper level of the first positive bandsystem (Williams, 1935; Zapesochnyi and Skubenich,1966), and for populating the a ~lla state, the upper levelof the Lyman-Birge-Hopfi~e!d band system (Holland,1968). Cross sections for the electron impact dissociationof N2 have been measured by Winters (1966). Engelhardtet al. (1964) have obtained an estimate of thecross section for a transition occurring near 6.7 eV,which probably corresponds to excitations of the B alI~and A aZ~+ states (Takayanagi and Takahashi, 1966).The cross sections measured by Zapesochnyi andSkubenich (1966) for the excitation of the B alIa stateare large, and we shall assume that direct excitation tothe A aE~+ state is negligible compared with cascadingfrom the B *II~ state. The A aE;~+ state, which is theupper level of the Vegard-Kaplan band system, is thelowest lying excited electronic state of Ns. Its thresholdoccurs at 6.5 eV (Miller, 1966). The inelastic scattering of electrons with energies inthe region of 500 eV has been investigated by Lassettreand Krasnow (1964), Silverman and Lassettre (1965),Geiger and Stickel (1965), Lassettre et al. (1965), andMeyer and Lassettre (1966); and Takayanagi andTakahashi (1966) have derived from the high-velocitydata the Born approximation to the cross sections forexcitation of the a ~IIo state, the b ~II~ state, and a groupof states of N2 near 14 eV. The a ~II~ state is the upperlevel of the Lyman-Birge-Hopfidd band system, andthe b ~II~ state the upper level of the Birge-Hopfieldand Janin systems. Below 6.5 eV, the photoelectrons lose energy throughexcitation of the vibrational levels of N~, a process thathas been studied experimentally by Haas (1957),Schulz (1959, 1962, 1964), Schulz and Koons (1966),Boness and Hasted (1966), and Andrick and Ehrhardt(1966). The experimental data are satisfactorily reproduced by the model calculations of Chen (1964). We have supplemented the experimental data by theuse of some simple rules relating cross, sections fortransitions of similar kinds. Thus, we assume foroptically allowed transitions that the cross sections havethe same shape as a function of E/W, where E is theelectron energy and W is the threshold energy, as thatmeasured for the ls-2p transition of atomic hydrogen(Fire and Brackmann, 1958; Fire et al., 1959) and tohave magnitudes Q ..... given by W2Q ..... 2.1X10-'4 eV2 cm2, (3)where f is the optical oscillator strength of the transition. For strong atomic transitions, the cross sectionswill usually be accurate to within a factor of 2 (cf.Seaton, 1962). For the cross sections of transitionsinvolving a change in spin multiplicity, we adopted :forthe appropriate shape as a function of E/W that' forthe I~S-2aS transition in helium .(Schulz and Fox, 1957)and we assumed that the magnitudes are given by W2Q~x= 1.5 X 10-'* eV~ cm--i (4)For forbidden transitions, not .involving a change, inspin multiplicity, we assmned that fhe cross sectionsJut, Y1969 A. DALGARNO, M. B. McELROY AND A. I. STEWART 755have the same shape as a function of E/W as thatmeasured for the ls-2s transition in atomic hydrogen(Stebbings et al., 1960), and we assumed (4) for themagnitudes. Some check on the optically allowed transitions isprovided by the requirement that at high electronener~es the energy loss rate be given by the BetheformuladE -- 1.9 X 10dx E iwhere ni is the number density of constituent i, and Ifits mean excitation energy, which takes the values of15.0 eV for atomic hydrogen, 42.3 eV for helium, 82 eVfor nitrogen, and 94 eV for atomic and molecularoxygen. There are no measurements for the atmospheric gasesof the distribution of secondary electrons produced byionization by the primary photoelectrons, but approximate theoretical values can be obtained from opticalphotoionization data by use of the Bethe dipole approximation (Seaton, 1959; Takayanagi and Takahashi,1966). The slow secondaries lose most of their energy inthe excitation of the vibrational levels of molecularnitrogen and in elastic collisions with the ambientelectron gas so that a gross representation of theirdistribution suffices for the prediction of most of thedayglow emission features. We assume that electronswith energies > 68 eV produce 1 ion-pair for every 34 eVof energy, that those with energies between 68 and25 eV produce 1 ion-pair, and that the secondaryelectrons after completion of the ionizing events have aMaxwellian velocity distribution characterized by atemperature equivalent to a mean energy of 5 eV. Secondary electrons are also produced by the radiative emission of ultraviolet photons from excited states,populated by photoionization and by electron impact.These sources can be included straightforwardly. Although the accuracy of the cross sections adoptedfor any specific collision process may not be high, thecollection of cross-section data should describe adequately the overall efficiency of energy loss as a functionof energy and yield a satisfactory representation of theequilibrium velocity distribution of the photoelectrons.4. Velocity distributions of the photoelectrons The energy loss functions or stopping cross sections, 1 ~-(i) L(Eli) = EeV cm2~, (6) n~ dxare illustrated in Fig. 2 for molecular nitrogen, molecular oxygen, atomic oxygen and helium, the heliumvalues being based on the measurements of Smith(1930), Maier-Leibnitz (1935), and Schulz and Fox(1957). The loss functions for IN2 and O2 are about a o 2.ol ; ~'~"~'"" ' I t~- '~ -i'"' I t I I ENERGY, eV ~m. :2. Stopping cross sections or loss [uncfio~s ~o~ O, 0~, ~,and He. Note the two vertical scales and the changes in the horizontal scale at 25 and at 100 eV.factor of 2 larger than those computed by Green andBarth (1967), and the loss function of O is about 50%larger. Green and Barth do not include helium as aconstituent. The differences afford a measure of theuncertainties in the calculation of energy loss rates. An energy loss function for the atmosphere at anygiven altitude can be defined by 52, ngL(E/i) L(E) = CeV cm23, (7) ~nl ithe summation including the contribution to energyloss arising from elastic collisions with the thermalelectron gas. The quantity L(E) varies slowly withaltitude except at ener~es below about 20 eV, as isclear from the similar shapes at energies above 20 eV ofthe individual loss functions. Suppose there are f(E)dE photoelectrons per unitvolume with energies lying between E and E-q-dE.Then, in equilibrium, the rate at which the photoelectrons leave the energy interval E, E+dE equals therate at which they enter. It follows that if py is the rateof production of electrons of energy Ei and we assumethat energy loss is a continuous function of E, then Y'. ps Ei >E f(E) EeV-~ cm-~3, (8) V ~,, niL(E) iwhere v is the electron velocity corresponding to anenergy E. The assumption of continuous energy loss becomes inadequate at low energies. Recent calculations byStewart-- suggest that dayglow intensities predicted onthe basis of continuous energy loss may be too high bya factor of up to 2, if the process leading to the emissionhas a threshold energy of only a few electron volts.Private communication.756 JOURNAL OF THE ATMOSPHERIC SCIENCES Vot. uM~ 26 ~. :.1~,/ p:~ ........ --%o, \l...l ........ Fro. 3. Equilibrium photoelectron fluxes vf(E) as a function ofenergy at various altitudes. Note the change in the horizontalscale at 20 eV. Formula (8) also assumes that the photodectrons areabsorbed locally. The assumption is satisfactory ataltitudes < 250 km, where most of the dayglow emissions occur, but it leads to overestimates of the intensities at higher altitudes. The calculated equilibrium photoelectron fluxesvf(E) of the photoelectrons for a zenith angle of 72-are illustrated in Fig. 3 as a function of energy atvarious altitudes. They are qualitatively similar to theresults of some less detailed calculations by Hoegy et al.(1965). The minimum, occurring near 2.5 eV at lowaltitudes, reflects the efficiency of vibrational excitationof N2. The minimum is followed by a broader maximumbetween 3.5 and 5 eV where the energy loss is mainlydue to the excitation of metastable states of oxygen.At altitudes >200km, elastic collisions with theambient electrons are the dominant energy-loss mechanism at low energies and the low-energy structure.disappears.5. The day airglow If ~r~(EIm) is the cross section for exciting level m ofconstituent i, the rate of population of level m byelectron impact, q (i] m), is given by q(ilm)=niff(t~)wri(EIm)dE [cm-3 sec-~-]. (9)To (9) must be added contributions from secondaryelectrons and from cascading from higher levds. The inclusion of energy losses to ambient electrons in(7) for the loss function affects the altitude dependenceof q(i[m) above about 225 km. At high altitudes thephotoelectrons are produced mainly from atomic oxygenand lose their energy to atomic oxygen and the electrongas. If their energy is greater than the critical energyEc, above which the most efficient cooling process isinelastic collisions with atomic oxygen and below whichit is inelastic collisions with ambient electrons (cf.I)algarno et al., 1963), the velocity distribution f(E)varies only slowly with altitude since both the numerator and the denominator in Eq. (8) vary as the atomicoxygen density; if their energy <E,, f(E) ocn(O)/n,,since in this case, the denominator varies as the electrondensity. Hence, if the major contribution to q(ilm)comes from photoelectrons with energies > E,, q(iI m)will be roughly proportional to n~; while if it comes fromenergies <E~, q(i[ m) will be roughly proportional tonin(O)/n,. The deviation from proportionality to n~ ismost noticeable for low-lying and metastable states, ascan be seen from Figs. 4, 7 and 8. All calculations referto a zenith angle of 72-.a. Atomic oxygen x 1302-1306z~ The resonance triplet of atomic oxygen, O(2pa3s3So) ---> O(2p~ aP)-khhconsists of three lines at 1302, 1304 and 1306 A. Wefind that for a solar angle of 72- the rate of populationof the aS- level by photoelectrons reaches a maximumof 250 cm-a sec-~ at an altitude of 175 km. The detailedprofile is presented in Fig. 4. The total zenith productionrate above 120 km is 2.8X10~ cm-~ sec-t. The valuesare comparable to those obtained for an overhead sunby Tohmatsu (1964) and Green and Barth (1967).IOO~$S$o3p:~ F,dSD~I00 200 300 400 ALTITUDE, km F~o. 4. Rates of population of excited states of atomic oxygen asfunctions of altitude. The dashed line is proportional to the atomicoxygen density.JuLY 1969 A. DALGARNO, M. B. McELROY AND A. I. STEWART 757 The 1304 A triplet has been observed in the dayglow(Chubb et al., 1958; Donahue and Fastie, 1963; Fastieand Crosswhite, 1964; Fastie et al., 1964; Kaplan et al.,1965; Katyushina, 1965; Fastie, 1968). Theoreticalinterpretations of the altitude profiles, based uponresonant scattering of sunlight, appeared to demand anadditional source of radiation near 200 km (Donahueand Fastie, 1963), and photoelectron impact wassuggested by Dalgarno (1964) and Tohmatsu (1964).There are several uncertainties in the original interpretation, and the position remains obscure (Kaplanand Kurt, 1965; Donahue, 1965; Tohmatsu, 1965).However, it is clear that photoelectron impact is amajor additional source that must be included in thetheoretical analysis.b. Atomic oxygen X 1356~i Donahue and Fastie (1963) and Fastie et al. (1964)have observed a dayglow feature at 1356 A, which theyidentify as a forbidden line of atomic oxygen arisingfrom the transition O ( 2p~3sSS-) ~ O(2p4 ~P) + h~.Donahue (1965) concluded that a local excitation sourcemust be invoked, and photoelectron impact is anobvious possibility (Dalgarno, 1964; Tohmatsu, 1964).The predicted excitation rate is shown in Fig. 4. The (2pa3s)SS2- level decays by spontaneous emissionto the ground ap state producing a photon at 1356IOOC50C~200~ I005OI I I I00 150 200 250 ALTITUDE, km FIG. 5. Overhead intensity of the X 13561 emission of atomicoxygen as a function of altitude. The upper branch of the solidcurve represents the intensity in the absence of absorption bymolecular oxygen, and the lower branch the intensity with thisabsorption included. The dashed curve is the observational dataof Fastie et al. (1964).IOOO "~ tO0 > Z ~- IO I I Iloo 200 300 400 ALTITUDE, kmF~o. 6. Overhead intensity of the X 8446_i. emission of atomic oxygen as a function of altitude.and to the metastable ~D state producing a photon at1728 ]l. The radiative probability for the a-P~-~S2 transition is 390 sec-~, for the aP~-~S2 it is 1300 sec-~, and forthe ~D?'~S2 it is 2 sec-~ (Garstang, 1961). l)eactivationis unlikely to affect the emission of 1356 ~, and theemission rate of 1356/k photons will be effectivdyidentical to the production rate in Fig. 4. The observed flux is affected by absorption bymolecular oxygen. Fig. 5 illustrates the overhead fluxas a function of altitude, with and without the inclusionof molecular oxygen absorption, and on the assumptionthat the atmosphere is optically thin to resonanceabsorption by atomic oxygen. The optical depth reachesunity at an altitude of about 120 km so that there issome uncertainty in the predicted emission profile atthe lowest altitudes. The observational data, included inFig. 5, are in substantial agreement with the theoreticalpredictions. The 3-0 Lyrnan-Birge-Hopfield band of N~is located in the region of 1354 A, and it is included inthe observations. Our calculations indicate that itcontributes 5% of the observed intensity. Green and Barth (1967) predicted a much greaterintensity, owing to the adoption of a cross section forthe excitation process that remains large over anextended energy range.c. Atomic oxygen X 8446 ~ The (2p~3p)aP state of atomic oxygen decays by anallowed transition to the (2pa3s)OS- state, emitting aphoton at 8446 A. It is a familiar feature of auroralspectra. The predicted altitude profile is illustrated inFig. 4 and the overhead intensity flux in Fig. 6. The dayglow emission will be augmented by fluorescence of solar Ls~nan ~, which can be absorbed byatomic oxygen into the (2pa3daD) state. The aD statethen radiates a photon at 11,340 A in a transition758 JOURNAl. OF THE ATMOSPHERIC SCIENCES VOLUME 26terminating at the upper level of the 8446 A line. Themechanism has been examined quantitativdy byShklovskii (1957) and Brandt (1959). Adopting aLyman ~ flux of 2 x 109 photons cm-2 sec-~ (Hintereggeret al., 1965) and appropriately modifying Brandt'sarguments, it appears that only 50 rayleighs of 8446 Aradiation will arise from the L?nan ~ source.d. Atomic oxygen X 7774~ The infrared line of atomic oxygen at 7774 A arisingfrom the (2pa3psP)-(2pas*S) transition is also a familiarfeature of auroral spectra. With our assumptions aboutcross sections, the emission intensity of 7774 A is comparable with that of 8446 ~k and the altitude profilesare essentially identical.e. Atomic oxygen x 1026~ Atomic oxygen has a resonance line at 1026/k arisingfrom the (2p~3daD-)-(2p4aP) transition. The atmosphere is optically thick in 1026/k and a substantialcontribution to the population of the upper level willresult from resonant scattering. The rate of populationof the 2po3dSD- state by photoelectron impact is small.Its altitude profile is illustrated in Fig. 4. The state candecay by radiating also at 11,340/k.IOOO'i" ~oot~Zbg Iot~ I00 200 300 400 ALTITUDE, km Fig. 7. Rates of population of the metastable ~D and ~S states ofatomic oxygen as functions of altitude. The dashed line is proportional to the atomic oxygen density.f. Other atomic oxygen ultraviolet lines There are other lines of atomic oxygen that shouldappear in the ultraviolet dayglow. In particular, a lineat 1152 J~ due to O(2p~3s~D-)-O(2p4~D) should besimilar in profile to 1356.1~ but less intense, and a lineat 989A due to O(2pa3saD-)-O(2p4aP) should besimilar to 1304 .i. in profile but less intense. Estimatesfor an overhead sun have been given by Green andBarth (1967). The dayglow at 989 A will be modified byresonance scattering.g. Atomic oxygen X 5577 ~ The photoelectron impact contribution to thepopulation of the ~S level of atomic oxygen is shown inFig. 7. Other excitation processes occur (Bates andDalgamo, 1954; Walker, 1965), but a detailed analysisof observational data carried out by Wallace andMcElroy (1966) established that photoelectron impactis a major source at high altitudes. The ~S level also decays by emitting photons at2972 and at 2958 A. The intensities will be 6% of thatof the green line at 5577 A.h. Atomic oxygen X 6300~ The photoelectron-impact contribution to the population of the ~D level of atomic oxygen is shown in Fig.7. The emission of the red line in the dayglow has beenthe subject of much discussion. Analysis by Noxon(1964) and Dalgarno and Walker (1964) showed thatthe ~D level must undergo severe deactivation, and theyargued that a high-altitude source in addition tophotodissociation and ionic recombination is required.The photoelectron contribution to the red-line emissionhas been calculated previously by Wallace and McElroy(1966), and our results serve as a confirmation of theirconclusions that photoelectron impact is indeed a majorhigh-altitude source. In most circumstances, the directimpact contribution by the energetic photoelectronswill be much larger than the contribution from thermalexcitation by the heated electrons, and the enhancementof the red Nine by conjugate-point photoelectrons isproduced directly by impact excitation rather thanindirectly by heating of the ambient electron gas.i. Dissociative excitation o/O~ The dissociative excitation of. molecular oxygen byphoton and electron impact, which are important lowaltitude sources of O(~D) atoms, may also be abundantlow-altitude sources of more highly excited oxygenatoms. Reliable quantitative estimates are precludedby the lack of information on the cross sections.j. First negative system of N~+ The production of N2+ molecules in the B2 Z~,+ stateby photoelectron impact with N2 is shown in Fig. 8.1969 A. DALGARNO, M. B. McELROY AND A. I. STEWART 759I000_ I00g~ to.Jo0.! ~00 200 300 400 ALTITUDE, km F~G. 8. Rates of population of excitcd states of N2 (curves 1-4)and 1XT2+ (curves 5 and 6) as functions of altitude. Curve 1, for theAa~+ state, includes the contribution from cascade from higherstates. The dashed line is proportional to the Nx density.The production is small compared with that fromresonance scattering of solar radiation by Ns+ molecules at high altitudes (cf. Wallace and McElroy, 1966).At lower altitudes, where the equilibrium density ofN2+ is small, the major source is probably simultaneousexcitation and ionization by solar radiation absorbed ina photoionizing transition (Dalgarno and McElroy,1963, 1966).k. The infrared Meinel system of N2+ The production of NT2+ molecules in the A ~1I~ stateby photoelectron impact with N.z is shown in Fig. 8.The production rate has a value of 80 cm-~ sec-~ at145 kin. The luminosity profile and the vibrational distribution will be modified by resonant and fluorescentscattering of solar radiation by the ambient N~.+ molecules, by simultaneous excitation and ionization of N~in photoionizing transitions, and possibly by ion-molecule reactions (Dalgarno and McElroy, 1966).l. The second positive band system of N2 The second positive band system of N2 is of particularinterest since photoelectron impact is the only significant source of N~(C a/l~) molecules in the atmosphereand its emission profile is unaffected by deactivationprocesses (Barth and Pearce, 1966). The predicted rate T^s~ I. Predicted vibrational distribution of the secondpositive-band system of N~, expressed as a percentage of thetotal emission.v' v" 0 1 2 3 4 5 ~v"28.5 17.4 6.5 1.9 0.5 0.1 54.920.0 15.7 8.2 2.2 0.6 0.2 57.0 55,015.9 6.5 5.9 4.9 2.3 0.8 30.815.9 9.3 5.7 5.7 4.1 1.1 34.5 27.0 2.1 4.4 0.4 0.6 1.3 1.0 10.5 2.0 5.9 0.~ 0.6 1.9 1.9 14.6 14.0 ~ Measurements o[ Jobe -t al. (1967). ~ Computed from Franck-Condon factors (Nicholls, 1964), ~ Computed from the absorption oscillator strengths of Chlnget al. (1967).of population is shown in Fig. 8 and the overheadintensity in Fig. 9. The results are comparable withthose of an earlier, more approximate calculation byNagy and Fournier (1965). The predicted vibrational distribution, based uponthe cross-section data of Jobe et al. (1967), is presentedin Table 1, as is the theoretical distribution, based uponthe Franck-Condon factors tabulated by Nicholls(1964). The calculated overhead intensity of the O-0106\\\\ \ \ \'\ '~. \ \'\ I I00 200 $00 400 ALTITUDE, ~mF~o. 9. Total rates of population of excited states of Ns abovea given altitude as functions of that altitude.760 JOURNAL OF THE ATMOSPHERIC SCIENCES VoJ. uME 26band at 3371 ~ above 165 km is 200 rayleighs, in fairaccord with the measured value of 400 rayleighs (Barthand Pearce, 1966).m. T[e /irst positive band system of N2 The first positive band system arises from theB alI~-A ~+ transition in N2. It is populated by directimpact and by cascading, its upper level being thelower level of the second positive system. The excitationfunctions of Zapesochnyi and Skubenich (1966) includethe cascading contributions, but they do not reportthe excitation functions for the individual vibrationallevels. The predicted rate of population is shown in Fig. 8and the overhead integrated rate of population in Fig. 9.The profile may be significantly modified by resonancescattering of solar radiation by the metastable A ~Zu+state (Dalgarno, 1964).n. The Vegard-Kaplan band system of N2 The Vegard-Kaplan band system arises from theforbidden A oZ~+-X ~Zo+ transition in N=. The majorsource of population is probably cascading in the firstpositive system. The rate of population is illustrated inFigs. 8. and 9. The emission profile is greatly modified by deactivation. Green and Barth (1967) have investigated theeffect, using electronic deactivation coefficients andtransition probabilities listed by Hunten and McElroy(1966). Because of vibrational interchange p~-ocessesN~(~ ~u+, v)+N2(X ~Zo+, ~=0) --~ N~(A a~+, v')+N~(X ~+, v"),the suppression of enfission from the higher vibrationallevels may be more severe than suggested by Greenand Barth.o. The Lyman-Birge-Hopfield band system of N= The Lyman-Birge-Hopfield band system arises fromthe a~IIo-X ~Z~+ transition in Ne, which proceedsthrough magnetic dipole and electric quadrupoleradiation. The rate of population by electron impact isillustrated in Figs. 8 and 9. An additional source is provided by cascading fromhigher levels and in particular from transitions originating in the h ~2:~+ and b ~1I~ states. According to Greenand Barth (1967), the total intensity may be increasedby cascading by a factor of nearly 5, whereas ourcalculations suggest an increase of about 2. Accordingto the measurements of Holland (1968), the enchancement does not exceed 40070 and may be as little as 5%. Green and Barth remark that the emission of theLyman-Birge-Hopfield system is unaffected by deactivation, but this may not be the case. The emission fromthe higher vibrational levels could be suppressed by avibrational interchange process similar to that noted forthe A ~E~+ state. Without more precise data on vibrational deactivation processes, the prediction of individual band intensities is subject to serious uncertainty.p. Other band systems Other band systems will also appear in the'dayglow.There are no measurements of the cross sections for theexcitation of the b ~II~ and h ~Z~+ states of N=, and thepredicted dayglow intensities of the resulting BirgeHopfield, Janin, Watson-Koontz and Herman-Gaydonband systems are largely arbitrary. We find with ourassumed cross sections a combined overhead intensityof 2 kilorayleighs compared with the value of 10kilorayleighs calculated by Green and Barth (1967) foran overhead sun. The altitude profiles are similar tothat for the C alI~ state. Similar uncertainties attend the prediction of theintensities of the first and second negative band systemsof Os. We obtain 400 rayleighs above 120 km, abouthalf the intensity above 120 km calculated by Greenand Barth (1967) for an overhead sun. The altitudeprofiles and intensities in the atmosphere will bemodified by fluorescence (Dalgarno and McElroy,1963, 1966). Acknowledgments. The work was in part supported byNASA grant NGR 06-003-052 and in part by NASAcontract NASw4726. Contribution 446 from the KittPeak National Observatory, operated by the Association of Universities for Research in Astronomy Inc.,under contract with the National Science Foundation. REFERENCESAarts, J. F, M., and F. J. de Heer, 1968: Preliminary report on thefirst negative band system of oxygen. Physlca (in press). , and D. A. Vroom, 1968: Emission cross sections of the first negative band system of N~ by electron impact. Physica, 40, 197.Andrick, D., and H. Ehrhardt, 1966: The angular dependence of the resonance scattering of low energy electrons from He, Ne, Ar and Nx. Z. Phys., 192, 99-106.Barth, C. A., and J. B. Pearce, 1966: Rocket measurement of the photoelectron excited ultraviolet dayglow. Space Research VI, London, Macmillan and Co., p. 381.Bates, D. R., and A. Dalgarno, 1954: Theoretical considerations regarding the dayglow. J. Atmos. Terr. Phys., 5, 329-344.Boness, M. J. W., and J. B. Hasted, 1966: Resonances in electron scattering by molecules. Phys. Letters, 21, 526-528.Brandt, J. C., 1959: Solar Lyman-~ fluorescence mechanism in the upper atmosphere. Astrophys. J., 130, 228-240.Burns, D. J., F. R. Simpson and J. W. McConkey, 1969: Absolute cross sections for electron excitation of the second positive bands of nitrogen. J. Phys. B (Proc. Phys. Soc.), 2, 52.Chen, J. C. Y., 1964: Theory of subexcitation electron scattering by molecules. II. Excitation and de-excitation of molecular vibration. J. Chem. Phys., 40, 3513-3520; Erratum. J. Chem. Phys., 41, 3263-3264.Ching, B. K., G. R. Cook and R. A. Becker, 1967: Oscillator strengths of the a, w, and e bands of N,.. f. Quant. Spectrosy. Radiative Transfer, 7, 323-337.Juicy 1969 A. DALGARNO, M. B. McELROY AND A. I. STEWART 761Chubb, T. A., E. T. Byram, It. Friedman and J. E. Kupperian,1958: The use of radiation absorption and luminescence inupper air density measurements. Ann. Geophys., 14, 109-116.Craggs, J. D., R. Thorburn and B. A. Tozer, 1957 :The attachment of slow electrons in oxygen. Proc. Roy. Soc. (London), A240, 473-483.Dalgarno, A., 1964: Corpuscular radiation in the upper atmos phere. Ann. Geophys., 20, 65-73.--, and M. B. McElroy, 1963: Fluorescence of solar ionizing radiation. Planetary Space Sci., 11, 727-728.----, and --, 1966: Twilight effects of solar ionizing radiation. Planetary Space Sci., 14, 1321-1329. and R. J. Moffett, 1963: Electron temperatures in the ionosphere. Planetary Space Sci., 11, 463-484. and J. C. G. Walker, 1967: The diurnal variation of ionospheric temperatures. Planetary Space Sci., 15, 331-345.--, and J. C. G. Walker, 1964: The red line of atomic oxygen in the day airglow. J. Atmos. Sci., 21, 463-474.Davidson, G., and R. O'Neil, 1965: Production of N2 1-N (0,0) radiation by 60 keV electrons. Proc. Fourth Intern. Conf. of Phys. of Electronic and Atomic Collisions.Donahue, T. M., 1965: Some considerations concerning radiation transport in the OI 1304 triplet in the upper atmosphere. Planetary Space Sci., 13, 871-888. , and W. G. Fastie, 1963: Observation and interpretation of resonance scattering of Lyman a and OI (1300) in the upper atmosphere. Space Research IV, Amsterdam, North-Holland Publ. Co., 304-324.Engelhardt, A. G., A. V. Phelps and G. G. Risk, 1964: Determina tion of momentum transfer and inelastic collision cross sections for electrons in nitrogen using transport coefficients. Phys. Rev., 135, A1566-1574.Fastie, W. G., 1968: Far ultraviolet day airglow studies. Planetary Space Sci., 16, 929-935.--, and H. M. Crosswhite, 1964: Far U. V. dayglow measure ments: Atomic oxygen. Planetary Space Sci., 12, 1021-1026. -- and D. F. Heath, 1964: Rocket spectrophotometer air glow measurements in the far ultraviolet. J. Geophys, Res., 69, 4129-4140.Fink, V. E., and K. H. Welge, 1964: Lebensdauer der elektro nenzust/inde N2(CalIu), N~+(B2Zu), NH(AalI), NH(c~ll), PH(glI). Z. Naturforsch., 19A, 1193-1201.Fite, W. L., and R. T. Brackmann, 1958: Collisions of electrons with hydrogen atoms. II. Excitation of Lyman-alpha radia tion near threshold. Phys. Rev., 112, 1151-1156. , and ---, 1959: Ionization of atomic oxygen on electron impact. Phys. Rev., 113, 815-816. , R. F. Stebbings and R. T. Brackmann, 1959: Collisions of electrons with hydrogen atoms. IV. Excitation of Lyman alpha radiation near threshold. Phys. Rev., 116, 356-357.Garstang, R. H., 1961: Mutual magnetic interactions and oscilla tor strengths in the first spectrum of oxygen. Proc. CambridgeGeiger, J., and W. Stickel, 1965: Energy losses of fast electronsin nitrogen. J. Chem. Phys., 43, 4535-4536.Green, A. E. S., and C. A. Barth, 1967: Calculations of the photo electron excitation of the dayglow. J. Geophys. Res., 72, 3975-3986.Haas, R., 1957: Investigation of the energy loss of slow electrons in nitrogen. Z. Phys., 148, 177-191.Hake, R. D., and A. V. Phelps, i967: Momentum-transfer and inelastic-collision cross sections for electrons in 02, CO, and CO2. Phys. Rev., 158, 70-84.Hayakawa, S., and H. Nishimura, 1964: Measurement of the excitation cross section of N2+ first negative band by electron impact. J. Geomag. Geoelect., 16, 72-74.Herrmann, O., 1936: Intensity measurements in the neon and argon spectra excited by electron collisions. Ann. Physik, 25, 143-165.Hinteregger, H. E., L. A. Hall and G. Schmidtke, 1965: Solar XUV radiation and neutral particle distribution in July 1963 thermosphere. Space Research V, Amsterdam, North Holland Publ. Co., 1175-1190.Hoegy, W. R., J. P. Fournier and E. G. Fontheim, 1965: Photo electron energy distribution in the F region. J. Geophys. Res, 70, 5464~5468.Holland, R. F., 1967: Cross sections for electron excitation of the 3914~ (0,0) band of the N2+ first negative system. Los Alamos Scientific Lab., Rept. LA-3783, 1-13.---, 1968: Excitation of nitrogen by electrons: The Lyman Birge-Hopfield system of N2. Los Alamos Scientific Lab., Rept. LA-DC-9468, 1-32.Hunten, D. M., and M. B. McElroy, 1966: Quenching of metas table states of atomic and molecular oxygen and nitrogen. Rev. Geophys., 4, 303-328.Jobe, J. D., F. A. Sharpton and R. M. St. John, 1967: Apparent cross sections of N2 for electron excitation of the second positive system. J. Opt. Soc. Amer., 57, 106-107.Kaplan, S. A., V. V. Katyushina and V. G. Kurt, 1965: Intensity measurements of scattered ultraviole tradiation (1216 * and 1300 ~) in the upper atmosphere. Space Research V, Amster dam, North-Holland Publ. Co., 595-611. , and V. G. Kurt, 1965: Interpretation of observations of the OI triplet (x= 1300 X) in the upper atmosphere. Kosmlch. lssled. Akad. Nauk SSSR, 3, 256-261.Katyushina, V. V., 1965: Measurements of intensity of upper atmospheric glow in triplet lines (X~1300 3,) at heights of 100-500 km. Kos~nich. Issled. Akad. Nauk SSSR, 3, 248-251.Kishko, S. M., and M. I. Kuchinka, 1959: Excitation functions of certain bands of the second positive system of Ne. Opt. Spektrosk., 6, 378-379.Lampe, F. W., J. L. Franklin and F. H. Field, 1957: Cross sec tions for ionization by electrons. J. Amer. Chem. Soc., 79, 6129-6135.Langstroth, G. O., 1934: The excitation of band systems by elec tron impact. Proc. Roy. Soc. (London), A146, 166-177.Lassettre, E. N., F. M. Glaser, V. D. Meyer and A. Skerbele, 1965: Determination of molecular excitation potentials by electron impact. An anomaly in the N2 spectrum. J. Chem. Phys., 42, 3429-3435.--, and M. E. Krasno~v, 1964: Collision cross-section study of two transitions in nitrogen. J. Chem. Phys., 40, 1248-1255.--, S. M. Silverman and M. E. Krasnow, 1964: Electronic collision cross sections and oscillator strengths for oxygen in the Schumann-Runge region. J. Chem. Phys., 40, 1261 1265.Maier-Leibnitz, H., 1935: Ausbeutmessungen beim Stoss lang samer elektronen mit Edelgasatomen. Z. Phys., 95, 499-523.McConkey, J. W., and J. D. Latimer, 1965: Absolute cross sec tions for simultaneous ionization and excitation of N2 by electron impact. Proc. Phys. Soc., 86, 463-466. , J. M. Woolsey and D. J. Burns, 1967: Absolute cross sections for electron impact excitation of 3914 3. N2+. Planetary Space Sci., 1~, 1332-1334.McGowan, J. W., E. M. Clarke, H. P. Hanson and R. F. Stebbings, 1964: Electron- and photon-impact ionization of 02. Phys. Rev. Letters, 13, 620-622.Meyer, V. D., and E. N. Lassettre, 1966: Weak transitions in excitation of N2 by electron impact and comparison with excitation by absorption of radiation. J. Chem. Phys., 44, 2535-2536.Miller, R. E., 1966: The absolute energy of the AaZ? state of nitrogen. J. Mol. Spectrosy., 19, 185-191.Nagy, A. F., and J. P. Fournier, 1965: Calculated zenith intensity of the second positive band of molecular nitrogen. J. Geophys. Res., 70, 5981-5982.Nicholls, R. W., 1964: Transition probabilities of aeronomically important spectra. Ann. Geophys., 20, 144-181.762 JOURNAL OF THE ATMOSPHERIC SCIENCES Vot~ugE 26Nishimura, H., 1966: Measurement of the excitation function of 02+ first negative bands by electron impact. J. Phys. Soc. Japan, 21, 1018-1019.--, 1968: Excitation of N2+, 02+ and CO2+ band by electron impact. J. Phys. Soc. Japan, 24, 130-143.Noxon, J. F., 1964: A study of the 6300 ~ oxygen line in the day airglow. J. Geophys. Res., 69, 3245-3255.Peterson, J. R., 1964: Electron-impact ionization of atoms and molecules using a fast crossed-beam method. Atomic Collision Processes, Amsterdam, North-Holland Publ. Co., 465473.Rapp, D., and D. D. Briglia, 1965: Total cross sections for ioniza tion and attachment in gases by electron impact. II. Nega tive-ion formation. J. Chem. Phys., 43, 1480-1489.--, and P. G. Englander-Golden, 1965: Total cross sections for ionization and attachment in gases by electron impact. I. Positive ionization. J. Chem. Phys., 43, 1464-1479.Rothe, E. W., F. L. Marino, R. H. Neynaber and S. M. Trujillo, 1962: Electron impact ionization of atomic hydrogen and atomic oxygen. Phys. Rev., 125, 582-583.Schram, B. L., F. J. de Heer, M. J. van der Wiel and J. Kiste maker, 1965: Ionization cross sections for electrons (0.6-20 keV) in noble and diatomic gases. Physica, 31, 94-112.--, H. R..Moustafa, J. Schutten and F. H. de Heer, 1966: Ionization cross sections for electrons (100-600 eV) in noble and diatomic gases. Physica, 32, 734-740.Schulz, G. J., 1959: Measurement of excitation of N2, CO, and He by electron impact. Phys. Rev., 116, 1141-1147. , 1962: Vibrational excitation of nitrogen by electron impact. Phys. Rev., 125, 229-232. , 1964: Vibrational excitation of N,2, CO, and H2 by electron impact. Phys. Rev., 135, A988-A994. , and J. T. Dowell, 1962: Excitation of vibrational and electronic levels in Ox by electron impact. Phys. Re'o, 128, 174-177. , and R. E. Fox, 1957: Excitation of metastable levels in helium near threshold. Phys. Rev., 106, 1179-1181. , and It. C. Koons, 1966: Energy levels of the compound state of N~ near 2.3 eV. J. Chem. Phys., 44, 1297-1298.Seaton, M. J., 1959: Electron impact ionization of Ne, O, and N. Phys. Rev., 113, p. 814. , 1962: Theory of excitatioli and ionization by electron im pact. Atomic and Molecular Processes, New York, Academic Press, 375-420.Sheridan, W. F., O Oldenberg and N. P. Carleton, 1961: Excita tion of nitrogen by controlled proton and electron impact. Proc. Second Intern. Conf. Physics of Electronic and Atomic Collisions, Boulder, Colo., p. 349.Shklovskii, I. S., 1957: A possible new type of fluorescence of the earth's atmosphere. Soy. Astron.-A. J., 1, 130-132.Silverman, S. M., and E. N. Lassettre, 1964: Collision cross sections for oxygen in the excitation energy range 10 to 80 V. J. Chem. Phys., 40, 2922-2932.--, and --, 1965: Generalized oscillator strengths and elec tronic collision cross sections for nitrogen at excitation energies above 10 eV. J. Chem. Phys., 42, 3420-3429.Smith, K., R. J. W. Henry and P. G. Burke, 1967: Calculations on the scattering of electrons by atomic systems with con figurations 2pq. Phys. Rev., 157, 51-68.Smith, P. T., 1930: The ionization of helium, neon, and argon by electron impact. Phys. Rev., 36, 1293-1302.Srivastava, B. N., and I. M. Mirza, 1968: Absolute cross sections for simultaneous ionization and excitation of N~ by electron impact. Phys. Rev., 168, 86-88.Stauffer, A. D., and M~. R. C. McDowell, 1966: An impact param eter treatment of the excitation of atoms by charged particles. Proc. Phys. Soc., 89, 289-298.Stebbings, R. F., W. L. Fire, D. G. Hummer and R. T. Brack mann, 1960: Collisions of electrons with hydrogen atoms. V. Excitation of metastable 2S hydrogen atoms. Phys. Rev., 119, 1939-1945.Stewart, D. T., 1956: Electron excitation functions of the first negative bands of N2+. Proc. Phys. Soc., A69, 437-440. , and E. Gabathuler, 1958: Some electron collision cross sections for nitrogen and oxygen. Proc. Phys. Xoc., 72, 287-289.Takayanagi, K., and T. Takahashi, 1966: Behavior of slow elec trons in atmospheric gases: Part III, collision cross section of molecular nitrogen. Rept. Ionospherlc Space Res. Japan, 20, 357-373..Tare, J. T., and P. T. Smith, 1932: The efficiencies of ionization and ionization potentials of various gases under electron impact. Phys. Rev., 39, 270-277.Thieme, O., 1932: Lichtausbeute im Helium-, Quecksilber-, und Stickstoff-Spektrum bei Anregung dutch Elektronenstoss. Z. Phys., 78, 412-422.Tohmatsu, T., 1964: Photo-electronic excitation of atomic oxygen 1302-4-6A triplet emission in the day airglow. Rept. Iono spheric Space Res. Japan, 18, 425-437.--, 1965: Photoelectronic excitation of atomic oxygen 1300 ~ triplet emission in the day airglo~v. II. The line intensity ratio, Repl. Ionospheric Space Res. Japan, 19, 509-514.Walker, J. C. G., 1965: The green line of atomic oxygen in the day airglow. Y. Atmos. Sci., 22, 361-369.Wallace, L., and M. B. McElroy, 1966: The visual dayglow. Planetary Space Scl., 14, 677-708.Williams, S. E., 1935: The efficiency of excitation of the nitrogen first positive bands by electron impact. Proc. Phys. Soc., A47, 420-423.Winters, H. F., 1966: Ionic adsorption and dissociation cross section for nitrogen. J. Chem. Phys., 44, 1472-:1476.Zapesochnyi, I. P., and S. M. Kishko, 1959: Some results of an investigation of excitation functions of the bands in the negative system of N~+. Izv. Akad. Nauk SSSR, 23, 965-967.--, and V. V. Skubenich, 1966: The cross sections for the ex citation of molecular nitrogen levels by electron collision. Opt. Spektrosk., 21, p. 83.