Fluorescence efficiencies of electrons in molecular nitrogen and oxygen gases

Planef. Space Sci.. Vol. 25, pp. 555 to 562. Pergemon Press, 1977. printed in Northern Ireland

FLUORESCENCE EFFICIENCIES OF ELECTRONS IN MOLECULAR NITROGEN AND OXYGEN GASES S. P. KHARE and A. KUMAR Department of Physics, Institute of Advanced Studies, Meerut University, Meerut (U.P.) 250001, India (Received 31 August 1976) Abstract-FJluorescence efficiencies of electrons in a large number of bands of the N1 First Positive and 02+ Fist Negative groups lying in the 4900-10,500 8, wavelength range have been investigated theoretically. The variation of transition moment with internuclear distance is taken into consideration. For the Fist Positive group of Nz the calculations are carried out at very low pressure as well as at 600 Torr. In general the present values are higher than the experimental values but in most of the cases fair agreement has been obtained. For the 0 2+ First Negative group no direct experimental data is avaiIable. However, the present ratio of the total efficiency in the O2 Fit Negative group to the

Nz+ First Negative group is found to be in good agreement with the experimental intensity ratio. 1. INT.RODUCl’ION

When gamma rays, X-rays or charged particles impinge upon our atmosphere, the fluorescence is principally produced as emission in the molecular nitrogen bands. The fraction of the kinetic energy of the incident particle which is converted into photon energy of a particular frequency is termed as fluorescence eficiency q for that wavelength and is regarded as an important parameter for upper atmospheric investigations (Dalgarno, 1964). Recently Khare and Kumar (1973, 1975) have calculated the efficiency 17 of electrons in various bands of the N,(2P) and N,+(lN) systems and have obtained good agreement with experimental data. A number of experimental data for the fluorescence efficiency of electrons, ions and X-rays for the N, First Positive group, i.e. N,(lP) are also available. At very low pressure Hartman (1968), Mitchell (1970) and Dunn and Holland (1971) have employed electrons, X-rays and heavy ions, respectively, as projectiles to measure their efficiencies for the N,(lP) band. The experimental data for 9 for a number of bands of the N,(lP) group are also available at 600 ton: pressure (Davidson and O’Neil, 1964). Furthermore, the intensity ratio of the N,(lP) and 02+ First Negative, i.e. O,+(lN) band systems with respect to the N,+(lN) band are also available experimentally as well as theoretically (Valiance Jones, 1969; O’Neil and Davidson, 1969; Stolarski and Green 1968). However, as emphasized by Phelps (1972), hardly any attempt has been made to compare the theoretical values of efficiency with experimental data. Hence, it is of interest to calculate r) for the N,(lP) and O,‘(lN) band systems.

It may be noted that the efficiency calculations require excitation cross sections. For some of the bands Khare and Kumar employed the intensity formula (Her&erg, 1961; Nishimura, 1968) to obtain ~known excitation cross sections in terms of known excitation cross section. According to this formula the ictensity of a particular band varies directly as the square of the transition momept. Khare and Kumar assumed that the transition moment is independent of the internuclear distance, which is not always correct. Hence, in the present calculation of q the variation of transition moment is taken into account. To consider the contribution of the secondary electrons to q which will be important for the exchange type of excitati&s, e.g. N,(lP), we require ionization cross section per unit energy range Q(E, E), where E is the energy of the secondary electron produced by an incident electron of energy E. Khare and Kumar (1973, 1975) have employed the relations of Khare (1969) for Q(E, E). However, these semi-empirical relations have a discontinuity at the switch over point and do not yield good agreement with the recent experimental data of Opal et at. (1971). Furthermore, the optical oscillator strength employed by Khare and Kumar are known to be 25% overestimated due to error in

the McLeod gauge (Skerbele and Lassettre, 1970). Recently, Jhanwar et al. (1975) have combined the two relations of Khare into one which is applicable at all the energy regions of the incident and secondary electrons. They have also employed corrected values of the optical oscillator strength. Their relation does not have any discontinuity and for the atmospheric gases the calculated values of Q(E, E)

S. P. KHARE and A. K~MAR

556

are in satisfactory agreement with the experimental data. Hence, in the present investigation we have employed the relation of Jhanwar et al. for Q(E, E) with corrected values of the oscillator strength to calculate n for the various bands of N,(lP) and O,+(lN). 2. THEORY

Due to electron impact the ground state N2(X1&+, v = 0) nitrogen molecules are excited to the Nz(B311,, u’) state. These excited states then decay radiatively to N,(A%,‘, u”) and thereby the N,(lP) band system is produced. Similarly in the production of the OZ’(lN) band system the ground state OZ(X’2,+, o = 0) molecules are simultaneously ionized and excited to the O,+(b%,-, u’) states. The radiative decay of these excited states to 02+(a411U, u”) produces the O,+(lN) group. On the assumption that all the excited states decay radiatively (no quenching) the fluorescence efficiency for the production of a photon of frequency v is given by: rl = g N. (E,), (1) 0 where N,(EJ is the number of excitations produced when a primary electron of energy E,, and all its secondaries are absorbed in a gas of uniform density. In the continuous slow down approximation N,(E,) is equal to c,, N,,(E,), where N,(E,) is the number of excitations produced by the nth generation electrons (n = 0 refer to primary electron). To calculate N,(E,) we employ the same expressions as used by Khare and Kumar. However, the values of the oscillator strength employed by Khare and Pa,dalia (1970) are multiplied by 0.754 to correct for the McLeod gauge error (Skerbele and Lassettre, 1970; Tisone, 1972a, b; Jhanwar et al., 1975). Furthermore, for Q(E, E), we have employed the expression given by Jhanwar et al. (1975). According to these authors

where the different symbols have their usual meanings (Khare, 1969). e,, is a parameter and is equal to 50 eV for N2 and 02. The experimental excitation cross sections Q(u’, 0”) for a number of bands of N,(lP) are given by Stanton and John (1969) in the energy range varying from the excitation threshold to 50 eV. Since the cross sections are sharply peaked at low energies without making any appreciable error we have taken Q(t)‘, u”) equal to zero for energy E > 50 eV. For several other bands only peak values of Q(u’, u”) are given. It may be pointed out that if the shapes of the excitation cross sections Q(u’, u”) are independent of (u’, u”) it can easily be shown that n(u’, u”) satisfies the following scaling relation

This relation was employed for the N,(2P) band system (Khare and Kumar, 1973). However, in the present case of the N,(lP) band system cascading takes place from the C311, level to the B3& level. Hence, the shapes of the Q(u’, I)“) curves for various bands having different u’ are not the same. Nevertheless, for the bands having the same u’ but different u” the shapes of the cross section curves are nearly the same (McConkey and Simpson, 1969; Stanton and John, 1969). Hence, equation (3) can be used to obtain the efficiency values q(u’, u”) for various bands of the N,(lP) and O,‘(lN) groups, having same v’ but different u”. To include other bands, for which even peak values of the cross sections are not available, we have used the following relation

Q(u2’, u2”) NV,’ v3(u*‘,uz”) QtuI’, Ul”) = Nvl’v3(u1’,u1’y x

ReZtYu2’, uzl) q(%‘, ~2’7 Re’(j&‘,

Q(E,&)=fitE,e)Q~(E,e)+fitE,&)Q~(E,e) to obtain the unknown cross (2) terms of known cross section

with

f,(E,e)=

(l-&)(&~lnrl~n~~-l)l 4mZR2We, 0)

Q,xtE, E)=--

E(E+I)

c3.s

ln

cE

~1”)qtul’, VI”)

(4)

section Q(uz’, u2”) in Q(ul’, ul”). No’ is the equilibrium population density. Re (&*) is the transition moment with internuclear distance yO,.,* and q(u’, u”) is the Franck Condon factor for (u’, 0”) transition. It may be noted that Nu,‘/Nu,’ can be replaced by q(0, q’)/q(O, u,‘) (Nishimura, 1968). The variation of Re (&“) with &. for the N,(2P), N,(lP), N,+(lN) systems has been discussed by various investigators (Turner and Nicholls, 1954; Wallace and Nicholls, 1955; Jain and Sahani, 1966, 1967; Jeunehomme, 1966). The values of Franck-Condon factors for these band systems are

TABLET. EFFICIENCXRATIOSOFTHE N,(lP) GROUPBANDSTOTHE Wavelength (A) 10510.0 8912.4 8723.0 7753.7 7626.8 7507.0 7397.0 7274.0 6875.2 6788.6 6704.8 6623.6 6544.8

(4.zYe”)

Mitchell* (1970)

-

3.94-l -

3914A~mo~N~+(lN) Hartman* (1968) 750 eV

-

2.70-V

1.37-r 1.84-l 1.68-l 2.20-r 1.80-l 1.00-r 6.00-* 4.00-* 8.00~’ 9.00-* 9.00-2 6.00-*

2.70-r 2.60-r 1.50-r

2.70-l 1.60-l 9.00-2 6.00-* 5.00-Z 7.00-2 8.00-* 1.00-r 6.00-*

Present

-

1.87-r 3.10-r 2.76-r 1.49-r

(1) (1) (3) (3)

1.18-l (1) 8.24-* (1)

* The values as quoted by Dunn and Holland (1971). t The indices give the power of 10 by which entries should be multiplied. $ Number inside the bracket denotes the equation employed to obtain 1). TABLE2. FLUORESCENCEEFFICIENCIOFELECII(ONSINVARIOUSBANDSOF Wavelength (A)

(I)‘, VU)

Efficiency At very low pressure

10510.0 9942.0 9682.0 9436.0 8723.0 8542.5 8205.5 8047.9 7753.7 7752.0 7626.8 7612.9 7479.0 7387.2 7164.8

$ ;j

6859.3 6957.7

$3 ;;

1.66C (1)t 1.96-4 (3) 4.33-4 (3) 3.84-4 (3) 1.08K3 (3) 3.79-4 (3) 2.38~’ (4) 7.92-s (4) 9.38-4 (1) 8.66-5 (4) 1.55-3 (1) 4.25~’ (4) 2.39-5 (4) 7.48-4 (3) Loo+ (3) 1.07-6 (4) 1.02-6 (4)

6468.5 6764.0

(8, j)

2.29-4 3.71-6 (1) (4)

6322.7 6394.7 6253.0 6186.8 6185.2 6127.4 6069.7 6013.6 5959.0 5906.0 5854.4 5804.0 5755.2 5478.2

I:? ;; (996)

5.49-s 1.09-4 2.86-5 2.53~’ 1.14-z ;g5

(3) (1) (3) (4) (4) g;

1:39+ 1.06-4 7.77-5 5.51-5 4.34-5 3.60-5 1.13-5

(3) (3) (3) (3) (3) (3) (3)

(0,O) I:? :; (4: 4) I? :; g: ;I $ ;; (3: 1) (9>8) I:“;,‘)

(4, b) (l2,9) I? :; (7: 3) (8,4) (925) (lo, 6) (1197)

At 600 Torr $ 1.21-7 1.64-’ 1.68-7 6.65-’ 1.43-7 1.16-* 4.13-s 5.78-’ $ 5.86-’ : 3.67-’ 4.08-7

N,(lP) GROUP

Expt.

Expt. accuracy*

1.50-6

I

1.70-6

I

4.30-7

PO

3.20-’

so

: : : $ 1.11-n $ 4.22-s 6.43-s 5.64-8 : : :

* PO: Partially overlapped, i.e. ~t35%. SO: Slightly overlapped, i.e. l20% . t The number inside the bracket denotes the equation employed to obtain n. $ Deactivation cross sections are not known. 557

-

I: Isolated, i.e. *lo%.

558

s. P. KnAaa and A. Km

given by different investigators (Nicholls, 1961; Zare et al. 1965; Benesch et al. 1966; Halman and Laulitch, 1966; Shumaker, 1969; Nicholls, 1965). In the present investigation to consider the variation of Re(j&) with internuclear distance we have used the results of Jain and Sahani (1966,1967) for three bands, namely N,(lP), N,(2P) and N,+(lN) while for the O,+(lN) group the expressions given by Jeunehomme (1966) are employed. The FranckCondon factors of Zare et al. (1965) and Nicholls (1965) for the N,(lP) and O,+(lN) groups, respectively, are employed. The efliciencies have also been calculated at higher pressure using equation (7) of Khare and Kumar (1973). For the N,(lP) band system the values of quenching coefficient tabulated by Mitchell (1970) are employed. However, it may be noted that due to uncertainties in the quenching cross sections the q values at high pressure are not very reliable. The present values of n at low as well as at high pressures for the N,(lP) band are shown in Tables 1 and 2. For the O,+(lN) group bands a number of inves1967; tigators (Skubenich and Zapesochnyi, Nishimura, 1968; Skubenich, 1968; Korol et al., 1968; McConkey and Woolsey, 1969; Srivastava, 1970, Borst and Zipf, 1970) have measured Q(u’, u”). In the present investigation the experimental data of Srivastava (1970) for the (1,0) 5632 A band in the energy range 100 eV to 5 keV have been employed. For E < 100 eV the experimental data of Borst and Zipf (1970) have been used. To calculate 1) for other bands for which Q(t)‘, v”) is not available we have employed equation (4). It may be noted that the values of N,, for u1= 0 to 3 have been tabulated by Nishimura (1968). In Table 3 the values of r~ for different vibrational bands are tabulated. Finally, the efficiencies are summed in order to obtain the total efficiency q~,,,.,[O,‘(lN)]. It may be noted that we have employed equations (l), (3) and (4) to calculate q. The values obtained from equation (1) are expected to be more accurate in comparison with those obtained from equations (3) or (4). RESULTS

AND

DISCUSSION

Figure 1 (a-d) shows the variation of N,(E,) and n for different bands of N,(lP) with E0 varying from 8 eV to about 850 eV. It is evident from the figures that for all the bands the value of N,(E,) becomes greater than N,(E,) for E,> 300 eV and q becomes independent of energy for E,> 150 eV. This behaviour accords with that expected. It may further be noted that the e5ciency curve for the

(0,O) band, shows only one peak (see Fig. la). Since for this band 90% of the excitation cross section is due to cascading, the peak in the e5ciency curve is also due to cascading. On the other hand, Figs. l(b) and (c) show two peaks in the efficiency curves, one at about 14 eV and the other at about 20 eV. The first peak at 14 eV is probably due to direct excitation, i.e. X’&++ B311, and the

second peak is expected due to cascading from C’II, to B311,. It is evident from the figures that as u’ increases the magnitude of the second peak decreases. However, Fig. Id shows that the magnitude of the second peak is greater than the first, although experimental excitation cross sections indicate small cascading. This may be due to the small values of the stopping power in the 14-20 eV energy region. In Table 1 the present values of the ratio n(u’, u”; N2( lP))/q(O, 0; N,+( 1N)) at very low pressure and high impact energies are shown for different bands of the N,(lP) group. To obtain the ratios, we have recently employed the calculated value of q for the (0,O) 3914A band of N,+(lN) (Khare and Kumar, 1976). This value of q with the use of TABLE 3.

FL~~RES~EN~E VARIOUS

Wavelength (A)

EFFICIENCY BANDS

(u’, u”)

OF

OF

ELECTRONS

IN

02+(1N)

7) (at very low pressure)

4992.0 4998.0 5005.6 5234.0 5241.0 5251.0 5259.0 5274.7 5295.7 5521.0 5540.7 5566.6 5597.5 5631.5 5814.0 5874.3 5883.4 5925.6 5973.4 6026.4 6351.0 6418.8 6856.3 7347.7 7891.1 *Number in the bracket denotes loyed to obtain r).

6.34-6 1.22-5 1.56~’ 5.30-’

(4)’ (4) (4) (4)

1.08-’ 8.28-4 8.84-4 1.47-6

(4) (4) (1) (4)

6.64-4 (4)

8.40-’ (4) the equation emp-

5.59

Fluorescence efficiences of electrons in molecular nitrogen and oxygen gases

0.08-

Incident

energy

4(eV)

I

(b)

Incident

FIG. l(a-d).

VARIATION

OF N,(E,)

AND

1) WITH

energy

INCIDENT

EJeV)

ENERGY

E. FOR

DIFFERENT

VIBRATIONAL

N,(lP) GROUP. N,(E,), N,(Ec) and Nz(Eo) are the number of excited states Nz(B3Q) due to the impact of primary Curve shows the variation of electrons, secondary electrons and tertiary electrons, respectively. oup. (a) (0,O) fluorescence e5ciency q with Ec for different vibrational bands of the N,(lP) 10510 A band; (b) (3,1) 7626 A band; (c) (5,2) 6705 A band; (d) (7,4) 6545 x band. BANDSOFTHE

4

S. P. SHARE and A. Kmmt

560

0.24-

0.20-

3 a

0.16-

I Q 0 E 'G 0.128 3 !3 s 0.08t

0.04 -

Incident energy

E&V)

(d)

Incident energy

FIG. 1

E,,(eV)

(CONTINUED)

Fluorescence efficiences of electrons in molecular nitrogen and oxygen gases

561

agreement with experimental data. These discrepancies may be due to highly uncertain values of the deactivation cross sections and quenching coefficients K,. It may be noted that the value of ;Kb for the (2,0) band obtained by Hartfuss and Schmillen (1968) is about 5 times lower than the value of Mitchell (1970) but is about 2.4 times higher than the value of G’Neil and Davidson. Hence more reliable values of & are needed. The total ethciency ratio ~=~~(NZ+(lN)Yrfr,~,(Nz(lP)] as obtained from Table 2 is 0.610. The experimental value of the corresponding intensity ratio is highly uncertain. The quoted values vary from 0.165 to 1.65 (O’Neil and Davidson, 1969). The present value of the above ratio lies within the experimental limit. On the other hand, the only other available theoretical value of Stolarski and Green (1967) is 0.132 and lies outside the above 500 1000 moo 10 100 50 experimental limit. Incident energy E&V) Figure 2 shows the variation of N,,(E,) and q with E0 for the (1,O) 5632 A band of the O,+(lN) FIG. 2. VARIATION OF M,(Ev) AND q WITH INCIDENT ENERGY E,, FOR ~133 (i,o) 5632/i BAND OF TIE group. The general features of the curve are as expected. In Table 3 the efficiency values for 25 N&E& N,(E,) and NZ(Eo) are the number of excited vibrational bands of O*+(lN) are shown. These states 02’(b4Xg-) due to the impact of primary eiectrons, e&ziencies are summed up in order to get total secondary electrons and tertiary electrons, respectively. efficiency qTots, for O,‘(lN). In the absence of Curve shows the variation of fluorescence efficiency experimental data a direct comparison is not possi7) with incident energy E. for the 5632A band in the Oz+(IN) group. ble. However, the ratio of ulToral[O,+(lN)] to ~=~~,(N~+(lN)] can be compared with the corresponding observed intensity ratio tabulated by Valequations (1) and (2) comes out to be 5.0~ 10m3 lance Jones (1969). The present ratio value, equal and is about 4% higher than the value obtained by to 0.70, is in good agreement with the experimental Khare (1969). A comparison of the present values value of the intensity ratio of 0.636 (Valiance with different experimental data shows that the Jones, 1969). difference between theory and experiment varies from about 8% to 50%. It may be noted that the Ac&nowledgemenfs-We wish to thank Dr. B. N. Srivastava, Radio Science Division, N.P.L., New Delhi for experimental accuracy in the Hartman measureuseful discussions. Financial assistance from the Univerments is not better than 30% as quoted by Dunn sity Grants Commission, New Delhi and the Indian Space and Holland (1971) while in the other two experiResearch Organization, Bangalore are gratefully acknowments the accuracy is about 40%. Furthermore, the ledged. table shows that for the (I, 0) band the experimental value of Mitchell of rl is about 3 times that of the value obtained by Hartman (1968). Hence, in Benesch, W., VandersIice, J. T., Tiiford, S. G. and Wilthe light of these experimental uncertainties the kinson, P. G. (1966). Astrophys. J.144,408. agreement between theory and experiment may be Borst, W. L. and Zipf, E. C. (1970). Phys. Rev. (A)l, 834. regarded as satisfactory.

t,Iy,

The values of up at 600 torr along with the experimental data are shown in Table 2. For the (3,1) and (53) bands the agreement between theory and experiment is satisfactory. However, for (2, l), and (2,O) where the experimental accuracy is high, the theoretical values are lower by a factor of about 2.5. It is interesting to note that for both these bands the ratio given in Table 1 shows fair

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3946. Dunn, J. 470. Halman, 2398. Hartfuss, 722. Hartman,

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KHARE

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