Flame spectroscopy of TiO

J”l’RNA1. OF YOT.EClJT.ARRPTWI’ROSCOPY69, 6670

Flame Radiative

Lifetimes

(1978)

of TiO

Spectroscopy

and Oscillator

of the a (C3~-Xsh) System 1

Strengths

R. E. STEELE Department

of Physics and Quantum Institute, University of California, Santa Barbara, California 93106

AND C. LINTON Physics

Department,

University oj New Brunswick,

Fredericton,

New Brunswick,

Canada

Lifetimes of the PA state of TiO have been measured for vibrational levels v’ = 0 to 2 from the decay of photoluminescence excited in a chemiluminescent flame by a short-pulsed (5 nsec) tunable dye laser. Radiative lifetimes of 7+,0 = 37 f 9 nsec, ~~,_r = 29 f 7 nsec, r,,f_~ = 28 f 7 nsec were obtained were found to be in good agreement

and were used to estimate oscillator strengths which with earlier values based on intensity measurements.

I. INTRODUCTION

AS the TiO spectrum is the major feature in absorption spectra of M-type stars, it can be used in obtaining quantitative information about stellar atmospheres. For this purpose, transition probability data are required. Molecular transition probabilities and related quantities have been discussed in detail by Tatum (1). A summary of basic expressions used in this present work is outlined below. The absolute transition probability A v,I,,, of a molecular band can be written A “,z,‘~= (64r4/3hh3g’)S,~,~~,

(1)

where X is the wavelength, in centimeters, of the transition, of the upper state, and S,~,~~ is the band strength.

g’ is the statistical

An important quantity band oscillator strength

spectroscopic

often

derived

from quantitative

data

weight is the

f v,y,r = (mcX2g’/8Pe2g”)Av~,~~ = (8n2mc/3he2g”h)S,,,~, where g” is the statistical 1Work supported

in part

(4

weight of the lower state and all quantities by the Air Force

Office of Scientific 66

0022.2852/78/0691-CiI66$02.00/0 Copyright 0 1978 by Academic Press Inc. All rights of reproduction in any form reserved.

Research,

are in c.g.s. units.

Contract

AFOSR-74-2724.

LIFETIRIES

AND OSCILLATOR

STRENGTHS

In order to calculate oscillator strengths, it is necessary S,,“!!, which, in many cases, may be written (I)

67

to know the band strengths,

,Y,.,,.,, = R,,@)2. y,,,+,,

(3)

where q,,,,, is the Franck-Condon factor, P is the Y centroid (2), and R,(F) is the electronic transition moment. Accurate determination of band strengths, and hence oscillator strengths, thus depends on knowledge of qU,?,,, which can be calculated, and the variation of R,(P) over the band system, which is harder to determine. Schadee

(.?) defined a wavelength

dependent

electronic

oscillator

jLl = .f”,,~,~/cl,W,

strength (4)

whose variation within a band system will depend on the variation of R,(P). Many results are presented in this way. The experimental determination of oscillator strengths may be approached in two ways. Absolute intensities of individual bands may be measured. This requires careful calibration of detector response characteristics. In order to derive oscillator strengths, accurate thermochemical data are required in order to calculate number densities of various species in the system. An alternative method, requiring no knowledge of number densities, is measurement of radiative lifetimes. This is related to the transition probability by

where 7Ul is the radiative lifetime of the upper state of the observed transition and the summation is over all lower states to which radiative transitions from r can occur. It can be shown (4) that the band oscillator strength is given by f

y,~,, = 1.~99g’s”,,,,/g”xr,~

c

&“,,~-3*

(6:)

Y”

This can only be calculated accurately if the variation of R,(P) over each emitted band system is known and if the branching ratios, i.e., relative probabilities of transitions to all possible lower states, are known. If it is assumed that only one band system is emitted from zl’, hence only one lower electronic state is involved, and that R,(P) is constant over this band system, then we can write

To date, two measurements of TiO cx (C3A-S”A) system oscillator strengths have been made (5-7) and are in quite good agreement with each other. Both experiments measured absolute intensities emitted by a shock heated mixture of Tic14 and OS. To date, the only published lifetime measurement has been T = 17.5 f 1.0 nsec for the cl% state (8). In this paper we report preliminary measurements of radiative lifetimes of some bands of the TiO (Ysystem. These have been converted to oscillator strengths to test whether the lifetimes are consistent with intensity data.

68

STEELE

AND LINTON

II. EXPERIMENTAL

DETAILS

The radiative decay rate was measured by monitoring the fluorescence of gas phase TiO at right angles to a brief (Snsec FWHM) incident laser pulse. The methods used for production of TiO have been described elsewhere (9, IO) and the flow system used for these studies is essentially the same as that used for the chemiluminescence work. The laser used was a nitrogen laser pumped tunable dye laser using 7-diethylamino-4trifluoromethyl-coumarin laser dye. The dye laser was tuned with an echelle and the spectral width was about 0.5 nm. The detection system consisted of a photomultiplier (lP28 at 1000 V) and oscilloscope (Tektronix 7904) and camera. The photomultiplier output was monitored using a 500-mHz bandwidth plug-in with a 50-O input. The oscilloscope was triggered by the incident laser pulse and the camera was used to record the trace following the pulse. By recording several traces on a single photograph a crude form of “signal averaging” was accomplished. Bandpass (-IO-nm FWHM) filters were placed in front of the photomultiplier to help reduce the incident blackbody radiation and chemiluminescence. These filters were centered at 466 and 500 nm depending on which bands were being studied. III. RESULTS (a)

AND DISCUSSION

Radiatire Lifetimes

On scanning the dye laser, peak signals were obtained in the regions of 476.5, 496.2, and 517.5 nm corresponding to the 2-0, l-0, and O-O bands of the TiO cr system. The photograph in Fig. 1 shows a typical oscilloscope trace of the decay of the photo-

FIG. 1. Oscilloscope trace of five decay pulses from 477-nm excitation.

LIFETIMES

AND

OSCILLATOR

61)

STRENGTHS

luminescence. The trace consists of superimposed data from three to five laser pulses. There was quite a lot of noise in the signals and it was not possible to attain very high accuracy in the lifetime measurements. Lifetimes obtained from logarithmic plots of these traces were 70 = 37 f

71 = 29 f

9 nsec,

7 nsec,

7! = 2% f

7 nsec.

(b) Oscillutor Strengths

In calculating oscillator strengths from these lifetimes it was assumed that onl> emission to the ground electronic state (X3A) took place. When it was also assumed that R,(f) did not vary over the band system, and Eq. (7) was used together with y,t,fr from Collins and Fay (II), values of fU,,,t and f el were obtained and are shown in Table I (columns 3 and 4). These are compared with values of fel measured by Price et ul. (6) and by Fairbairn et al. (7) and show reasonable agreement with each set. It should be pointed out that we used the same spectroscopic constants as Price et al. (6) whereas Fairbairn et al. (7) used earlier data. From their oscillator strengths, Fairbairn et al. (7) calculated that the electronic transition moment varied as R,(P) cc exp(5.28

- 2.31?).

(8)

It is possible that this might be slightly different if the more recent constants (6, 11) were used in analysis of their data. However, in order to investigate how variation of R,(F) would affect our calculations, the above expression was combined with the radiative lifetimes and Eq. (6) was used together with r centroids calculated by McCallum et al. (12) and yielded the oscillator strengths shown in columns 5 and 6 of Table I. It is clear from these calculations that the transition moment variation can play a significant role in the computation of oscillator strengths but it must be pointed out that the calculation of the sum in Eq. (6) involved extrapolation of Eq. (8) well beyond the range of P covered by the experimental intensity measurements (7), and is therefore of doubtful validity. Previous relative intensity measurements (13) had yielded T:\BLE Oscillator

Strengths

of Bands

I

of the TiO LY(PA-PA)

System

STEELE

70

AND LINTON

R, a exp(4.82 - 2.57F) (24), whereas a much smaller variation was observed by Linton and Nicholls (15). The above data show that, although the transition moment variation is important in converting lifetimes into oscillator strengths, there is still insufficient data to be able to do this accurately for TiO. However, the agreement between these preliminary results and earlier intensity data (5-7) is very encouraging and indicates that the thermochemical data used in the shock tube experiments must be fairly accurate. The assumption that all transitions from C3A go to X3A ignores any possible transitions to the B311, A%, and B3n’ states. All of these transitions are allowed and would be in the infrared region beyond the limit of present observations. The Xm3factor in Eq. (6) would add only about 4 or 5yo to the sum of transition probabilities, all other parameters being equal, and it is expected that the overall contribution from these transitions would be small. The fact that no visible transitions have ever been observed from higher triplet states to these states, even though their X” factors are more favorable, tends to support this conclusion. Contributions from forbidden transitions to low lying singlet states are also expected to be small. Ignoring all these contributions to the sum would mean that, if band strengths were accurately known, the calculated oscillator strengths would represent an upper limit to the actual values. In conclusion, it has been shown that oscillator strengths for the TiO Q! system calculated from radiative lifetimes are in good agreement with those calculated from intensity measurements. In order to improve lifetime calculations, more information must be obtained about the variation of the electronic transition moment and about branching ratios of transitions from the C3A state. ACKNOWLEDGMENTS The authors RECEIVED:

wish to thank June

Professor

H. P. Broida

for his continued

support

of this work.

13, 1977 REFERENCES

1. 2. 3. -I. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15.

J. B. TATUM, Astrophys. J. Suppl. Ser. 14, 21 (1967). P. A. FRASER, Canad. J. Phys. 32, 515 (1954). A. SCHADEE,J. Qua&. Spectrosc. Radiat. Transfer 7, 169 (1967). S. E. JOHNSON,J. Chem. Phys. 56, 6264 (1972). M. L. PRICE, K. G. P. SULZMANN,AND S. S. PENNER, J. Quunt. Spectrosc. Radiat. Transfer 11, 427 (1971). M. L. PRICE, K. G. P. SUUMANN, END S. S. PENNER, J. Qua&. Spectrosc. Radial. Trwzsfer 14, 1273 (1974). A. R. FAIRBAIRN,S. J. WOLNIK, AND R. 0. BERTHEL,Astrophys. J. 193, 273 (1974). J. FEINBERG,M. G. BILAL, S. P. DAVIS, ANDJ. G. PHILLIPS,Astrophys. Lett. 12, 147 (1976). J. B. WEST, R. S. BRADFORD,JR., J. D. EVERSOLE,ANDC. R. JONES,Rev. Sci. Instrum. 46,164-168 (1975). C. LINTONAND H. P. BROIDA,J. Mol. Spectrosc. 64, 382 (1977). J. G. COLLINSANDT. D. FAY, JR., J. Qzmnt. Spcctrosc. Ra&zt. Transfer 14, 1259 (1974). J. C. MCCALLUM ANDR. W. NICHOLLS,unpublished. J. G. PHILLIPS,Astrophys. J. 119, 275 (1954). F. S. ORTENBERG,Opt. Spcctrosc. 9, 80 (1960). C. LINTONANDR. W. NICIIOLLS,J. Qzrmt. Spcctrosc. Kudiot. TrurrsJcr10, 311 (1970).