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The Tl∗ + I dissociative state in thallium lodide
JOURNAL
OF MOLECULAR
SPECTROSCOPY
109,202-204
(1985)
NOTES The TI’ + I Dissociative State in Thallium Iodide Experiments have been performed to determine the fluorescence yield of the 535~nm transition in photodissociated thallium iodide vapor as a function of the excitation wavelength in the range from 182 to 209 nm. The spectral dependence of the fluorescence yield, together with the known structure of the molecular ground state, allowed the calculation of the slope of the Tl* + I dissociative potential. (~1IYXSAcndemlc Press. IK TII is one of the most efficient materials for the operation of photodissociation lasers. For optimum pumping the wavelength dependence of the excitation leading to dissociation in excited thallium 72S,,2 and ground-state iodine has to be known. Early spectroscopic work on the thallium halides has been already performed in 1932 by Frank (I) and Terenin (2). Today, the molecular ground state of thallium iodide is well known (3-5); the form of the dissociative Tl * + I state, however, has not yet been determined. A measurement of the wavelength dependence of the excitation allows, together with the form and population of the electronic ground state, one to calculate the properties of the excited dissociative level. The irradiation of uv light in a wavelength range around 200 nm can produce various types of excitation in Tl vapor. Besides dissociation into Tl* and I, ionization and possibly excitation into higher lying bound states (6) also occurs. Each of the three excitations has its own dependence on excitation wavelength. The sum of the relative contributions is given by the absorption spectrum. In order to measure the excitation into the dissociative Tl* + I state alone without the admixture of ionization or excitation into bound states, the population of the Tl 72Si,2 has to be determined. This can be performed by quantitative measurement of the green 535~nm or the uv 377.6-nm resonance emissions from the excited 72S,,2 state to the metastable 62P3,2 and the 6’P,,2 ground state of thallium, respectively. In this letter we report on experiments to determine the 535~nm fluorescence yield. Subsequently, based on these data, a calculation of the slope of the dissociative state in TII is presented. In the experiment we used a “Suprasil” quartz cell with a quadratic base of 1 cm, filled with thallium iodide without buffer gas. This cell was placed in an oven in order to produce a vapor pressure of about 1 Torr. The whole experimental arrangement was installed in a vacuum chamber filled with helium at ambient pressure. The experimental arrangement is shown in Fig. I. The emission of a deutetium lamp (Glen Creston 91 UV 40) was filtered with a 200-mm scanning monochromator of 1.75 nm resolution. The transmitted light was focused into the vapor with a lens of 45 mm focal length. The relative intensity of the fluorescence at 535 nm radiated at 90” with respect to the pump beam was monitored as a function of the exciting wavelength. The spectral intensity of the pump light was detected with a photodiode (EG + G FND 100). The spectral response of this detector decreased linearly from 75 mA/W at 210 nm to 34 mA/W at 180 nm. For the detection of the green TII fluorescence, a high-sensitivity spectrometer in combination with a multichannel analyzer (Tracer Northern TN 1770) was used. The experiment has been performed at a cell temperature of 711 K. The resulting fluorescence curve, calibrated with respect to excitation power, is shown in Fig. 2, together with earlier values (7). The optimum excitation to the 72S,,2 state of thallium was found at a wavelength of 194 f 1.75 nm. Figure 2 also shows. for the first time the short-wavelength side of the fluorescence curve. The deviation of our curve from that of Ref. (7) is due to a different calibration of the spectral light intensity incident to the thallium vapor. In (7) the response of the Tracer Northern TN 1770 spectrometer has been taken as constant for the calibration of the fluorescence yield, while in our experiment the wavelength dependence of the sensitivity of the EC + G FND 100 photodiode has been taken into account. The comparison of the two curves, however, shows a relatively good correspondence for the two different methods of calibration.
0022-2852185 Copyright 0
$3.00
1985 by Academic Press. Inc.
All rights of reproduction in any form reserved.
202
203
NOTES
VACUUM
F
CHAMBER I
L-l SP
FIG. 1. Experimental arrangement: DL, deuterium lamp; MC, monochromator; filter; SP, spectrometer; PD, photodiode.
QC, quartz cell; F,
With the measured curve and with the known ground state of the TII molecule, the form of the upper dissociating level can be calculated. In the following treatment we considered only the vibrational states of the molecules. A good approximation for the potential curve of the electronic ground state has been given by Morse (8). With this potential, the Schrijdinger wave equation can be solved rigorously. The resulting energy values are given, for example, in (3. 9, 10). For the computer calculation, vibrational constants (5) w, = 141 cm-’ and W,J~= 0.225 cm-‘, a dissociation energy of 2.76 eV (II), an equilibrium internuclear distance (12) of r, = 0.281367 nm, and a reduced mass (I 1) w” = 78.38 atomic weight units have been used. Various theoretical simulations of absorption spectra were performed where parameters of the assumed upper repulsive potential were varied. For the calculations, we considered the transitions of the 30 lowest vibrational levels of the electronic ground state into the upper state. The spectral contributions of the individual vibrational levels were added, whereby the Frank-Condon principle had to be taken into consideration. The quantum mechanical formulation of this principle shows that the intensity of a band of a given electronic transition in absorption is proportional (3) to Y- [J 0:. qk:-dr]‘, where *: and w: are the vibrational eigenfunctions of the upper and the lower states. Coolidge et al. (12) have shown that the repulsive eigenfunctions can be replaced by properly normalized 6 functions if the repulsive potential curve is steep. This condition is fulfilled in our case, at least at an internuclear distance up to 0.287 nm. In this case the transition probability becomes proportional to the square of the vibrational eigenfunctions of the lower state (3). The form of the repulsive potential was varied until the best fit of the resulting fluorescence yield with the experimental data was obtained. The best fit of the fluorescence yield is shown as the solid line in Fig. 2. The calculated curve has also been adjusted to correspond to a spectral resolution of 21.75 nm. Comparing the measured values with the calculated curve, a good agreement
180
190 WAVELENGTH
200 [nm
210
1
FIG. 2. Fluorescence yield (535 nm) as a function of the wavelength of the pump light (circles). Black dots, values of (7) for comparison; solid line, calculated fluorescence yield (best fit).
204
NOTES
was found in the region of 182 to 197 nm. In this fit the repulsive potential has been approximated by a
straight line that can be described by y = (-2.3 x 1014)r+ I.158 x lo’, with r < 0.287 nm and y in cm-‘. The correspondance is somewhat worse in the long-wavelength region, where the potential slope bends toward the value at the infinite internuclear distance of 48 686 cm-‘. The fitting shows a markedly lower conformity to the calculated curves if the slope is changed by more than 10%. In conclusion, we have measured the wavelength dependence of the pumping of TlI to the Tl 72Si,2 + I state in the range below 190 nm for the first time. With the knowledge of this curve and the properties of the electronic ground state of TII, the form of the potential curve dissociating in ground state iodine and 72S,,2 thallium atoms has been deduced. It is found that, at an internuclear distance of 0.2 to 0.29 nm, the potential curve can be approximated by a straight line. ACKNOWLEDGMENTS We would like to thank H. J. Weder for technical assistance. This work was supported in part by the Swiss Commission for the Encouragement of Scientific Research. REFERENCES 1. J. M. FRANK, Phys. Z. Sowjetunion 2, 319-336 (1932). A. TERENIN,Phys. Z. Sowjetunion 2, 377-382 (1932). G. HERZBERG,“Spectra of Diatomic Molecules,” Van Nostrand, New York, 1950. P. T. RAO AND K. R. RAO, Ind. .I. Phys. 20, 49 (1946). R. SCHMIELE,W. LOTHY, T. GERBER,AND P.-D. HENCHOZ,J. Mol. Specfrosc. 96, 378-382 (1982). J. MAYA,IEEE J. Quantum Eleclron. QE-15, 579-594 (1979). W. LUTHY, P. BURKHARD,T. E. GERBER,AND H. P. WEBER,Opf. Commun. 38.413-415 (1981). 8. P. M. MORSE,Phys. Rev. 34, 57-64 (1929). 9. F. NORLING,Z. Phys. 104, 177-204 (1937). 10. P. H. DWIWEDIANDJ. N. HUFFAKER,J. Chem. Phys. 66, 1726-1735 (1977). 1 I. K. P. HUBERANDG. HERZBERG,“Constants of Diatomic Molecules,” Van Nostrand-Reinhold, New York, 1978. 12. H. HAPP, Z. Phys. 147, 567-572 (1957). 13. A. S. COOLIDGE,H. M. JAMES,AND R. D. PRESENT,J. Chem. Phys. 4, 193-2 I 1 (1936). 2. 3. 4. 5. 6. 7.
S. SCHNELL W. LOTHY H. P. WEBER Institute of Applied Physics University of Bern CH-3012 Bern, Switzerland Received April 12, 1984
OF MOLECULAR
SPECTROSCOPY
109,202-204
(1985)
NOTES The TI’ + I Dissociative State in Thallium Iodide Experiments have been performed to determine the fluorescence yield of the 535~nm transition in photodissociated thallium iodide vapor as a function of the excitation wavelength in the range from 182 to 209 nm. The spectral dependence of the fluorescence yield, together with the known structure of the molecular ground state, allowed the calculation of the slope of the Tl* + I dissociative potential. (~1IYXSAcndemlc Press. IK TII is one of the most efficient materials for the operation of photodissociation lasers. For optimum pumping the wavelength dependence of the excitation leading to dissociation in excited thallium 72S,,2 and ground-state iodine has to be known. Early spectroscopic work on the thallium halides has been already performed in 1932 by Frank (I) and Terenin (2). Today, the molecular ground state of thallium iodide is well known (3-5); the form of the dissociative Tl * + I state, however, has not yet been determined. A measurement of the wavelength dependence of the excitation allows, together with the form and population of the electronic ground state, one to calculate the properties of the excited dissociative level. The irradiation of uv light in a wavelength range around 200 nm can produce various types of excitation in Tl vapor. Besides dissociation into Tl* and I, ionization and possibly excitation into higher lying bound states (6) also occurs. Each of the three excitations has its own dependence on excitation wavelength. The sum of the relative contributions is given by the absorption spectrum. In order to measure the excitation into the dissociative Tl* + I state alone without the admixture of ionization or excitation into bound states, the population of the Tl 72Si,2 has to be determined. This can be performed by quantitative measurement of the green 535~nm or the uv 377.6-nm resonance emissions from the excited 72S,,2 state to the metastable 62P3,2 and the 6’P,,2 ground state of thallium, respectively. In this letter we report on experiments to determine the 535~nm fluorescence yield. Subsequently, based on these data, a calculation of the slope of the dissociative state in TII is presented. In the experiment we used a “Suprasil” quartz cell with a quadratic base of 1 cm, filled with thallium iodide without buffer gas. This cell was placed in an oven in order to produce a vapor pressure of about 1 Torr. The whole experimental arrangement was installed in a vacuum chamber filled with helium at ambient pressure. The experimental arrangement is shown in Fig. I. The emission of a deutetium lamp (Glen Creston 91 UV 40) was filtered with a 200-mm scanning monochromator of 1.75 nm resolution. The transmitted light was focused into the vapor with a lens of 45 mm focal length. The relative intensity of the fluorescence at 535 nm radiated at 90” with respect to the pump beam was monitored as a function of the exciting wavelength. The spectral intensity of the pump light was detected with a photodiode (EG + G FND 100). The spectral response of this detector decreased linearly from 75 mA/W at 210 nm to 34 mA/W at 180 nm. For the detection of the green TII fluorescence, a high-sensitivity spectrometer in combination with a multichannel analyzer (Tracer Northern TN 1770) was used. The experiment has been performed at a cell temperature of 711 K. The resulting fluorescence curve, calibrated with respect to excitation power, is shown in Fig. 2, together with earlier values (7). The optimum excitation to the 72S,,2 state of thallium was found at a wavelength of 194 f 1.75 nm. Figure 2 also shows. for the first time the short-wavelength side of the fluorescence curve. The deviation of our curve from that of Ref. (7) is due to a different calibration of the spectral light intensity incident to the thallium vapor. In (7) the response of the Tracer Northern TN 1770 spectrometer has been taken as constant for the calibration of the fluorescence yield, while in our experiment the wavelength dependence of the sensitivity of the EC + G FND 100 photodiode has been taken into account. The comparison of the two curves, however, shows a relatively good correspondence for the two different methods of calibration.
0022-2852185 Copyright 0
$3.00
1985 by Academic Press. Inc.
All rights of reproduction in any form reserved.
202
203
NOTES
VACUUM
F
CHAMBER I
L-l SP
FIG. 1. Experimental arrangement: DL, deuterium lamp; MC, monochromator; filter; SP, spectrometer; PD, photodiode.
QC, quartz cell; F,
With the measured curve and with the known ground state of the TII molecule, the form of the upper dissociating level can be calculated. In the following treatment we considered only the vibrational states of the molecules. A good approximation for the potential curve of the electronic ground state has been given by Morse (8). With this potential, the Schrijdinger wave equation can be solved rigorously. The resulting energy values are given, for example, in (3. 9, 10). For the computer calculation, vibrational constants (5) w, = 141 cm-’ and W,J~= 0.225 cm-‘, a dissociation energy of 2.76 eV (II), an equilibrium internuclear distance (12) of r, = 0.281367 nm, and a reduced mass (I 1) w” = 78.38 atomic weight units have been used. Various theoretical simulations of absorption spectra were performed where parameters of the assumed upper repulsive potential were varied. For the calculations, we considered the transitions of the 30 lowest vibrational levels of the electronic ground state into the upper state. The spectral contributions of the individual vibrational levels were added, whereby the Frank-Condon principle had to be taken into consideration. The quantum mechanical formulation of this principle shows that the intensity of a band of a given electronic transition in absorption is proportional (3) to Y- [J 0:. qk:-dr]‘, where *: and w: are the vibrational eigenfunctions of the upper and the lower states. Coolidge et al. (12) have shown that the repulsive eigenfunctions can be replaced by properly normalized 6 functions if the repulsive potential curve is steep. This condition is fulfilled in our case, at least at an internuclear distance up to 0.287 nm. In this case the transition probability becomes proportional to the square of the vibrational eigenfunctions of the lower state (3). The form of the repulsive potential was varied until the best fit of the resulting fluorescence yield with the experimental data was obtained. The best fit of the fluorescence yield is shown as the solid line in Fig. 2. The calculated curve has also been adjusted to correspond to a spectral resolution of 21.75 nm. Comparing the measured values with the calculated curve, a good agreement
180
190 WAVELENGTH
200 [nm
210
1
FIG. 2. Fluorescence yield (535 nm) as a function of the wavelength of the pump light (circles). Black dots, values of (7) for comparison; solid line, calculated fluorescence yield (best fit).
204
NOTES
was found in the region of 182 to 197 nm. In this fit the repulsive potential has been approximated by a
straight line that can be described by y = (-2.3 x 1014)r+ I.158 x lo’, with r < 0.287 nm and y in cm-‘. The correspondance is somewhat worse in the long-wavelength region, where the potential slope bends toward the value at the infinite internuclear distance of 48 686 cm-‘. The fitting shows a markedly lower conformity to the calculated curves if the slope is changed by more than 10%. In conclusion, we have measured the wavelength dependence of the pumping of TlI to the Tl 72Si,2 + I state in the range below 190 nm for the first time. With the knowledge of this curve and the properties of the electronic ground state of TII, the form of the potential curve dissociating in ground state iodine and 72S,,2 thallium atoms has been deduced. It is found that, at an internuclear distance of 0.2 to 0.29 nm, the potential curve can be approximated by a straight line. ACKNOWLEDGMENTS We would like to thank H. J. Weder for technical assistance. This work was supported in part by the Swiss Commission for the Encouragement of Scientific Research. REFERENCES 1. J. M. FRANK, Phys. Z. Sowjetunion 2, 319-336 (1932). A. TERENIN,Phys. Z. Sowjetunion 2, 377-382 (1932). G. HERZBERG,“Spectra of Diatomic Molecules,” Van Nostrand, New York, 1950. P. T. RAO AND K. R. RAO, Ind. .I. Phys. 20, 49 (1946). R. SCHMIELE,W. LOTHY, T. GERBER,AND P.-D. HENCHOZ,J. Mol. Specfrosc. 96, 378-382 (1982). J. MAYA,IEEE J. Quantum Eleclron. QE-15, 579-594 (1979). W. LUTHY, P. BURKHARD,T. E. GERBER,AND H. P. WEBER,Opf. Commun. 38.413-415 (1981). 8. P. M. MORSE,Phys. Rev. 34, 57-64 (1929). 9. F. NORLING,Z. Phys. 104, 177-204 (1937). 10. P. H. DWIWEDIANDJ. N. HUFFAKER,J. Chem. Phys. 66, 1726-1735 (1977). 1 I. K. P. HUBERANDG. HERZBERG,“Constants of Diatomic Molecules,” Van Nostrand-Reinhold, New York, 1978. 12. H. HAPP, Z. Phys. 147, 567-572 (1957). 13. A. S. COOLIDGE,H. M. JAMES,AND R. D. PRESENT,J. Chem. Phys. 4, 193-2 I 1 (1936). 2. 3. 4. 5. 6. 7.
S. SCHNELL W. LOTHY H. P. WEBER Institute of Applied Physics University of Bern CH-3012 Bern, Switzerland Received April 12, 1984