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Radiation trapping and vapor density of indium confined in quartz cells
Optics Communications North-Holland
OPTlCS COMMUNICATIONS
106 ( 1994) 197-20 1
Radiation trapping and vapor density of indium confined in quartz cells P. Bicchi, C. Marinelli, E. Mariotti, M. Meucci and L. Moi Dipartimento di Fisica, Universitci di Siena, via Banchi di Sotto 55, 53100 Siena. Italy
Received 3 September 1993; revised manuscript received 14 December 1993
We have measured, in the 700-950°C temperature range, the effective lifetime of the 6S1,2 excited level of indium vapor confined in quartz cells. The self trapping results much lower than expected suggest an effective vapor density lower than the one calculated at the thermal equilibrium. A possible explanation of this large deviation has been found in the increasing adsorption rate of indium at the cell walls. Partial fluorescence spectrum of the adsorbed atoms is reported.
1. Introduction
The experimental analysis of collisional processes in very dense laser-excited vapors is an important tool for studying the energy repartition among the atomic excited levels and/or between bound states and the continuum. Sometimes, in order to get high vapor densities, high temperatures have to be reached with the consequence that technical problems become determinant. In the past, different solutions have been adopted like, for example, the heat-pipeoven made from stainless-steel. Even in this case, problems are not completely eliminated and the one of the strong chemical reactivity of the analyzed elements may remain unresolved, the analysis of the vapor-wall interaction becoming a part of the experiment. This is the case for indium which has a very low saturated vapor pressure up to very high temperatures (for example the saturated atomic density nsat is ~10’~ cmm3 at T=900°C [l]). At these temperatures indium reacts with stainless-steel so that heat-pipe-ovens cannot be conveniently used for long time [ 2 1. Recently energy-pooling collisions (EPC) and energy-pooling ionization ( EPI ) have been experimentally demonstrated in indium confined in quartz cells by Bicchi et al. [ 3 1. A quantitative study of the cross section of EPC has been possible only after the vapor-quartz interaction, whose main effect is a de-
crease in the vapor density, has been taken into account [4]. This paper reports a measurement of the effective indium vapor density in quartz cell at high temperature. Results have been obtained by deriving the effective vapor density neff from the measured effective decay time reff of the laser excited level. reff is determined both by the self-trapping and by the LI level configuration of indium. The analysis has been made by comparing the experimental results with the theoretical ones predicted by the Holstein theory [ 5,6] and with those obtained with a Monte Carlo simulation. The results will prove to be useful in many applications, in particular in the possible realization of an indium atomic line filter following the scheme already adopted for thallium [ 71.
2. Experimental apparatus and results The experimental .apparatus is sketched in fig. 1. Indium is distilled under vacuum in the side arm of a quartz cell (diameter 3 cm; length 10 cm) that is then filled with 10 Torr of neon as a buffer gas. This side arm is connected to the cell body through a capillary (3 mm in diameter and 2-5 cm long). The cell is positioned inside an oven which can be heated up to about 1000°C. The temperature, that is uniform
0030-4018/94/%07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDZ 0030-4018(93)E0619-Q
197
Volume 106, number
4,5,6
OPTICS
COMMUNICATIONS
15 March
1994
Digital scope
F
---
Dye laser
Nd-YAG laser
Fig. 1. Experimental block diagram: BS = beam splitter, L = lenses, F= filter, PM = photomultiplier, PD = photodiode.
in the central part, is stabilized within 1°C. Indium atoms are resonantly excited to the 6S,,2 level, whose natural lifetime is r, = 7.4 ns [ 8 1, by a pulsed laser beam tuned to 410.3 nm. The selected wavelength is obtained by mixing in a KDP crystal the output of a dye laser tuned at 667.8 nm with the residual of the fundamental wavelength of the NdYAG laser ( 1064 nm). The laser repetition rate is 10 Hz, its pulse duration 10 ns and its maximum peak power 600 kW. During the measurements the beam is properly attenuated. The bandwidth of the resonant laser beam is 0.8 cm-’ and it is mainly due to the bandwidth of the infrared Nd-YAG beam. The induced fluorescence is collected at right angle, dispersed by a low resolution (60 cm- ’ ) monochromator and detected with a photomultiplier. A fast transient digitizer performs the temporal analysis of the signals which are then elaborated by a personal computer. From the 6S,,2 level, indium atoms decay back to the 5P,,2 and 5P3,2 ground states, separated by AEc2212.56 cm-‘. In fig. 2 a diagram of the involved levels is shown. The fluorescence spectrum consists of two lines, at 1,=410.3 nm and at At,= 45 1.1 nm, respectively. The relative transitions involve ground state levels with a population density in a ratio close to 10 : 1. This results in an escaping competition between the two emitted photons with the consequence of an effective fluorescence decay time strongly different from the one expected for twolevel atoms. We have measured the fluorescence decay time as 198
Fig. 2. h level structure formed by the two ground sublevels 5P,,,, 5P,,, and the excited 6S,,2 level in indium. The excitation energy as well as the fine structure energy of the ground state are also reported.
50
1
o650
750
650
950
T(“C) Fig. 3. Effective lifetime of the 6S,,2 level measured from the decay of the fluorescence signals relative to the transition 6S,,2+ 5P,,* (45 1.1 nm) in a quartz cell with In and 10 torr of Ne as a function of temperature.
a function of the temperature and we have derived the effective lifetime of the 6S1,2 excited level. In fig. 3 the measured effective lifetime reff of the first excited level 6S,,2 is reported as a function of temperature. reff increases to (40 f 4) ns for the highest reached temperature. This lifetime increase is due to the radiation trapping, the efficiency of which is, however, much lower than expected. For a fixed temperature, no variation of reff manifests when the laser power is changed over a wide range, typical working laser power being of the order of few kW. The theoretical evaluation of reff is not straightforward because of the three-level structure of indium. This problem is of fundamental interest and its solution of practical importance. Colbert and Wexler have recently analyzed the radiation trapping for thallium (that has a similar level structure) in the presence of non uniform reflective boundaries by
Volume
106, number
OPTICS
4,5,6
starting from the Holstein equations properly modified [9]. This approach can be easily extended to the indium system. In our experiment the laser beam, whose diameter is much smaller than that of the cell, excites the atoms along the major axis of the cell. Therefore the blue and violet photons emitted by the indium atoms, before escaping from the cell and reaching the photomultiplier, cross a region where the atoms are in the ground states with a population ratio determined, in first approximation, by the thermal equilibrium. The Holstein analytic solution for a two-level atom can be taken into consideration for the two SPl,Z and S-P3,2 transitions separately, in case of a cylindrical geometry and assuming negligible optical pumping effects. The effective lifetime can then be derived, as already done by Holt [ lo] for low vapor densities in Na, by properly weighting their relative contributions. The effective lifetime reff is given by r.?fr= rolg >
(1)
where g is the “escape factor”, g= 1.6O/k,RJw
given by (2)
for a cylindrical The reciprocal and absorptions the cell. R is the
15 March
COMMUNICATIONS
geometry. of g gives the number of emissions of a photon prior to its escape from cell radius and k. is
1994
effective lifetime almost coincides with the lifetimes calculated for the S-P3,2 transition. This has also been verified through a Monte Carlo simulation. In fig. 4 the reff values calculated according to the Holstein theory (separately for the S-P,,2 and SPSI2 transitions) as well as via the Monte Carlo simulation, are reported as a function of the vapor density. By referring to the tables reported by Nesmeyanov [ 11, the corresponding temperatures are also shown for comparison. Up to 850-900°C the Monte Carlo simulation and the Holstein calculation for the S-P3,* transition give roughly the same values. For higher temperatures the contribution due to the SPiI2 transition is not negligible any more and the two sets of values diverge. It is in any case evident (see fig. 3 and fig. 4) that the effective lifetime should be much larger than measured and that reff does not increase in the experiment as expected. An estimate, in excess, of the pressure broadening due to the buffer gas presence in the cell shows it to be slightly less than the natural linewidth and so it can not be the reason of the difference between the calculated and measured values of reff which is larger than one order of magnitude. We have, anyhow, taken it into account in the estimated errors of our measurements. The explanation of this large disagreement is possibly due to the diffusion of the indium atoms inside the quartz cell walls when the temperature exceeds a threshold that for indium is about 850°C. In other words the indium
n x 10”(cme3)
where g, and g, are the statistical weights of the excited and ground state respectively, ilo the resonant wavelength and v. = (2kTIM) ‘I*. The absorption coefficients for the 410 nm and 450 nm photons are k, and kb, respectively. It is easy to verify that their ratio n=
ky = kt, ’ 1
49
1-exp( -~lW exp( -AE/kT)
changes, between 35 and 16, in the temperature range between 727 and 1027°C. That means that the mean freepath of the 410 nm photons is 35 to 16 times shorter than 450 nm ones. This huge difference has the consequence that, until the mean freepath of the blue photons is comparable with the cell radius, the
0.14 4000
’
630
24
I
,
a A
o!.:,*:: 650
650 W’C)
, 1050
Fig. 4. rceffvalues versus temperature and vapor density calculated according the Holstein theory separately for the S-P,,2 (0 ) and S-P,,, (A ) transitions as well as via the Monte Carlo simulation ( + ) .
199
Volume 106, number 4,5,6
OPTICS COMMUNICATIONS
density at the highest temperatures does not reach the equilibrium value, but lower ones. The effective indium density can be derived from the measurement of the effective lifetime of the excited level by shifting the experimental data to lower densities till they match the calculated ones. In our experiment, at 950°C we derive an effective density neff= ( 1.6 f 0.5) x 1OL3cmw3 which is about one order of magnitude less than the corresponding saturated density nsat. This is a manifestation of a porosity of the cell walls which increases with temperature. The indium atoms are adsorbed at the quartz surface where they, then, migrate inside the quartz lattice. This has a direct experimental evidence in the emission spectra obtained for a cell filled with indium and buffer gas when it is operated at high temperature for the first time and after one day of operation. In fig. 5a and 5b respectively, two fluorescence spectra are reported in a wavelength range where there are no indium or buffer gas lines. The strong signal in fig. 5b is due to laser induced fluorescence (LIF) of the quartz walls “contaminated” by the indium atoms. This “contamination” once created is permanent. In fact the LIF spectrum of quartz from operated cells always manifests the same fluorescence, even at room temperature. As the metallic indium is at the bottom of the cell side arm, the diffusion time is not fast enough to maintain the saturated density. The diffusion time becomes very fast if the buffer gas is eliminated, but in this case the cell walls get immediately and heavily contaminated. It is worth noticing that incorporation of impurities of Al, which belongs to the same chemical group of In, in the quartz structure are reported in the literature [ 111. This indium-quartz interaction is by itself an interesting effect which may have important applications also in fields of physics other than the atomic and molecular one. For this reason further experiments are in progress to better characterize these observations.
15 March 1994
b 470“mo
475
a)
480
b)
;’
1‘k I
I
470
475
‘c I
480
il hm)
Fig. 5. LIF spectra detected in a cell with In and 10 Torr of Ne as buffer gas at T= 900°C. (a) Cell operated for the first time. (b ) Cell after one day of operation. The sensitivity in (b) is 5 times less than in (a).
in the establishment of an effective vapor density. We have determined neff by measuring the effective lifetime of the excited level. As to the latter, we discuss how its behaviour as a function of temperature in the case of a three-level element such as indium, strongly differs from the two-level atoms one. We also indicate which important applications these results may have.
Acknowledgments 3. Conclusions We have demonstrated that in very dense laser excited vapors the interaction between the vapor itself and the walls of its container may play a major role 200
We wish to thank Prof. R. Capelletti and M. Tonelli for many helpful discussions on the quaxtz-indium interaction. We like also to acknowledge the technical help of Messrs. M. Badalassi, E. Corsi, P.
Volume 106, number 4,5,6
OPTICS COMMUNICATIONS
Mannucci and A. Marchini. This work has been supported by the Italian CNR, INFM and MURST.
References [ 1 ] A.N. Nesmeyanov, Vapor pressure of the chemical elements (Elsevier, Amsterdam, 1963) p. 447. [2] C.J. Lorenzen, K. Niemaz and K.H. Weber, Optics Comm. 52 (1984) 178. [ 31 P. Bicchi, A. Kopystynska, M. Meucci and L. Moi, Phys. Rev. A, Rapid Commun. 41 (1990) 5257.
15 March 1994
[ 41 P. Bicchi, C. Marinelli, E. Mariotti, M. Meucci and L. Moi, J. Phys. B: At. Mol. Opt. Phys. 26 (1993) 1. [S] T. Holstein, Phys. Rev. 72 (1947) 1212. [6] T. Holstein, Phys. Rev. 83 (1951) 1159. [ 7 ] A.F. Molisch, B.P. Oehry, W. Schupita and G. Magerl, Optics Comm. 90 (1992) 245. [ 81 A.A. Radzig and B.M. Smimov, Reference data on atoms, molecules and ions (Springer, Berlin, 1985) p. 242. [9] T.M. Co1bertandB.L. Wexler,Phys.Rev.A47 (1993) 2156. [lo] H.K. Holt, Phys. Rev. A 13 (1976) 1442. [ 111 J.H. Schulman and W.D. Compton, Color center in solids (Pergamon, London, 1962) p. 295.
201
OPTlCS COMMUNICATIONS
106 ( 1994) 197-20 1
Radiation trapping and vapor density of indium confined in quartz cells P. Bicchi, C. Marinelli, E. Mariotti, M. Meucci and L. Moi Dipartimento di Fisica, Universitci di Siena, via Banchi di Sotto 55, 53100 Siena. Italy
Received 3 September 1993; revised manuscript received 14 December 1993
We have measured, in the 700-950°C temperature range, the effective lifetime of the 6S1,2 excited level of indium vapor confined in quartz cells. The self trapping results much lower than expected suggest an effective vapor density lower than the one calculated at the thermal equilibrium. A possible explanation of this large deviation has been found in the increasing adsorption rate of indium at the cell walls. Partial fluorescence spectrum of the adsorbed atoms is reported.
1. Introduction
The experimental analysis of collisional processes in very dense laser-excited vapors is an important tool for studying the energy repartition among the atomic excited levels and/or between bound states and the continuum. Sometimes, in order to get high vapor densities, high temperatures have to be reached with the consequence that technical problems become determinant. In the past, different solutions have been adopted like, for example, the heat-pipeoven made from stainless-steel. Even in this case, problems are not completely eliminated and the one of the strong chemical reactivity of the analyzed elements may remain unresolved, the analysis of the vapor-wall interaction becoming a part of the experiment. This is the case for indium which has a very low saturated vapor pressure up to very high temperatures (for example the saturated atomic density nsat is ~10’~ cmm3 at T=900°C [l]). At these temperatures indium reacts with stainless-steel so that heat-pipe-ovens cannot be conveniently used for long time [ 2 1. Recently energy-pooling collisions (EPC) and energy-pooling ionization ( EPI ) have been experimentally demonstrated in indium confined in quartz cells by Bicchi et al. [ 3 1. A quantitative study of the cross section of EPC has been possible only after the vapor-quartz interaction, whose main effect is a de-
crease in the vapor density, has been taken into account [4]. This paper reports a measurement of the effective indium vapor density in quartz cell at high temperature. Results have been obtained by deriving the effective vapor density neff from the measured effective decay time reff of the laser excited level. reff is determined both by the self-trapping and by the LI level configuration of indium. The analysis has been made by comparing the experimental results with the theoretical ones predicted by the Holstein theory [ 5,6] and with those obtained with a Monte Carlo simulation. The results will prove to be useful in many applications, in particular in the possible realization of an indium atomic line filter following the scheme already adopted for thallium [ 71.
2. Experimental apparatus and results The experimental .apparatus is sketched in fig. 1. Indium is distilled under vacuum in the side arm of a quartz cell (diameter 3 cm; length 10 cm) that is then filled with 10 Torr of neon as a buffer gas. This side arm is connected to the cell body through a capillary (3 mm in diameter and 2-5 cm long). The cell is positioned inside an oven which can be heated up to about 1000°C. The temperature, that is uniform
0030-4018/94/%07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDZ 0030-4018(93)E0619-Q
197
Volume 106, number
4,5,6
OPTICS
COMMUNICATIONS
15 March
1994
Digital scope
F
---
Dye laser
Nd-YAG laser
Fig. 1. Experimental block diagram: BS = beam splitter, L = lenses, F= filter, PM = photomultiplier, PD = photodiode.
in the central part, is stabilized within 1°C. Indium atoms are resonantly excited to the 6S,,2 level, whose natural lifetime is r, = 7.4 ns [ 8 1, by a pulsed laser beam tuned to 410.3 nm. The selected wavelength is obtained by mixing in a KDP crystal the output of a dye laser tuned at 667.8 nm with the residual of the fundamental wavelength of the NdYAG laser ( 1064 nm). The laser repetition rate is 10 Hz, its pulse duration 10 ns and its maximum peak power 600 kW. During the measurements the beam is properly attenuated. The bandwidth of the resonant laser beam is 0.8 cm-’ and it is mainly due to the bandwidth of the infrared Nd-YAG beam. The induced fluorescence is collected at right angle, dispersed by a low resolution (60 cm- ’ ) monochromator and detected with a photomultiplier. A fast transient digitizer performs the temporal analysis of the signals which are then elaborated by a personal computer. From the 6S,,2 level, indium atoms decay back to the 5P,,2 and 5P3,2 ground states, separated by AEc2212.56 cm-‘. In fig. 2 a diagram of the involved levels is shown. The fluorescence spectrum consists of two lines, at 1,=410.3 nm and at At,= 45 1.1 nm, respectively. The relative transitions involve ground state levels with a population density in a ratio close to 10 : 1. This results in an escaping competition between the two emitted photons with the consequence of an effective fluorescence decay time strongly different from the one expected for twolevel atoms. We have measured the fluorescence decay time as 198
Fig. 2. h level structure formed by the two ground sublevels 5P,,,, 5P,,, and the excited 6S,,2 level in indium. The excitation energy as well as the fine structure energy of the ground state are also reported.
50
1
o650
750
650
950
T(“C) Fig. 3. Effective lifetime of the 6S,,2 level measured from the decay of the fluorescence signals relative to the transition 6S,,2+ 5P,,* (45 1.1 nm) in a quartz cell with In and 10 torr of Ne as a function of temperature.
a function of the temperature and we have derived the effective lifetime of the 6S1,2 excited level. In fig. 3 the measured effective lifetime reff of the first excited level 6S,,2 is reported as a function of temperature. reff increases to (40 f 4) ns for the highest reached temperature. This lifetime increase is due to the radiation trapping, the efficiency of which is, however, much lower than expected. For a fixed temperature, no variation of reff manifests when the laser power is changed over a wide range, typical working laser power being of the order of few kW. The theoretical evaluation of reff is not straightforward because of the three-level structure of indium. This problem is of fundamental interest and its solution of practical importance. Colbert and Wexler have recently analyzed the radiation trapping for thallium (that has a similar level structure) in the presence of non uniform reflective boundaries by
Volume
106, number
OPTICS
4,5,6
starting from the Holstein equations properly modified [9]. This approach can be easily extended to the indium system. In our experiment the laser beam, whose diameter is much smaller than that of the cell, excites the atoms along the major axis of the cell. Therefore the blue and violet photons emitted by the indium atoms, before escaping from the cell and reaching the photomultiplier, cross a region where the atoms are in the ground states with a population ratio determined, in first approximation, by the thermal equilibrium. The Holstein analytic solution for a two-level atom can be taken into consideration for the two SPl,Z and S-P3,2 transitions separately, in case of a cylindrical geometry and assuming negligible optical pumping effects. The effective lifetime can then be derived, as already done by Holt [ lo] for low vapor densities in Na, by properly weighting their relative contributions. The effective lifetime reff is given by r.?fr= rolg >
(1)
where g is the “escape factor”, g= 1.6O/k,RJw
given by (2)
for a cylindrical The reciprocal and absorptions the cell. R is the
15 March
COMMUNICATIONS
geometry. of g gives the number of emissions of a photon prior to its escape from cell radius and k. is
1994
effective lifetime almost coincides with the lifetimes calculated for the S-P3,2 transition. This has also been verified through a Monte Carlo simulation. In fig. 4 the reff values calculated according to the Holstein theory (separately for the S-P,,2 and SPSI2 transitions) as well as via the Monte Carlo simulation, are reported as a function of the vapor density. By referring to the tables reported by Nesmeyanov [ 11, the corresponding temperatures are also shown for comparison. Up to 850-900°C the Monte Carlo simulation and the Holstein calculation for the S-P3,* transition give roughly the same values. For higher temperatures the contribution due to the SPiI2 transition is not negligible any more and the two sets of values diverge. It is in any case evident (see fig. 3 and fig. 4) that the effective lifetime should be much larger than measured and that reff does not increase in the experiment as expected. An estimate, in excess, of the pressure broadening due to the buffer gas presence in the cell shows it to be slightly less than the natural linewidth and so it can not be the reason of the difference between the calculated and measured values of reff which is larger than one order of magnitude. We have, anyhow, taken it into account in the estimated errors of our measurements. The explanation of this large disagreement is possibly due to the diffusion of the indium atoms inside the quartz cell walls when the temperature exceeds a threshold that for indium is about 850°C. In other words the indium
n x 10”(cme3)
where g, and g, are the statistical weights of the excited and ground state respectively, ilo the resonant wavelength and v. = (2kTIM) ‘I*. The absorption coefficients for the 410 nm and 450 nm photons are k, and kb, respectively. It is easy to verify that their ratio n=
ky = kt, ’ 1
49
1-exp( -~lW exp( -AE/kT)
changes, between 35 and 16, in the temperature range between 727 and 1027°C. That means that the mean freepath of the 410 nm photons is 35 to 16 times shorter than 450 nm ones. This huge difference has the consequence that, until the mean freepath of the blue photons is comparable with the cell radius, the
0.14 4000
’
630
24
I
,
a A
o!.:,*:: 650
650 W’C)
, 1050
Fig. 4. rceffvalues versus temperature and vapor density calculated according the Holstein theory separately for the S-P,,2 (0 ) and S-P,,, (A ) transitions as well as via the Monte Carlo simulation ( + ) .
199
Volume 106, number 4,5,6
OPTICS COMMUNICATIONS
density at the highest temperatures does not reach the equilibrium value, but lower ones. The effective indium density can be derived from the measurement of the effective lifetime of the excited level by shifting the experimental data to lower densities till they match the calculated ones. In our experiment, at 950°C we derive an effective density neff= ( 1.6 f 0.5) x 1OL3cmw3 which is about one order of magnitude less than the corresponding saturated density nsat. This is a manifestation of a porosity of the cell walls which increases with temperature. The indium atoms are adsorbed at the quartz surface where they, then, migrate inside the quartz lattice. This has a direct experimental evidence in the emission spectra obtained for a cell filled with indium and buffer gas when it is operated at high temperature for the first time and after one day of operation. In fig. 5a and 5b respectively, two fluorescence spectra are reported in a wavelength range where there are no indium or buffer gas lines. The strong signal in fig. 5b is due to laser induced fluorescence (LIF) of the quartz walls “contaminated” by the indium atoms. This “contamination” once created is permanent. In fact the LIF spectrum of quartz from operated cells always manifests the same fluorescence, even at room temperature. As the metallic indium is at the bottom of the cell side arm, the diffusion time is not fast enough to maintain the saturated density. The diffusion time becomes very fast if the buffer gas is eliminated, but in this case the cell walls get immediately and heavily contaminated. It is worth noticing that incorporation of impurities of Al, which belongs to the same chemical group of In, in the quartz structure are reported in the literature [ 111. This indium-quartz interaction is by itself an interesting effect which may have important applications also in fields of physics other than the atomic and molecular one. For this reason further experiments are in progress to better characterize these observations.
15 March 1994
b 470“mo
475
a)
480
b)
;’
1‘k I
I
470
475
‘c I
480
il hm)
Fig. 5. LIF spectra detected in a cell with In and 10 Torr of Ne as buffer gas at T= 900°C. (a) Cell operated for the first time. (b ) Cell after one day of operation. The sensitivity in (b) is 5 times less than in (a).
in the establishment of an effective vapor density. We have determined neff by measuring the effective lifetime of the excited level. As to the latter, we discuss how its behaviour as a function of temperature in the case of a three-level element such as indium, strongly differs from the two-level atoms one. We also indicate which important applications these results may have.
Acknowledgments 3. Conclusions We have demonstrated that in very dense laser excited vapors the interaction between the vapor itself and the walls of its container may play a major role 200
We wish to thank Prof. R. Capelletti and M. Tonelli for many helpful discussions on the quaxtz-indium interaction. We like also to acknowledge the technical help of Messrs. M. Badalassi, E. Corsi, P.
Volume 106, number 4,5,6
OPTICS COMMUNICATIONS
Mannucci and A. Marchini. This work has been supported by the Italian CNR, INFM and MURST.
References [ 1 ] A.N. Nesmeyanov, Vapor pressure of the chemical elements (Elsevier, Amsterdam, 1963) p. 447. [2] C.J. Lorenzen, K. Niemaz and K.H. Weber, Optics Comm. 52 (1984) 178. [ 31 P. Bicchi, A. Kopystynska, M. Meucci and L. Moi, Phys. Rev. A, Rapid Commun. 41 (1990) 5257.
15 March 1994
[ 41 P. Bicchi, C. Marinelli, E. Mariotti, M. Meucci and L. Moi, J. Phys. B: At. Mol. Opt. Phys. 26 (1993) 1. [S] T. Holstein, Phys. Rev. 72 (1947) 1212. [6] T. Holstein, Phys. Rev. 83 (1951) 1159. [ 7 ] A.F. Molisch, B.P. Oehry, W. Schupita and G. Magerl, Optics Comm. 90 (1992) 245. [ 81 A.A. Radzig and B.M. Smimov, Reference data on atoms, molecules and ions (Springer, Berlin, 1985) p. 242. [9] T.M. Co1bertandB.L. Wexler,Phys.Rev.A47 (1993) 2156. [lo] H.K. Holt, Phys. Rev. A 13 (1976) 1442. [ 111 J.H. Schulman and W.D. Compton, Color center in solids (Pergamon, London, 1962) p. 295.
201