PHYSICAL REVIEW A VOLUME 54, NUMBER 2 AUGUST 1996

…7P,6D,8S,4F؍Energy-pooling collisions in cesium: 6PJ؉6PJ˜6S؉„nl Z. J. Jabbour,* R. K. Namiotka, and J. Huennekens Department of , Lehigh University, 16 Memorial Drive East, Bethlehem, Pennsylvania 18015

M. Allegrini,† S. Milosˇevic´,‡ and F. de Tomasi§ Unita` INFM, Dipartimento di Fisica, Universita` di Pisa, Piazza Torricelli 2, 56126 Pisa, Italy ͑Received 25 September 1995͒

We report experimental rate coefficients for the energy-pooling collisions Cs(6P1/2) ϩCs(6P ) Cs(6S )ϩCs(nl ) and Cs(6P )ϩCs(6P ) Cs(6S )ϩCs(nl ) where nl ϭ7P , 1/2 → 1/2 JЈ 3/2 3/2 → 1/2 JЈ JЈ 1/2 7P3/2,6D3/2,6D5/2,8S1/2,4F5/2,or4F7/2. Atoms were excited to either the 6P1/2 or 6P3/2 state using a single-mode Ti:sapphire . The excited-atom density and spatial distribution were mapped by monitoring the absorption of a counterpropagating single-mode ring dye laser beam, tuned to either the 6P 8S or 1/2→ 1/2 6P 7D transitions, which could be translated parallel to the pump beam. Transmission factors, which 3/2→ 3/2,5/2 describe the average probability that emitted within the fluorescence detection region can pass through the optically thick vapor without being absorbed, were calculated for all relevant transitions. Effective lifetimes of levels populated by energy-pooling collisions are modified by radiation trapping, and these factors were calculated using the Molisch theory. These calculated quantities have been combined with the measured excited-atom densities and fluorescence ratios to yield absolute energy-pooling rate coefficients. It was found that the rate for production, in all cases, is greatest for 6D, but that 1/2-1/2 collisions are significantly more efficient than 3/2-3/2 collisions for populating 7P. It was also found that 7P1/2 is populated two to three times more efficiently than 7P3/2 in 1/2-1/2 collisions, but that the 7P fine-structure levels are approximately equally populated in 3/2-3/2 collisions. ͓S1050-2947͑96͒00508-2͔

PACS number͑s͒: 34.50.Rk, 34.90.ϩq

I. INTRODUCTION renko. However, energy pooling in cesium is of current in- terest because such collisions could be an important loss In 1972, Klyucharev and Lazarenko ͓1͔ reported that mechanism in ultracold laser traps, especially now that trap when cesium vapor was resonantly excited to the 6P levels, densities of 1011 to 1012 cmϪ3 are within range ͓16͔.Inad- fluorescence from the 6D atomic levels, which lie near twice dition, the large fine-structure of the cesium 6PJ levels the 6P energy, could be observed. The population in the makes the study of cesium energy pooling more interesting, high-lying levels was attributed to excited-atom-excited- since the combinations 6P1/2ϩ6P1/2,6P1/2ϩ6P3/2, and atom collisions in which the two atoms pool their internal 6P3/2ϩ6P3/2 are more or less resonant with various highly energy to produce one ground-state atom and one in a more excited states ͑see Fig. 1͒. The large fine-structure splittings highly excited state nlJЈ ͑in this case nlJЈϭ6D3/2,5/2͒ also allow study of the role of angular momentum in the energy-pooling process. To the best of our knowledge, there Cs͑6P ͒ϩCs͑6P ͒ Cs͑nl ͒ϩCs͑6S ͒. ͑1͒ have been only a few quantitative studies to date on energy J J ⇒ JЈ 1/2 pooling in cesium. In their original paper, Klyucharev and Collisions of this type have since come to be called ‘‘energy- Lazarenko ͓1͔ estimated from experiment that the cross sec- pooling collisions’’ and they have been the subject of much tion for process ͑1͒ was less than 10Ϫ13 cm2 for nlϭ6D at a study in alkali-metal homonuclear ͓2–5͔ and heteronuclear temperature of 528 K. Later, Borodin and Komarov ͓17͔ ͓6,7͔ systems, as well as in other metal vapors ͓8–15͔ over determined theoretically that the cross section exceeds the last 20 years. 1.5ϫ10Ϫ15 cm2 for this process at Tϭ500 K. Yabuzaki et al. While the majority of previous alkali-metal work has con- ͓18͔ carried out an experimental study of the inverse process, centrated on sodium, ͓2–4͔ there has been little work on Cs͑6D͒ϩCs͑6S͒ Cs͑6P͒ϩCs͑6P) and found a cross sec- ϩ1.5 → Ϫ14 2 cesium following the initial paper by Klyucharev and Laza- tion of ͑1.5Ϫ0.7͒ϫ10 cm at 530 K. Preliminary experi- mental results on the process Cs(6P3/2)ϩCs(6P3/2) Cs(7P )ϩCs(6S ) have recently been obtained ͓19͔ → JЈ 1/2 *Present address: Automated Production Technology Division, and additional results for 6P1/2 excitation, along with details Sound A147, NIST, Gaithersburg, Maryland 20899. of the 6P3/2 experiment will appear shortly ͓20͔. †Present address: Dipartimento di Fisica della Materia, Geofisica e It is the purpose of this manuscript to present quantitative Fisica dell’Ambiente, Universita` di Messina, Salita Sperone 31, experimental results for rate coefficients and cross sections 98166 Sant’ Agata, Messina, Italy. for the cesium energy-pooling process ͓Eq. ͑1͔͒. Such mea- ‡Permanent address: Institute of Physics, University of Zagreb, surements are complicated by the need to know both the P.O. Box 304, Zagreb 41000, Croatia. density and the spatial distribution of excited atoms in the §Present address: Laboratoire de Physique des , Universite´ vapor. In this work, the excited-atom density and spatial dis- Paris-Nord, Avenue J. B. Clement, 93430 Villetaneuse, France. tribution were measured using a weak probe laser. In addi-

1050-2947/96/54͑2͒/1372͑13͒/$10.0054 1372 © 1996 The American Physical Society 54 ENERGY-POOLING COLLISIONS IN CESIUM: . . . 1373

FIG. 1. ͑a͒ Energy levels of cesium showing transitions studied in this work. Wavelengths are given in nm. ͑b͒ Cesium atomic levels lying near twice the 6PJ level energies. 6PJϩ6PJ energies are represented by dashed lines. Energies are taken from Ref. ͓56͔.

tion, radiation trapping, radiative cascade, optical pumping, II. THEORY and other effects must also be considered. Rate coefficients A. Rate equations for energy pooling with product states nlJЈϭ7P1/2 ,7P3/2, The energy-pooling process described by Eq. ͑1͒ produces 6D3/2,6D5/2,8S1/2,4F5/2, and 4F7/2 are reported. This paper is organized as follows. Section II presents a atoms in the highly excited states nlJЈ which lie near twice rate equation model used to extract the energy-pooling rate the energy of the pumped resonance state ͓see Fig. 1͑b͔͒. coefficients from the measured fluorescence ratios. It also Rate equations can be used to derive theoretical expressions discusses radiation trapping and related prob- for the populations in these higher excited states, which in lems in detail. Experimental details, including a description turn yield expressions for the energy-pooling rate coeffi- of the excited-atom density measurement are presented in cients. Note that, for the most part, this discussion follows Sec. III. Results are given in Sec. IV along with a discussion that of Neuman, Gallagher, and Cooper ͓15͔. The steady- of various sources of error. Finally, our conclusions are pre- state rate equation for the population in state nlJЈ following sented in Sec. V. pumping of 6PJ reads 1374 Z. J. JABBOUR et al. 54

k ͓n ͑r͔៝͒2 n ͑r៝͒ Factors such as the absolute detection efficiency and col- nlJЈ 6PJ nlJЈ n˙ ͑r៝͒ϭ0ϭ Ϫ , ͑2͒ lection solid angle are experimentally difficult to determine. nlJЈ 2 ␶eff nlJЈ Therefore it is advantageous to measure fluorescence ratios. Specifically, we measure the ratio of fluorescence from the which has the solution state nlJЈ , populated through energy pooling, to fluorescence 1 2 eff observed on the directly pumped resonance transition; i.e., nnl ͑r៝͒ϭ 2 knl ͓n6P ͑r͔៝͒ ␶ , ͑3͒ JЈ JЈ J nlJЈ on the 6P 6S transition J→ 1/2 eff nat Here, knl is the rate coefficient for process ͑1͒, and ␶nl is JЈ JЈ Inl n l ␭6P 6S ␧nl n l ⌫nl n l JЈ→ Ј ЈJЉ J→ 1/2 JЈ→ Ј ЈJЉ JЈ→ Ј ЈJЉ the effective lifetime for atoms in state nlJЈ . Note that in the ϭ nat I6P 6S ␭nl nЈlЈ ␧6P 6S ⌫6P 6S absence of quenching collisions and radiation trapping, J→ 1/2 JЈ→ JЉ J→ 1/2 J→ 1/2 (␶eff )Ϫ1 is just the sum of the Einstein A coefficients for nlJ eff 2 3 Ј Tnl n l knl ␶nl ͓͐n6P ͑r͔៝͒ d r transitions connecting state nl to all lower levels. However, JЈ→ Ј ЈJЉ JЈ JЈ J JЈ ϫ 3 . at higher atom densities, radiation trapping will reduce the T6P 6S 2 ͐n6P ͑r៝͒d r J→ 1/2 J effective radiative rate for transitions to the ground state. We ͑5͒ will find that radiation trapping can also occur, under some circumstances, for transitions terminating on levels directly Finally, we can solve Eq. ͑5͒ for the rate coefficient k populated by the laser. Note that the factor 2 introduced in nlJЈ Eq. 2 is due to the fact that the 6P atoms are identical. ͑ ͒ J I /␧ 2 nlJЈ nЈlЈJЉ nlJЈ nЈlЈJЉ Therefore [n6P] /2 is proportional to the number of excited- k ϭ → → nlJ atom pairs in the volume, as first pointed out in Ref. ͓21͔. Ј ͩ I6P 6S /␧6P 6S ͪ J 1/2 J 1/2 We are interested in the fluorescence corresponding to the → → ⌫nat transition nlJ nЈlЈJ emitted by atoms in the particular ␭nl nЈlЈ 6P 6S T6P 6S 2 Ј→ Љ JЈ→ JЉ J→ 1/2 J→ 1/2 volume which is imaged onto the slits of our monochro- ϫ nat eff ␭6P 6S ⌫ Tnl n l ␶ J 1/2 nl n l JЈ Ј ЈJЉ nlJ mator. This is given by the following: → JЈ→ Ј ЈJЉ → Ј 3 ͐n6P ͑r៝͒d r 3 J I ϭ I ͑r៝͒d r ϫ 2 3 . ͑6͒ nlJЈ nЈlЈJЉ ͵ nlJЈ nЈlЈJЉ ͓͐n ͑r͔៝͒ d r → Vol → 6PJ

hc d⍀ In the present experiment, the detection volume is a thin strip ϭ ␧nl n l ␭ JЈ→ Ј ЈJЉ 4␲ of height ⌬yϳ150 ␮m oriented along the z ͑laser propaga- nlJЈ nЈlЈJЉ → tion͒ axis ͓see Fig. 2͑b͔͒. If we assume that the excitation is nat 3 uniform along the z axis, and because ⌬y is small, we write ϫ⌫ Tnl n l nnl ͑r៝͒d r nlJЈ nЈlЈJЉ JЈ Ј ЈJЉ͵ JЈ the volume integrals in Cartesian coordinates, and immedi- → → Vol ately carry out the integrations over y and z hc d⍀ nat ϭ ␧nl n l ⌫ JЈ Ј ЈJЉ nlJ nЈlЈJ Inl n l /␧nl n l ␭nl n l → 4␲ Ј→ Љ JЈ→ Ј ЈJЉ JЈ→ Ј ЈJЉ JЈ→ Ј ЈJЉ k ϭ nlJЈ I / eff ͩ 6P 6S ␧6P 6S ͪ J 1/2 J 1/2 knl ␶ → → JЈ nlJЈ ϫT ͓n ͑r͔៝͒2d3r. nat nlJЈ nЈlЈJЉ ͵ 6PJ ␭nl nЈlЈ ⌫6P 6S T6P 6S → 2 J J J 1/2 J 1/2 Vol ϫ Ј→ Љ → → ␭ ⌫nat ␶nat T 4 6PJ 6S1/2 nl n l nl nlJЈ nЈlЈJЉ ͑ ͒ → JЈ→ Ј ЈJЉ JЈ → R Here hc/␭ is the energy of a fluorescence ͐ϪRn6P ͑x͒dx nlJЈ nЈlЈJЉ 2 J → nat ϫ , ͑7͒ ͑␭ is the transition wavelength͒, ⌫ is the eff nat R 2 nlJ nЈlЈJ nl n l ͑␶nl /␶nl ͒ ͐ϪR͓n6P ͑x͔͒ dx Ј→ Љ JЈ→ Ј ЈJЉ JЈ JЈ J natural radiative rate of the transition, ␧nl n l is the de- JЈ→ Ј ЈJЉ tection system efficiency ͑including effects due to the photo- where R is the cell radius. Note that, in this expression, nat nat multiplier, monochromator grating, and any filters used͒ at ⌫nl n l ␶nl is the branching ratio for the nlJЈ nЈlЈJЉ JЈ→ Ј ЈJЉ JЈ → the frequency of interest, and d⍀/4␲ is the probability that transition, and (␶eff /␶nat ) is a factor which characterizes the the fluorescent photon is emitted into the finite collection nlJЈ nlJЈ effect of radiation trapping on the nl state lifetime. solid angle of the detection system. Here we have assumed JЈ that collisions and radiation trapping quickly destroy any atomic alignment or orientation, and thus the emissions are B. Radiation trapping and optical depth effects isotropic. Finally, Tnl n l is the average probability that Because of the high density of ground-state atoms and the JЈ→ Ј ЈJЉ the photon emitted in the detection direction will pass strength of the resonance transitions, it is unlikely that reso- through the vapor between its point of origin and the cell nance photons can escape the cell without being reabsorbed. walls without being absorbed. This probability depends on Thus the excitation lives longer in the vapor than one natural the distribution of both the nlJЈ and nЈlЈJЉ atoms in the excited-state lifetime. There are two major effects of radia- vapor as well as on the details of the transition line shape. tion trapping in the present context. The spatial distribution The calculation of Tnl n l will be described in Sec. II B. of excited atoms is different than the distribution initially JЈ→ Ј ЈJЉ 54 ENERGY-POOLING COLLISIONS IN CESIUM: . . . 1375

FIG. 2. ͑a͒ Experimental setup. The Ti:sap- phire laser was used to pump the 6S1/2 6PJ transition. The monochromator and photomulti-→ plier tube 1 ͑PMT-1͒ were used to spectrally re- solve the cesium atomic line fluorescence. PMT-2 was used to monitor total resonance line ͑D1 or D2͒ fluorescence, and PMT-3 monitored the transmission of the Ti:sapphire beam through the cell. The ring dye laser was used to probe the 6PJ level density at various positions in the cell ͑determined by the position of the translating mirror͒. PMT-4 was used to monitor the dye laser transmission. IF, LP, SP, and ND represent inter- ference, long-pass, short-pass and neutral density filter, respectively. ͑b͒ insert showing the cell ge- ometry and the region from which fluorescence was detected.

produced by the pump laser, and the effective lifetime of the Here ␴ (␻) is the absorption cross section at angu- nlJЈ nЈlЈJЉ excited atoms and hence the time in which they can undergo ← ͑ lar frequency ␻. Thus, ␴nl n l (␻)/͐␴nl n l (␻)d␻ JЈ← Ј ЈJЉ JЈ← Ј ЈJЉ energy-pooling collisions͒ is lengthened over the natural ra- is the normalized probability that a photon of frequency ␻ diative lifetime. Both of these effects are properly taken into will be emitted at any position x, and account in Eq. ͑7͒, which uses calculated effective lifetimes R exp͓Ϫ␴nl nЈlЈ (␻)͐x nnЈlЈ (xЈ)dxЈ͔ is the probability that the and transmission factors, and spatial integrals over the mea- JЈ← JЉ JЉ photon of frequency ␻ emitted at x can escape through the sured steady-state distribution of excited atoms. ͑possibly nonuniform͒ distribution of lower-state atoms The normalized transmission factors in Eq. ͑7͒ are defined n (xЈ) and reach the cell wall a distance (RϪx) away. as follows: nЈlЈJЉ For a line with hyperfine structure, the absorption coeffi- cients add; k (␻)ϭ͚ ͚ k (␻) Tnl n l nlJЈ nЈlЈJЉ F FЈ nlJЈ(F) nЈlЈJЉ(FЈ) JЈ→ Ј ЈJЉ ← ← ϭ͚F͚F ␴nl (F) n l (F )(␻)nn l (F ) . Thus if we as- Ј JЈ ← Ј ЈJЉ Ј Ј ЈJЉ Ј escape sume that the lower-state hyperfine levels are populated sta- ϭ n ͑r៝͒P ͑r៝͒d3r n ͑r៝͒d3r nlJ nl n l nlJ ͵Vol Ј JЈ→ Ј ЈJЉ Ͳ͵Vol Ј tistically, we may define a line-shape factor ␴nl n l (␻) JЈ← Ј ЈJЉ for the full transition R R escape ϭ nnl ͑x͒P ͑x͒dx nnl ͑x͒dx, ͵ JЈ nlJЈ nЈlЈJЉ ͵ JЈ knl n l ͑␻͒ ϪR → Ͳ ϪR JЈ Ј ЈJЉ ← ␴nl n l ͑␻͒ϵ JЈ← Ј ЈJЉ n ͑8͒ nЈlЈJЉ g͑FЈ͒ ϭ ␴ ͑␻͒ , ͚ ͚ nlJЈ͑F͒ nЈlЈJЉ͑FЈ͒ g F where our specific detection system geometry, described F FЈ ← ͚FЈ ͑ Ј͒ above Eq. ͑7͒, has been used in the last step. The escape escape ͑10͒ factor Pnl n l (x) is the probability that nlJЈ nЈlЈJЉ JЈ→ Ј ЈJЉ → photons emitted at position x can escape the cell in the de- where g(FЈ)ϭ2FЈϩ1 is the statistical weight of level tection direction through the vapor path length (RϪx) with- nЈlЈJЉ(FЈ). Finally, the absorption cross sections for indi- out being reabsorbed vidual hyperfine transitions are each given by a Voigt func- tion of the form

escape ␴nl ͑F͒ n l ͑F ͒͑␻͒ P ͑x͒ JЈ ← Ј ЈJЉ Ј nlJЈ nЈlЈJЉ → nat 2 ⌫ ⌫ ␭ g͑F͒ nlJ nЈlЈJ nl n l Ј→ Љ JЈ→ Ј ЈJЉ ϭ ␴ ͑␻͒exp Ϫ␴ ͑␻͒ ϭ 1/2 nlJ nЈlЈJ nlJ nЈlЈJ 8 g F ͵ Ј← Љ ͫ Ј← Љ ␲ ͑ Ј͒ ␲ ⌬ 2 2 R ϱ exp͓Ϫ͑␻ЈϪ␻nl ͑F͒ n l ͑F ͒͒ /⌬ ͔ JЈ → Ј ЈJЉ Ј ϫ nnЈlЈ ͑xЈ͒dxЈ d␻ ␴nl nЈlЈ ͑␻͒d␻. ϫ d␻Ј 2 2 , ͵x JЉ ͬ ͵ JЈ← JЉ ͵Ϫϱ ͑␻Ϫ␻Ј͒ ϩ͑⌫nl n l /2͒ Ͳ JЈ Ј ЈJЉ → ͑9͒ ͑11͒ 1376 Z. J. JABBOUR et al. 54 where ⌫nl n l is the Lorentzian linewidth ͓full width at ͓29–30͔ and Milne ͓31͔ theories in the limits k0lу10 and JЈ→ Ј ЈJЉ half maximum ͑FWHM͒ in angular frequency units͔, ⌬ k0lр10, respectively, as has been shown in Refs. ͓26͔ and ϭ1/␭ͱ2kT/m is the Gaussian ͑Doppler͒ linewidth ͑full ͓28͔. Here k0 is the line-center absorption coefficient, and l width at 1/e maximum in angular frequency units͒, and is the effective escape distance. However, to model the re- sults of the present experiment, we use the Molisch et al. ␻nl (F) nЈlЈ (FЈ) is the line-center frequency of the JЈ → JЉ theory of radiation trapping ͓32,33͔͑see also Ref. ͓34͔͒ nl (F) n l (F ) transition. k is Boltzmann’s constant, JЈ Ј ЈJЉ Ј which reduces to the Holstein and Milne results in the ap- T is the→ absolute temperature, and m is the cesium atomic propriate limits. The most severe, and in the context of the mass. Thus the normalized transmission factors Tnl n l JЈ→ Ј ЈJЉ present experiment most significant, trapping occurs on the in Eq. ͑7͒ can be calculated for any transition from Eqs. 6PJ 6S1/2 resonance transition. However, these trapping ͑8͒–͑11͒ if the hyperfine structure and Lorentzian linewidth effects→ are all included in the transmission factor of the transition, and the spatial distribution of the lower- T6P 6S . The 7PJЈ 6S1/2 transitions are the only transi- state n l atoms is known. The only significant assumption J→ 1/2 → Ј ЈJЉ tions to the ground state for which we must calculate effec- that has been made is that the lower-state hyperfine levels are tive radiative rates. populated in a statistical ratio. This assumption will be dis- According to the general formulation of Holstein ͓29,30͔, cussed further below. For each hyperfine transition of the Payne and Cook ͓35͔, and van Trigt ͓36͔, for certain geom- various nl nЈlЈ and 6P 6S transitions of interest, JЈ→ JЉ J→ 1/2 etries, the steady-state excited-atom spatial distribution n(r៝) and at each temperature, we calculate ␴nl (F) n l (F )(␻) JЈ ← Ј ЈJЉ Ј can be expanded in a series of orthogonal eigenmodes as a function of frequency using the Voigt algorithm of Refs. n(r៝)ϭ͚ ja jn j(r៝). Each eigenmode is a mathematical solu- ͓22͔ and ͓23͔͑see also ͓24͔͒. tion of the radiation diffusion equation characterized by a Note that we have not taken optical pumping into account nat single exponential decay rate ␤ jϭg j⌫ . Here, g j is the es- nat when discussing the 6PJ 6S1/2 transmission factor. Since cape factor for mode j, and is the natural radiative rate → ⌫ the pump laser we use is single mode, with a linewidth for the excited state. Note that the individual eigenmode so- which is small compared to the ground-state hyperfine split- lutions are nonphysical, since ͑except for the fundamental ting of 9.193 GHz, we pump atoms almost exclusively from mode͒ each has regions of negative amplitude ͑see, for ex- one hyperfine component. Due to optical pumping, atoms ample, Figs. 1 and 2 of Ref. ͓36͔͒. Nevertheless, these eigen- will tend to accumulate in the other ͑unpumped͒ hyperfine modes form a complete set, and any actual excited-atom spa- level. For example, if we pump the tial distribution can be expanded as a linear superposition of 6S1/2(Fϭ4) 6P1/2(FЈϭ4) transition, atoms will accumu- them. → late in the 6S1/2(Fϭ3) level. Consequently, reabsorption of We model our cell as a cylinder of radius Rϭ1.05 cm and photons at the 6P1/2 6S1/2(Fϭ3) transition frequency will length L, with LӷR. In this experiment we measure the → be much more severe than for those at the cylindrically symmetric steady-state excited-atom spatial dis- 6P 6S (Fϭ4) frequency. However, this optical pump- 1/2 1/2 tribution n6P (r), and we assume that the 7PJ density is ing only→ occurs within the pump laser column which is sur- J Ј proportional to ͓n (r)͔2 according to Eq. ͑3͒. Thus we can rounded by a much larger volume of ground-state atoms 6PJ where the ratio of hyperfine level populations is approxi- calculate the mode amplitudes from mately statistical. The transmission factor is determined pri- R R 2 2 marily by these atoms outside the laser column. Thus we a jϭ ͓n6P ͑r͔͒ n j͑r͒rdr ͓n6P ͑r͔͒ rdr. believe that use of a transmission factor based on a statistical ͵0 J Ͳ͵0 J ͑13͒ distribution of atoms in the 6S1/2 hyperfine levels is justified. However, this assumption of a statistical ratio of ground- eff Finally, the effective radiative rate ⌫7P 6S , or escape state hyperfine level populations used in these calculations is JЈ→ 1/2 factor g7P 6S , is given by a weighted average of the a significant source of uncertainty in our analysis. JЈ→ 1/2 From Eq. ͑7͒ it can be seen that the effective lifetime of decay rates for the individual eigenmodes the state nl is also needed in order to determine the energy- JЈ eff nat pooling rate coefficient k . In the present context, colli- ⌫7P 6S ϭg7P 6S ⌫7P 6S nlJЈ JЈ→ 1/2 JЈ→ 1/2 JЈ→ 1/2 sional quenching of nlJЈ atoms can be neglected. However, nat 3 ⌫7P 6S ͚ jg ja j͐n j͑r͒d r due to radiation trapping, JЈ→ 1/2 ϭ 3 ͚ ja j͐n j͑r͒d r Ϫ1 eff ϭ eff nat R ␶nl ͚ ⌫nl n l ⌫7P 6S ͚ jg ja j͐0 n j͑r͒rdr JЈ JЈ→ Ј ЈJЉ JЈ 1/2 ͫ nЈlЈJ ͬ → Љ ϭ . ͑14͒ ͚ a ͐Rn ͑r͒rdr Ϫ1 j j 0 j ϭ g ⌫nat , ͑12͒ ͚ nlJ nЈlЈJ nl n l Ј→ Љ JЈ→ Ј ЈJЉ In the present work, we model our results using the ͫ nЈlЈJ ͬ Љ Molisch theory of radiation trapping ͓32,33͔. This theory is eff based upon numerical integration of the Holstein radiation where ⌫nl n l is the effective radiative rate ͑and JЈ→ Ј ЈJЉ diffusion equation and yields analytic fitting equations for gnl n l is the escape factor͒ of the transition. the escape factors and eigenmodes. Most important, Molisch JЈ→ Ј ЈJЉ Radiation trapping has been studied extensively for Dop- et al. give escape factors for the ten lowest eigenmodes pler broadened alkali resonance lines ͓25–28͔. Effective ra- which allows an accurate expansion of the excited-atom spa- diative rates can be calculated accurately using the Holstein tial profile in Eq. ͑14͒. In this case, where the radiation trap- 54 ENERGY-POOLING COLLISIONS IN CESIUM: . . . 1377 ping is dominated by the Doppler core of the line, the escape The hyperfine levels of 6P1/2 are sufficiently separated in factor for the jth mode is given according to Molisch et al. energy that transitions to 6P1/2(FЈϭ3) and 6P1/2(FЈϭ4) ͓33͔ by the expression are treated separately. The hyperfine level separation in the 6P3/2 state is much smaller, however, and we treat transitions 1 to 6P as a composite line as discussed above. Trapping gDϭ 1ϩ k Rͱln͓͑k R/2͔ϩe͒ 3/2 j ͫ mD 0 0 corrections of this type reduce the effective radiative rates by j up to 80%, but are typically less than 60% for the cD k R ln͑k R͒ϩcD k RϩcD ͑k R͒2 Ϫ1 0 j 0 0 1 j 0 2 j 0 6DJЈ 6PJ transitions and always less than 6% for the Ϫ D D 2 . ͑15͒ 8S →6P transition where 6P is the level pumped by the 1ϩc k0Rϩc ͑k0R͒ ͬ 1/2 J J 3 j 4 j → eff laser. Again, the effects on ␶nl are typically less than those D D JЈ The coefficients m j and c ij for the first ten modes are tabu- on the effective radiative rates; Ͻ26% except in two cases lated in Table 1 of Ref. ͓33͔͑the superscript D stands for ͑see Table I͒ for nlJЈϭ6D3/2,5/2 and Ͻ2% for nlJЈϭ8S1/2 . Doppler line shape͒, and k0R is the line-center opacity. Note Note that trapping on transitions terminating on the fine- that the escape factor g D used here is the inverse of the j structure level 6PJ which is not directly populated by the Molisch trapping factor g defined in Ref. ͓33͔. Ј eff laser is generally quite small, since fine-structure level To calculate ⌫7P 6S we first determined the Molisch changing collisions JЈ→ 1/2 Doppler line-shape cylinder eigenfunctions as described in Ref. ͓33͔͑see also Ref. ͓34͔͒. We then calculated the mode Cs͑6PJ͒ϩCs͑6S1/2͒ Cs͑6PJ ͒ϩCs͑6S1/2͒ ͑17͒ ⇒ Ј amplitudes of the experimentally measured excited-atom 2 are relatively rare at the densities of this experiment. Trap- spatial distribution n7P (r៝)ϰ͓n6P (r៝)͔ using Eq. ͑13͒. This JЈ J ping on transitions which terminate on levels other than 6S information was used in Eq. ͑14͒, along with the lowest ten 1/2 and 6P can always be neglected. mode escape factors from Eq. ͑15͒, to calculate the radiative J escape factor of each hyperfine transition. In our use of Eq. ͑15͒ for lines with unresolved hyperfine III. THE EXPERIMENT structure, we replace the line-center optical depth k0R, cal- A. Setup and fluorescence measurements culated for the line without structure, by kmaxR, where kmax is the maximum absorption coefficient for the line with struc- The experimental setup is shown in Fig. 2. Cesium metal ture ͑see Refs. ͓26͔, ͓28͔, and ͓37͔͒. The latter is the lower is contained in a cylindrical Pyrex cell ͑Environmental Op- state density times the maximum absorption cross section of tical Sensors, Inc.͒ of inner length 7.0 cm and inner radius the composite line from Eq. ͑10͒. In the case of the 1.05 cm. The cell is contained in a cross-shaped brass oven ͑not shown in the figure͒, with four quartz windows, which is 7PJЈ 6S1/2 transitions, the lower-state hyperfine structure is well→ resolved, but the upper-state structure is not. Thus we heated with resistive heater tapes. Three thermocouples are calculate attached to the cell in order to monitor temperature. Typi- cally the three temperatures agree to within 5–6 °C, and are eff nat ⌫ ϭg7P 6S Fϭ3 ⌫ constant to within 2 °C over the course of a set of measure- 7PJ 6S1/2 JЈ 1/2͑ ͒ 7PJ 6S1/2͑Fϭ3͒ Ј→ → Ј→ ments. The liquid cesium metal can be seen to sit at the site nat ϩg7P 6S Fϭ4 ⌫ , ͑16͒ where the coldest temperature is registered. JЈ 1/2͑ ͒ 7PJ 6S1/2͑Fϭ4͒ → Ј→ The density of cesium atoms in the vapor phase is calcu- where we consider the upper-state hyperfine levels to be lated from the Nesmeyanov vapor pressure formula ͓39͔.At populated in statistical equilibrium by the energy-pooling room temperature, the various hyperfine components of the eff cesium D line are optically thin. Thus the line-center ab- process. Values of ⌫7P 6S calculated using the procedure 1 JЈ→ 1/2 sorption coefficient can be used to obtain an accurate value described above are used to determine ␶eff /␶nat , and these 7PJЈ 7PJЈ for the atom density at that temperature. We find that the are listed in Table I where the results are presented. value obtained in this manner is larger than the Nesmeyanov Under our conditions, radiative rates are reduced by trap- value by 4.5%. Since this corresponds to a temperature dis- ping by less than 45% for the 7P1/2 6S1/2 transition, but by crepancy of only 1/2 °C ͑which is equal to the uncertainty in as much as 90% for the 7P 6→S transition, using the 3/2→ 1/2 our temperature measurement͒, we assume that the Nesmey- natural radiative rates of Warner ͓38͔. However, values of anov curve is fairly accurate in this temperature range. We eff nat ␶7P 6S differ from ␶7P 6S by 70% in the most ex- estimate that ground-state densities obtained in this manner JЈ→ 1/2 JЈ→ 1/2 treme case. are accurate to ϳ5–10% in the temperature range 23–92 °C. Finally, with strong pumping we must worry about trap- The cesium atoms are excited to particular hyperfine com- ping on transitions which terminate on the 6PJ levels. These ponents of the 6P1/2 and 6P3/2 states using a single-mode transitions, which include 8S1/2 6PJ and 6DJЈ 6PJ , are Ti:Sapphire laser ͑Coherent model 899-29, pumped by 10 W of sufficiently low optical depth→ under the conditions→ of the all lines from an argon-ion laser͒. Typical Ti:Sapphire laser present experiment that we treat them using the Molisch power was 580 mW at the D1 line and 650 mW at the D2 theory, but retain only the fundamental mode of the expan- line. Laser linewidth was ϳ1 MHz. Although several excita- sion. The 6PJ level populations are not uniformly distributed tion geometries were tried, our most accurate data were taken in space since the pump excitation is not uniform. However with the Ti:Sapphire laser ͑hereafter called the pump laser͒ we measure the spatial distribution of the laser excited 6PJ gently focused into the cell usinga4mfocal length lens. A atoms ͑see Sec. III͒. Therefore we can estimate an effective 2.03 mm aperture just before the entrance window was used escape radius for photons resonant with these transitions. to better approximate a top-hat spatial profile, which was nat 7 Ϫ1 nat 7 Ϫ1 1378 TABLE I. Measured rate coefficients for the cesium energy-pooling collisions Cs(6PJ)ϩCs(6PJ) Cs(nlJЈ)ϩCs(6S1/2). Note: ⌫6P 6S ϭ2.89ϫ10 s and ⌫6P 6S ϭ3.26ϫ10 s → 1/2→ 1/2 3/2→ 1/2 from Warner ͓38͔.

Cs(6P3/2)ϩCs(6P3/2) Cs(nlJЈ)ϩCs(6S1/2) → eff ͐R n ͑x͒dx Monitored I /␧ ␶ ϪR 6P3/2 nl nЈlЈ nl nЈlЈ nat nat nlJ Temp n Transition JЈ→ JЉ JЈ→ JЉ ⌫ ␶ Ј k 6S1/2 R 2 nlJЈ nЈlЈJЉ nlJЈ nat nlJЈ 12 Ϫ3 T ͐ ͓n ͑x͔͒ dx I /␧ →Ϫ1 T ␶ 3 Ϫ1 nl ͑°C͒ ͑10 cm ͒ 6P3/2 6S1/2 ϪR 6P3/2 nl nЈlЈ 6P3/2 6S1/2 6P3/2 6S1/2 ͑s ͒ nlJЈ nЈlЈJЉ ͑s͒ nlJЈ ͑cm s ͒ JЈ → JЈ→ JЉ → → → 7P 64 1.25 0.0249 ͑3.88ϫ1010͒Ϫ1 7P 6S 2.69ϫ10Ϫ8 1.58ϫ106 0.934 1.55ϫ10Ϫ7 1.02 2.59ϫ10Ϫ12 1/2 1/2→ 1/2 74 2.62 0.0109 ͑1.01ϫ1011͒Ϫ1 2.06ϫ10Ϫ7 0.862 1.04 3.54ϫ10Ϫ12 74 2.62 0.0130 ͑1.62ϫ1011͒Ϫ1 8.73ϫ10Ϫ7 0.883 1.04 1.09ϫ10Ϫ11 85 5.62 0.00548 ͑4.44ϫ1011͒Ϫ1 2.14ϫ10Ϫ6 0.739 1.08 4.73ϫ10Ϫ12 85 5.62 0.00607 ͑4.27ϫ1011͒Ϫ1 2.57ϫ10Ϫ6 0.749 1.08 6.45ϫ10Ϫ12 91.5 8.63 0.00440 ͑8.23ϫ1011͒Ϫ1 6.71ϫ10Ϫ6 0.627 1.12 7.34ϫ10Ϫ12 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 3.69ϫ10Ϫ6 0.627 1.12 5.88ϫ10Ϫ12 7P 64 1.25 0.0249 ͑3.88ϫ1010͒Ϫ1 7P 6S 3.12ϫ10Ϫ8 4.18ϫ106 0.689 1.10ϫ10Ϫ7 1.22 1.81ϫ10Ϫ12 3/2 3/2→ 1/2 74 2.62 0.0109 ͑1.01ϫ1011͒Ϫ1 2.35ϫ10Ϫ7 0.465 1.38 2.99ϫ10Ϫ12 74 2.62 0.0130 ͑1.62ϫ1011͒Ϫ1 8.64ϫ10Ϫ7 0.523 1.38 7.29ϫ10Ϫ12 11 Ϫ1 Ϫ6 Ϫ12 85 5.62 0.00548 ͑4.44ϫ10 ͒ 2.11ϫ10 0.236 1.60 5.25ϫ10 JABBOUR J. Z. 85 5.62 0.00607 ͑4.27ϫ1011͒Ϫ1 2.46ϫ10Ϫ6 0.254 1.59 6.56ϫ10Ϫ12 91.5 8.63 0.00440 ͑8.23ϫ1011͒Ϫ1 6.22ϫ10Ϫ6 0.137 1.68 1.09ϫ10Ϫ11 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 2.89ϫ10Ϫ6 0.132 1.70 7.62ϫ10Ϫ12 6D 64 1.25 0.0249 ͑3.88ϫ1010͒Ϫ1 6D 6P 2.62ϫ10Ϫ6 9.86ϫ106 1.00 7.92ϫ10Ϫ8 1.01 1.43ϫ10Ϫ10 3/2 3/2→ 1/2 74 2.62 0.0109 ͑1.01ϫ1011͒Ϫ1 8.07ϫ10Ϫ6 0.996 1.02 7.34ϫ10Ϫ11 tal. et 74 2.62 0.0130 ͑1.62ϫ1011͒Ϫ1 1.42ϫ10Ϫ5 0.994 1.03 9.53ϫ10Ϫ11 85 5.62 0.00548 ͑4.44ϫ1011͒Ϫ1 8.52ϫ10Ϫ5 0.962 1.07 8.78ϫ10Ϫ11 85 5.62 0.00607 ͑4.27ϫ1011͒Ϫ1 3.97ϫ10Ϫ5 0.988 1.06 4.61ϫ10Ϫ11 91.5 8.63 0.00440 ͑8.23ϫ1011͒Ϫ1 2.08ϫ10Ϫ4 0.904 1.19 8.89ϫ10Ϫ11 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 1.43ϫ10Ϫ4 0.957 1.07 9.38ϫ10Ϫ11 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 6D 6P 2.95ϫ10Ϫ5 2.67ϫ106 0.767 7.92ϫ10Ϫ8 1.07 9.37ϫ10Ϫ11 3/2→ 3/2 6D 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 6D 6P 2.05ϫ10Ϫ4 1.49ϫ107 0.244 6.68ϫ10Ϫ8 2.44 1.89ϫ10Ϫ10 5/2 5/2→ 3/2 4F 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 4F 5D 1.80ϫ10Ϫ5 2.26ϫ107 1.00 3.88ϫ10Ϫ8 1.00 1.23ϫ10Ϫ11 5/2 5/2→ 3/2 4F 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 4F 5D 3.15ϫ10Ϫ5 2.03ϫ107 1.00 4.61ϫ10Ϫ8 1.00 2.04ϫ10Ϫ11 7/2 7/2→ 5/2 8S 74 2.62 0.0130 ͑1.62ϫ1011͒Ϫ1 8S 6P 7.79ϫ10Ϫ7 1.97ϫ106 1.00 1.05ϫ10Ϫ7 1.01 1.74ϫ10Ϫ11 1/2 1/2→ 1/2 85 5.62 0.00607 ͑4.27ϫ1011͒Ϫ1 3.10ϫ10Ϫ6 1.00 1.03 1.21ϫ10Ϫ11 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 1.12ϫ10Ϫ5 0.998 1.02 2.42ϫ10Ϫ11 85 5.62 0.00607 ͑4.27ϫ1011͒Ϫ1 8S 6P 3.39ϫ10Ϫ6 3.62ϫ106 0.977 1.05ϫ10Ϫ7 1.03 7.67ϫ10Ϫ12 1/2→ 3/2 92 8.92 0.00424 ͑5.42ϫ1011͒Ϫ1 2.08ϫ10Ϫ5 0.980 1.02 2.60ϫ10Ϫ11 54 TABLE I. ͑Continued.͒ 54

Cs(6P1/2)ϩCs(6P1/2) Cs(nlJЈ)ϩCs(6S1/2) → eff ͐R n ͑x͒dx Monitored I /␧ ␶ ϪR 6P1/2 nl nЈlЈ nl nЈlЈ nat nat nlJ Temp n Transition JЈ→ JЉ JЈ→ JЉ ⌫ ␶ Ј k 6S1/2 R 2 nlJЈ nЈlЈJЉ nlJЈ nat nlJЈ 12 Ϫ3 T ͐ ͓n ͑x͔͒ dx I /␧ →Ϫ1 T ␶ 3 Ϫ1 nl ͑°C͒ ͑10 cm ͒ 6P1/2 6S1/2 ϪR 6P1/2 nl nЈlЈ 6P1/2 6S1/2 6P1/2 6S1/2 ͑s ͒ nlJЈ nЈlЈJЉ ͑s͒ nlJЈ ͑cm s ͒ JЈ → JЈ→ JЉ → → → 7P 64 1.25 0.0897 a͑3.25ϫ109͒Ϫ1 7P 6S 6.09 ϫ 10Ϫ8 1.58ϫ106 0.934 1.55 ϫ 10Ϫ7 1.02 2.14 ϫ 10Ϫ10 1/2 1/2→ 1/2 74 2.62 0.0365 a͑1.99ϫ1010͒Ϫ1 4.98 ϫ 10Ϫ7 0.862 1.04 1.23 ϫ 10Ϫ10 0.0365 b͑2.03ϫ1010͒Ϫ1 4.98 ϫ 10Ϫ7 0.862 1.04 1.21 ϫ 10Ϫ10 85 5.62 0.0151 ͑9.28ϫ1010͒Ϫ1 2.22 ϫ 10Ϫ6 0.732 1.08 5.52 ϫ 10Ϫ11 85 5.62 0.0172 ͑1.90ϫ1011͒Ϫ1 1.31 ϫ 10Ϫ5 0.759 1.08 1.74 ϫ 10Ϫ10 91.5 8.63 0.0101 ͑3.03ϫ1011͒Ϫ1 1.63 ϫ 10Ϫ5 0.625 1.12 9.40 ϫ 10Ϫ11 11 Ϫ1 Ϫ6 Ϫ11 92 8.92 0.00917 ͑1.46ϫ10 ͒ 8.62 ϫ 10 0.623 1.12 9.41 ϫ 10 . . . CESIUM: IN COLLISIONS ENERGY-POOLING 7P 64 1.25 0.0897 a͑3.25ϫ109͒Ϫ1 7P 6S 2.54 ϫ 10Ϫ8 4.18ϫ106 0.689 1.10 ϫ 10Ϫ7 1.22 5.35 ϫ 10Ϫ11 3/2 3/2→ 1/2 74 2.62 0.0365 a͑1.99ϫ1010͒Ϫ1 2.18 ϫ 10Ϫ7 0.465 1.38 3.99 ϫ 10Ϫ11 0.0365 b͑2.03ϫ1010͒Ϫ1 2.18 ϫ 10Ϫ7 0.465 1.38 3.90 ϫ 10Ϫ11 85 5.62 0.0151 ͑9.28ϫ1010͒Ϫ1 7.95 ϫ 10Ϫ7 0.231 1.58 2.26 ϫ 10Ϫ11 85 5.62 0.0172 ͑1.90ϫ1011͒Ϫ1 4.70 ϫ 10Ϫ6 0.271 1.59 6.32 ϫ 10Ϫ11 91.5 8.63 0.0101 ͑3.03ϫ1011͒Ϫ1 4.92 ϫ 10Ϫ6 0.138 1.68 4.51 ϫ 10Ϫ11 92 8.92 0.00917 ͑1.46ϫ1011͒Ϫ1 2.49 ϫ 10Ϫ6 0.131 1.69 4.52 ϫ 10Ϫ11 6D 74 2.62 0.0365 a͑1.99ϫ1010͒Ϫ1 6D 6P 4.12 ϫ 10Ϫ6 9.86ϫ106 0.928 7.92 ϫ 10Ϫ8 1.07 5.54 ϫ 10Ϫ10 3/2 3/2→ 1/2 0.0365 b͑2.03ϫ1010͒Ϫ1 4.12 ϫ 10Ϫ6 0.926 1.07 5.42 ϫ 10Ϫ10 85 5.62 0.0151 ͑9.28ϫ1010͒Ϫ1 2.39 ϫ 10Ϫ5 0.746 1.22 3.09 ϫ 10Ϫ10 85 5.62 0.0172 ͑1.90ϫ1011͒Ϫ1 5.62 ϫ 10Ϫ5 0.574 1.47 4.36 ϫ 10Ϫ10 91.5 8.63 0.0101 ͑3.03ϫ1011͒Ϫ1 1.31 ϫ 10Ϫ4 0.424 1.82 4.09 ϫ 10Ϫ10 92 8.92 0.00917 ͑1.46ϫ1011͒Ϫ1 9.66 ϫ 10Ϫ5 0.700 1.26 4.99 ϫ 10Ϫ10 92 8.92 0.00917 ͑1.46ϫ1011͒Ϫ1 6D 6P 3.22 ϫ 10Ϫ5 2.67ϫ106 0.999 7.92 ϫ 10Ϫ8 1.26 4.52 ϫ 10Ϫ10 3/2→ 3/2 6D 92 8.92 0.00917 ͑1.46ϫ1011͒Ϫ1 6D 6P 7.20 ϫ 10Ϫ5 1.49ϫ107 0.993 6.68 ϫ 10Ϫ8 1.01 2.70 ϫ 10Ϫ10 5/2 5/2→ 3/2 4F 92 8.92 0.00917 ͑1.46ϫ1011͒Ϫ1 4F 5D Ͻ6 ϫ 10Ϫ6 2.26ϫ107 1.00 3.88 ϫ 10Ϫ8 1.00 Ͻ2.8 ϫ 10Ϫ11 5/2 5/2→ 3/2 4F 92 8.92 0.00917 ͑1.46ϫ1011͒Ϫ1 4F 5D Ͻ6 ϫ 10Ϫ6 2.03ϫ107 1.00 4.61 ϫ 10Ϫ8 1.00 Ͻ2.7 ϫ 10Ϫ11 7/2 7/2→ 5/2 8S 85 5.62 0.0172 ͑1.90ϫ1011͒Ϫ1 8S 6P Ͻ5.58 ϫ 10Ϫ8 1.97ϫ106 0.974 1.05 ϫ 10Ϫ7 1.00 Ͻ1.2 ϫ 10Ϫ12 1/2 1/2→ 1/2 91.5 8.63 0.0101 ͑3.03ϫ1011͒Ϫ1 1.07 ϫ 10Ϫ7 0.957 1.01 8.74 ϫ 10Ϫ13 91.5 8.63 0.0101 ͑3.03ϫ1011͒Ϫ1 8S 6P 3.13 ϫ 10Ϫ7 3.62ϫ106 1.00 1.05 ϫ 10Ϫ7 1.01 1.39 ϫ 10Ϫ12 1/2→ 3/2 an obtained from the measured value of n when pumping the D line at the same temperature, scaled by the fluorescence ratio; i.e., 6P1/2 6P3/2 2 nat ͑n6P ͒Pump D1 ͑I6P 6S /␧6P 6S ͒Pump D1 ͑T6P 6S ͒Pump D2 ⌫6P 6S ␭6P 6S 1/2 1/2→ 1/2 1/2→ 1/2 3/2→ 1/2 3/2→ 1/2 1/2→ 1/2 ϭ nat . ͑n6P ͒Pump D2 ͑I6P 6S /␧6P 6S ͒Pump D2 ͑T6P 6S ͒Pump D1 ⌫6P 6S ␭6P 6S 3/2 3/2→ 1/2 3/2→ 1/2 1/2→ 1/2 1/2→ 1/2 3/2→ 1/2 bn measured at the center of the cell. The spatial profile of n (x) was taken to be the same as the excited-atom spatial profile measured when pumping the D line at the same temperature. 6P1/2 6P1/2 2 1379 1380 Z. J. JABBOUR et al. 54 measured at the position of the center of the cell using a used to attenuate the strong D1 and D2 line signals so that two-dimensional charge-coupled-device ͑CCD͒ array ͑Spec- they could be recorded using the same monochromator slits traSource Instruments LYNXX PC Plus͒. The beam diameter and PMT voltage. The wavelength-dependent relative detec- at the cell center was found to be ϳ1.3 mm under these tion system efficiency, including the effects of all filters, was conditions. measured using a calibrated tungsten-halogen lamp ͓40͔.A The pump laser could be tuned to particular hyperfine free-standing photomultiplier ͑PMT2-Hamamatsu R406 or transitions of either the D or D line of cesium. For D line 1 2 1 R636͒ was used with either a D1 or D2 line interference filter excitation, the full hyperfine structure of both upper and to monitor the resonance line radiation ͑see Fig. 2͒. This lower states is well resolved. However, for D2 excitation, the allowed constant monitoring to guard against frequency or upper-state hyperfine splittings are smaller than the Doppler power drift of the pump laser. widths. Thus we pump a combination of upper hyperfine levels; either 6S (Fϭ3) 6P (FЈϭ2,3,4) or 1/2 → 3/2 B. Measurement of the excited atom density 6S1/2(Fϭ4) 6P3/2(FЈϭ3,4,5). Optical pumping of the ground-state→ hyperfine levels reduces the number of atoms and spatial distribution that can be pumped to the excited state. However, this is not A single-mode cw dye laser ͑Coherent 699-29, using LD- a problem in the present work since the density and spatial 700 dye pumped bya6Wkrypton ion laser͒ was used to distribution of excited atoms is directly measured. probe the density and spatial distribution of the atoms ex- Transmission of the pump-laser beam through the cell cited to the 6PJ levels. The probe-laser power was reduced was monitored using photomultiplier PMT3 ͑Hamamatsu to typically 10–100 nW using neutral density filters, and the model R406͒͑see Fig. 2͒. At the lower densities studied in probe beam diameter was reduced to 0.75 mm or less at the this work, the attenuation of the laser beam along the length center of the cell usinga1mfocal length lens and an aper- of the cell could generally be neglected even when the laser ture. Both pump- and probe-laser beams were well colli- was tuned directly to resonance. However, at high density, mated over the length of the cesium cell. absorption at line center of a particular hyperfine transition The probe beam could be moved spatially across the cell caused severe attenuation of the laser beam before it reached diameter using the mirror mounted on the translation stage the observation region at the center of the cell. In either case, shown in Fig. 2. The probe laser frequency was scanned we set the laser frequency to maximize 6P 6S fluores- across the various hyperfine transitions of either the J→ 1/2 cence from the observation region. At higher densities this 6P3/2 7D3/2, the 6P3/2 7D5/2, or the 6P1/2 8S1/2 transi- meant that the laser frequency was slightly detuned from line tion and→ the absorption of→ the probe intensity→ was monitored center, so that again the attenuation could generally be ne- using photomultiplier PMT4 ͑Hamamatsu R928͒. In this glected. Thus the density of excited atoms could be consid- case, the probe beam was chopped, but the pump beam was ered to be independent of z ͓see Fig. 2͑b͔͒. This turns out to not ͑see Fig. 2͒. be a very good approximation at our low densities, and is The transmission of the probe-laser beam through a length still reasonable at the higher densities. L of the vapor is given by A pair of lenses and an image rotator were used to image ϪknЈlЈ 6P ͑␻͒L Ϫ␴nЈlЈ 6P ͑␻͒n6P L fluorescence onto the slits of a 0.22 m monochromator ͑Spex I␻͑L͒ϭI␻͑0͒e JЉ← J ϭI␻͑0͒e JЉ← J J model 1681͒ with 1200 groove/mm grating blazed at 500 ͑18͒ nm. With 300 ␮m slits ͑providing a spectral resolution of ϳ1 nm͒ and 1:2 imaging, the volume from which fluorescence for light of frequency ␻. Here I␻(0) is the incident intensity, was collected was a strip of width ⌬yϳ150 ␮m and length ␴n l 6P is the absorption cross section at frequency ␻, Ј ЈJЉ← J 0.5 cm oriented along the laser propagation (z) axis. A GaAs and n is the density of atoms in the lower state of the 6PJ ͑Hamamatsu model R636͒ photomultiplier tube ͑PMT1͒ was probe transition ͑which is assumed to be independent of z͒. used to detect the resolved 6P1/2 6S1/2,6P3/2 6S1/2, Equation ͑18͒ can be solved for n as → → 6PJ 7P1/2 6S1/2,7P3/2 6S1/2, and 6D3/2 6P1/2 fluorescence on each→ data run. An→ S-1 PMT ͑Hamamatsu→ model R-406͒ 1 I␻͑0͒ replaced the GaAs tube for one data run at 92 °C to record n ϭ ln . ͑19͒ 6PJ ␴ L ͩ I ͑L͒ͪ n l 6P ␻ near-infrared 4F7/2 5D5/2,4F5/2 5D3/2,6D5/2 6P3/2, Ј ЈJЉ← J and 6D 6P →fluorescence,→ in order to obtain→ 4F 3/2→ 3/2,1/2 JЈ and 6D5/2 energy-pooling rates relative to the more system- We carried out calculations of the maximum absorption atically studied 7PJЈ and 6D3/2 rates. 8S1/2 6PJ fluores- cross sections of each of the three probe transitions used in cence was also recorded using either PMT→ on a few runs. the experiment, based on oscillator strengths given by The pump laser was chopped, and the PMT signals were Warner ͓38͔, and hyperfine level branching ratios calculated processed by a lock-in amplifier and displayed on a chart from the formulas of Condon and Shortley ͓41͔. Hyperfine recorder. level splittings were taken from Ref. ͓42͔ and each compo- A long-pass filter ͑either Schott RG-610 or RG-695͒ was nent was modeled as a Voigt line with Lorentzian width placed in front of the monochromator entrance slits for all determined by resonance broadening in the lower level, and but the 7P 6S fluorescence to eliminate 2nd order scatter- Gaussian width determined by Doppler broadening at the ing from the→ grating. A short-pass filter ͑Reynard 942 or 944, particular cell temperature. The absorption cross section was with cut-on wavelength of 675 or 700 nm, respectively͒ was calculated as a function of frequency, and the maximum of used to block scattered D1 and D2 line fluorescence ͑which this function was used with the measured maximum probe- could otherwise leak through the monochromator͒ when re- laser beam attenuation in Eq. ͑19͒ to obtain an absolute de- cording the 7P fluorescence. Neutral density filters were termination of the excited-atom density. The spatial distribu- 54 ENERGY-POOLING COLLISIONS IN CESIUM: . . . 1381 tion of excited atoms was mapped from the measured probe- may be uncertain by as much as 30–40%, due primarily to beam absorption versus position as the probe beam was the assumption that the ground-state hyperfine level popula- translated across the cell diameter parallel to the pump beam. tions are in a statistical ratio. Considering these various sources of statistical uncertainty, we estimate overall errors IV. RESULTS AND DISCUSSION of ϳ50% in our measured energy-pooling rate coefficients. In addition, various other systematic effects and uncer- Position dependent 6P state densities, n (x), were re- J 6PJ tainties should also be considered before we arrive at final corded as described in Sec. III. These values, and their energy-pooling rate coefficients. First, the cesium ground- squares were numerically integrated over the observation state atom density was obtained from the Nesmeyanov vapor zone ͑cell diameter͒ to yield the factors pressure formula ͓39͔ and the measured temperature. We es- ͐R n (x)dx/͐R ͓n (x)͔2dx in Eq. ͑7͒. The 6P densi- ϪR 6PJ ϪR 6PJ J timate the uncertainty in the ground-state density at 5–10% ties were also used in Eqs. ͑8͒–͑11͒, with the hyperfine level in our temperature range, but this uncertainty only affects the splittings of Ref. ͓42͔ and the resonance broadening rates of energy-pooling results through its influence on the transmis- Ref. ͓43͔, to calculate the transmission factors T6P 6S . J→ 1/2 sion factors and 7PJЈ effective lifetimes, where it is roughly Measured values of ͓n (r)͔2 were used to calculate the 6PJ a linear effect in the Doppler broadened limit ͓29,30͔. Sec- radiation diffusion mode amplitudes a j ͓Eq. ͑13͔͒ for the ond, all oscillator strengths used in this work were taken from the theoretical paper of Warner 38 , since a complete 7PJЈ 6S1/2 transitions. These amplitudes, in turn, were ͓ ͔ combined→ with the oscillator strengths of Warner ͓38͔ to find and self-consistent set is available in this one reference. eff However, considerable discrepancy exists between various the effective radiative rates ⌫7P 6S using Eqs. ͑14͒–͑16͒. J→ 1/2 Effective radiative rates for the fundamental radiation diffu- sets of theoretical oscillator strengths for cesium ͓38,44–47͔, and any systematic errors in the chosen values will directly sion mode were determined using the measured 6PJ atom density and spatial distribution for relevant transitions, as introduce systematic errors in our final results. Based on the various available oscillator strengths, we estimate uncertain- described in Sec. II B. Finally, the effective and natural ra- nat nat diative rates were summed to obtain the effective lifetimes ties in ⌫nl n l ␶ nl ranging from 2% to 23% for the JЈ→ Ј ЈJЉ JЈ ␶eff as in Eq. ͑12͒. All of this information was then com- 6D 6P and 8S 6P transitions. However, for nlJ Ј 7P → 6S the uncertainty→ can be more than a factor of 2. bined with the measured fluorescence ratios ͑corrected for JЈ→ 1/2 detection system efficiency͒ in Eq. ͑7͒ to yield values for the Thus, the 4F5/2,7/2,8S1/2 and 6D3/2,5/2 energy-pooling rates various energy-pooling rate coefficients. The rate coefficient are not seriously affected by uncertainty in the oscillator values obtained for different transitions and at different tem- strengths, but the 7PJЈ rates can be strongly affected. peratures are given in Table I. As can be seen from the rate equation for the state nlJЈ ͓Eq. ͑2͔͒, we have neglected cascade from higher-lying lev- Despite the care that was taken in accounting for the 6PJ spatial distribution and radiation trapping on all transitions of els which are also populated by the energy-pooling process. interest, it is clear from Table I that significant discrepancies Inclusion of this process would involve the addition of a term ͚ ⌫eff n to the right-hand side of Eq. exist between values of k7P , or values of k6D , taken at nЉlЉJ n l nl nЉlЉJ JЈ 3/2 Љ Љ ЉJЉ→ JЈ Љ different temperatures or with different pump geometries. ͑2͒. From the radiative rates of Warner ͑modified by trapping This is, in part, due to the fact that the uncertainties in indi- calculations where needed͒ and the measured energy-pooling vidual measurements are fairly large. Fluorescence ratios rate coefficients ͑Table I͒ we find that cascade processes do probably have an uncertainty of as much as 25% due to the not affect our D1 pumping results by more than 10% in the use of neutral density filters to attenuate the D1 and D2 line worst case. For D2 pumping, we find that both 6D and 8S fluorescence. We estimate the uncertainties in the ratio cascade could be responsible for major contributions to the R R 2 ͐ n (x)dx/͐ ͓n (x)͔ dx to be approximately 15%. 7P signals. However the error bars on k8S are quite large and ϪR 6PJ ϪR 6PJ eff the rate coefficient may be strongly temperature dependent Uncertainties in Tnl n l and ␶ largely offset each JЈ Ј ЈJЉ nlJЈ → eff nat since energy pooling to 8S is highly endothermic ͑8S fluo- other when the product Tnl n l (␶nl /␶nl ) is taken. This JЈ→ Ј ЈJЉ JЈ JЈ rescence signals were small and very noisy at temperatures is because an over estimation of the amount of radiation below 85 °C͒. Moreover, if the 7P signals in the D2 pump- trapping results in a transmission factor which is too low, but ing case are due primarily to 8S 7P cascade, we would → an effective lifetime which is too high. Values of expect to see 7P3/2 6S1/2 fluorescence signals that are T (␶eff /␶nat ) are probably good to within 25%, twice as large as the→ 7P 6S signals, and experimen- 7P3/2 6S1/2 7P3/2 7P3/2 1/2 1/2 → eff nat tally this is not the case. Thus→ we can neither confirm nor while the values of T7P 6S (␶7P /␶7P ) are accurate to 1/2→ 1/2 1/2 1/2 rule out a significant cascade contribution to the 7P signals at least 10% because the trapping is much less severe on this in the D pumping case. transition. Similarly, even though the 6P densities are non- 2 J We must also consider collisional mixing among fine- uniform, which considerably complicates the calculation of structure levels ͑i.e., 7P ϩM 7P ϩM͒ and collisional trapping corrections for transitions which terminate on these 3/2 ⇔ 1/2 eff nat excitation transfer processes such as 6DϩM 7PϩM, levels, the values of Tnl n l (␶nl /␶ nl ) for the 4F,8S, ⇔ JЈ→ Ј ЈJЉ JЈ JЈ where M is a ground-state cesium or impurity atom. Such and 6D states are accurate to within 15% ͑except in one or processes can also distort the apparent energy-pooling rate two cases͒ since both corrections are small and tend to can- coefficients. We can estimate the concentration of impurities cel. Finally, the largest source of statistical uncertainty in the in our sealed cell by analysis of the ratio of sensitized fluo- rate coefficients listed in Table I is that due to T6P 6S . rescence ͑i.e., fluorescence from the level 6P that is not J→ 1/2 JЈ These transmission factors are as small as 0.004 and they pumped by the laser͒ to direct fluorescence at room tempera- 1382 Z. J. JABBOUR et al. 54 ture. The measured ratio is much too large to be explained by when pumping the D2 transition. cesium-cesium collisions according to the experimental cross Considering only the statistical sources of uncertainties, sections of Czajkowski and Krause ͓48͔, and thus must be we have determined a set of best values of the measured rate attributed to collisions with impurities. Czajkowski, McGil- coefficients which is presented in Table II. However, it lis, and Krause ͓49͔ have investigated excitation transfer should be kept in mind that the overall accuracy of these results may be limited by the various systematic effects dis- among the cesium 6PJ levels due to collisions with inert gas atoms, but their measured cross sections, which range from cussed above. 2ϫ10Ϫ21 to 3ϫ10Ϫ19 cm2, are also much too small to ac- count for the amount of transfer we observe in our sealed V. CONCLUSIONS cell. However, the impurities in our cell are more likely to be diatomic molecules which possess internal degrees of free- The energy-pooling rate coefficients reported here can be expressed as velocity-averaged cross sections using the rela- dom, and excitation transfer in collisions of cesium 6PJ at- oms with such molecules is likely to involve relatively large tion rate coefficients. If we assume an excitation transfer rate co- Ϫ10 3 Ϫ1 k ϭ͗␴ ͑v͒v͘Ϸ␴ ¯v. ͑20͒ efficient of 10 cm s , then an impurity gas pressure of nlJЈ nlJЈ nlJЈ ϳ3.7ϫ10Ϫ3 Torr ͑ϳ1ϫ1014 cmϪ3 impurity density͒ is re- Here ␴ (v) and ␴ are the velocity-dependent and quired to produce the observed population transfer. Based nlJЈ nlJЈ upon this impurity density, and assuming relatively large rate velocity-averaged cross sections, respectively, v is the colli- coefficients for various excitation transfer processes ͑see, sion velocity, and ¯v is the mean collision velocity given by e.g., Refs. ͓50–54͔͒, we can show that 8S 4F transfer by ↔ 1/2 impurities contributes less than 10% uncertainty to our 8RT M1ϩM2 ¯vϭ ϭ1.78ϫ103T1/2 cm/s. ͑21͒ energy-pooling rates in the worst case, and that 6D 7P ͩ ␲ M M ͪ 1 2 collisional excitation transfer produces an effect on→ the energy-pooling results which is comparable to that of In this last expression, Rϭ8.31 J/͑K mole͒ is the gas con- 6D 7P radiative cascade. Excitation transfer within the stant, T is the absolute temperature, and M and M are the → 1 2 7PJЈ and 6DJЈ manifolds, due to collisions with impurities molar masses of the two colliding atoms. The last equality in or ground-state cesium atoms, can cause a skewing of the Eq. ͑21͒ is appropriate for collisions between two cesium ratio of the energy-pooling rates to the various fine-structure atoms ͑M 1ϭM 2ϭ0.1329 kg/mole͒. levels. This is probably the cause of the decrease of Values of ␴nl for the energy-pooling processes studied in k /k with increasing temperature for both D and D 7P1/2 7P3/2 1 2 this work ͑obtained by averaging all data collected over the line pumping. range 337–365 K͒ are presented in Table II along with the Finally, we note that in this experiment we only measure few values that have been obtained by other authors. Our the population of atoms in the directly excited 6PJ fine- cross sections for energy pooling to the 6D levels are con- structure level. However, due to excitation transfer from one sistent with the experimental estimates of Klyucharev and fine-structure level to the other ͑induced by collisions with Lazarenko ͓1͔ and Yabuzaki et al. ͓18͔ as well as with the ground-state atoms and impurities͒ there is always some theoretical estimate of Borodin and Komarov ͓17͔. Our val- population in the other 6PJ level as well. The density in the ues of the rate coefficients for the process collisionally populated level is too small to be measured us- Cs͑6P3/2͒ϩCs͑6P3/2͒ Cs͑7P1/2,3/2͒ϩCs͑6S1/2͒ obtained at ing our absorption technique, but it can be inferred from the low density are in agreement→ within the rather large error D1/D2 line fluorescence ratio. At the highest temperature bars with the values we have obtained under very different used in this experiment, we find that the density ratio of experimental conditions ͓19,20͔. atoms in the collisionally populated level to those in the level The results of Table II show that 6P1/2ϩ6P1/2 collisions directly populated by the laser is less than 0.04. From the are more effective than 6P3/2ϩ6P3/2 collisions at populating rate coefficients given in Table I and the relative populations, the 7PJЈ levels. This is expected from consideration of the it is clear that 6P1/2-6P1/2 collisions cannot significantly in- energy deficits. Similarly, 8S and 4F are populated much fluence the results obtained for the 6P3/2-6P3/2 rates and vice more effectively by 3/2-3/2 than by 1/2-1/2 collisions. In versa. However, 6P1/2-6P3/2 collisions might have a system- addition, when pumping with D1 light, 7P1/2 is two to three atic effect on these results, since the rate coefficients for the times more likely to be populated than 7P3/2. For D2 pump- latter process could be significantly greater than those for ing, 7P1/2 and 7P3/2 are approximately equally populated. 6P3/2-6P3/2, where the energy defect for nlϭ7P or 6D in For the 6DJЈ levels we find that 6D3/2 is more strongly Eq. ͑1͒ is considerably smaller for 1/2-3/2 collisions than for populated than 6D5/2 by 1/2-1/2 collisions while 6D5/2 is 3/2-3/2 collisions. For the 6D product state, the 1/2-3/2 en- more strongly populated than 6D3/2 by 3/2-3/2 collisions. ergy deficit is comparable to the 1/2-1/2 deficit, but it is However, in the latter case, the error bars are large and not positive for 1/2-3/2 collisions and negative for 1/2-1/2 colli- much data exists. Thus these conclusions must be taken with sions. Similarly, 1/2-3/2 collisions may significantly affect a grain of salt. In previous studies of energy pooling in Sr the measured 1/2-1/2 rate coefficient for populating 8S.At ͓10,55͔ and Ba ͓15͔ it was found that the energy deficit does present, we have no way to estimate the magnitude of this not play a strong role in determining the rate coefficients. In effect ͑which we plan to investigate through a two-laser ex- Sr, the rates fall off somewhat with ⌬E for endothermic citation experiment͒. It is possible that this effect is respon- processes, since only a fraction of collision pairs have a rela- sible for the slight increase in the apparent energy-pooling tive kinetic energy greater than ⌬E. In the case of Ba, the rate coefficients k and k with increasing temperature energy-pooling rates are largely independent of energy defi- 7P1/2 7P3/2 54 ENERGY-POOLING COLLISIONS IN CESIUM: . . . 1383

TABLE II. Best values for the cesium energy-pooling rate coefficients and cross sections obtained in this work, along with those obtained by other workers.

Cs(6P )ϩCs(6P ) Cs(nl )ϩCs(6S ) 3/2 3/2 → JЈ 1/2 Rate coefficient ͑cm3 sϪ1͒ Cross section ͑cm2͒ nlJ This work ͑a͒ Other values This work ͑a͒ Other values Ј Ϫ12 Ϫ12 ͑b͒ Ϫ16 Ϫ16 ͑b͒ 7P1/2 ͑5.9Ϯ2.7͒ϫ10 ͑3.1Ϯ1.6͒ϫ10 ͑1.8Ϯ0.8͒ϫ10 ͑0.9Ϯ0.5͒ϫ10 Ϫ12 Ϫ12 ͑b͒ Ϫ16 Ϫ16 ͑b͒ 7P3/2 ͑6.1Ϯ3.1͒ϫ10 ͑3.8Ϯ1.9͒ϫ10 ͑1.8Ϯ0.9͒ϫ10 ͑1.1Ϯ0.5͒ϫ10 Ϫ11 Ϫ9 ͑c͒ Ϫ15 Ϫ13 ͑c͒ 6D3/2 ͑9.0Ϯ2.9͒ϫ10 Ͻ4ϫ10 ͑2.7Ϯ0.9͒ϫ10 Ͻ10 Ͼ6ϫ10Ϫ11 ͑d͒ Ͼ1.5ϫ10Ϫ15 ͑d͒ ϩ6.2 Ϫ10 ͑e͒ ϩ1.5 Ϫ14 ͑e͒ ͑6.2Ϫ2.9͒ϫ10 ͑1.5Ϫ0.7͒ϫ10 Ϫ10 Ϫ9 ͑c͒ Ϫ15 Ϫ13 ͑c͒ 6D5/2 ͑1.9Ϯ1.0͒ϫ10 Ͻ4ϫ10 ͑5.6Ϯ2.8͒ϫ10 Ͻ10 Ͼ6ϫ10Ϫ11 ͑d͒ Ͼ1.5ϫ10Ϫ15 ͑d͒ Ϫ11 Ϫ16 4F5/2 ͑1.2Ϯ0.6͒ϫ10 ͑3.6Ϯ1.8͒ϫ10 Ϫ11 Ϫ16 4F7/2 ͑2.0Ϯ1.0͒ϫ10 ͑6.0Ϯ3.0͒ϫ10 Ϫ11 Ϫ16 8S1/2 ͑1.7Ϯ0.8͒ϫ10 ͑5.2Ϯ2.2͒ϫ10

Cs(6P )ϩCs(6P ) Cs(nl )ϩCs(6S ) 1/2 1/2 → JЈ 1/2 Rate coefficient ͑cm3 sϪ1͒ Cross section ͑cm2͒ nlJ This work ͑a͒ Other values This work ͑a͒ Other values Ј Ϫ10 Ϫ15 7P1/2 ͑1.3Ϯ0.6͒ϫ10 ͑3.8Ϯ1.8͒ϫ10 Ϫ11 Ϫ15 7P3/2 ͑4.5Ϯ1.4͒ϫ10 ͑1.3Ϯ0.4͒ϫ10 Ϫ10 Ϫ9 ͑c͒ Ϫ14 Ϫ13 ͑c͒ 6D3/2 ͑4.4Ϯ0.9͒ϫ10 Ͻ4ϫ10 ͑1.3Ϯ0.3͒ϫ10 Ͻ10 Ͼ6ϫ10Ϫ11 ͑d͒ Ͼ1.5ϫ10Ϫ15 ͑d͒ ϩ6.2 Ϫ10 ͑e͒ ϩ1.5 Ϫ14 ͑e͒ ͑6.2Ϫ2.9͒ϫ10 ͑1.5Ϫ0.7͒ϫ10 Ϫ10 Ϫ9 ͑c͒ Ϫ15 Ϫ13 ͑c͒ 6D5/2 ͑2.7Ϯ1.4͒ϫ10 Ͻ4ϫ10 ͑8.0Ϯ4.0͒ϫ10 Ͻ10 Ͼ6ϫ10Ϫ11 ͑d͒ Ͼ1.5ϫ10Ϫ15 ͑d͒ Ϫ11 Ϫ16 4F5/2 Ͻ3ϫ10 Ͻ8ϫ10 Ϫ11 Ϫ16 4F7/2 Ͻ3ϫ10 Ͻ8ϫ10 Ϫ12 Ϫ17 8S1/2 ͑1.1Ϯ0.6͒ϫ10 ͑3.3Ϯ1.7͒ϫ10 aTϭ337Ϫ365 K. Note that error bars given in the table reflect statistical uncertainties only. We believe that these values are probably accurate to within ϳ50% when estimates of possible systematic uncertainties are included. See text. bExperimental values from Ref. ͓19͔. Tϭ370 K. cUpper limit from experimental work of Ref. ͓1͔. Tϭ528 K. dLower limit from theoretical work of Ref. ͓17͔. Tϭ500 K. eExperimental estimate of rate coefficient for the inverse process Cs͑6D ͒ϩCs͑6S ͒ Cs(6P)ϩCs(6P). Tϭ530 K. From 3/2 1/2 → Ref. ͓18͔. cit, even for endothermic processes. This surprising result D2 pumping seems to indicate that, in some cases, angular was attributed, in part, to the fact that levels with the largest momentum may play a role in the energy-pooling process, energy deficit also have the largest statistical weights ͓15͔.In such that processes which require the conversion of angular addition, these studies found no strong angular-momentum momentum associated with the orbital motion of the two propensity rules. High-lying singlet and triplet states were colliding atoms, into internal electronic angular momentum, populated with approximately equal rates, and although lev- occur with lower rates. els with higher L values are more strongly populated than In the near future, we plan to extend the present set of those with lower L values, this may also be due to the higher measurements by adding another laser to the experimental statistical weights of the former ͓15͔. These effects were as- setup. With this modification, we will be able to simulta- cribed to the breakdown of LS coupling in the heavy Sr and neously populate the 6P1/2 and 6P3/2 levels, and thus we will Ba atoms. Because of this breakdown, propensity rules con- be able to study the 6P1/2ϩ6P3/2 collisions which may have cerning total electronic angular momentum J might be more the largest energy-pooling cross sections. 1 relevant. The Sr and Ba results indicate that F3 states are 1 1 3 3 strongly populated by P1ϩ P1 and P1ϩ P1 collisions. ACKNOWLEDGMENTS Our present results for cesium indicate a contrary trend. Here we also find a breakdown of LS coupling in cesium, which Financial support for this work was provided by the Na- lies next to barium in the periodic table. However, in cesium tional Science Foundation under Grant PHY-9119498. The all relevant levels are spin doublets, and thus spin changing authors from Pisa also acknowledge support from the EEC collisions are not observable in the present experiment. Nev- Network Grant ERBCHRXCT 930344. One of the authors ertheless, the fairly dramatic difference between the ratio of ͑S.M.͒ is grateful to ICTP, Trieste, for financial support dur- 7P1/2 and 7P3/2 energy-pooling rate coefficients for D1 vs ing his stay in Pisa. 1384 Z. J. JABBOUR et al. 54

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