PHYSICAL REVIEW A VOLUME 54, NUMBER 2 AUGUST 1996 Energy-pooling collisions in cesium: 6PJ16PJ˜6S1„nl57P,6D,8S,4F… Z. J. Jabbour,* R. K. Namiotka, and J. Huennekens Department of Physics, 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 1995! We report experimental rate coefficients for the energy-pooling collisions Cs(6P1/2) 1Cs(6P ) Cs(6S )1Cs(nl ) and Cs(6P )1Cs(6P ) Cs(6S )1Cs(nl ) where nl 57P , 1/2 → 1/2 J8 3/2 3/2 → 1/2 J8 J8 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 laser. 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 photons 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. @S1050-2947~96!00508-2# PACS number~s!: 34.50.Rk, 34.90.1q 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 @1# 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 cm23 are within range @16#.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 6P1/216P1/2,6P1/216P3/2, and atom collisions in which the two atoms pool their internal 6P3/216P3/2 are more or less resonant with various highly energy to produce one ground-state atom and one in a more excited states ~see Fig. 1!. The large fine-structure splittings highly excited state nlJ8 ~in this case nlJ856D3/2,5/2! also allow study of the role of angular momentum in the energy-pooling process. To the best of our knowledge, there Cs~6P !1Cs~6P ! Cs~nl !1Cs~6S !. ~1! have been only a few quantitative studies to date on energy J J ) J8 1/2 pooling in cesium. In their original paper, Klyucharev and Collisions of this type have since come to be called ‘‘energy- Lazarenko @1# estimated from experiment that the cross sec- pooling collisions’’ and they have been the subject of much tion for process ~1! was less than 10213 cm2 for nl56D at a study in alkali-metal homonuclear @2–5# and heteronuclear temperature of 528 K. Later, Borodin and Komarov @17# @6,7# systems, as well as in other metal vapors @8–15# over determined theoretically that the cross section exceeds the last 20 years. 1.5310215 cm2 for this process at T5500 K. Yabuzaki et al. While the majority of previous alkali-metal work has con- @18# carried out an experimental study of the inverse process, centrated on sodium, @2–4# there has been little work on Cs~6D!1Cs~6S! Cs~6P!1Cs~6P) and found a cross sec- 11.5 → 214 2 cesium following the initial paper by Klyucharev and Laza- tion of ~1.520.7!310 cm at 530 K. Preliminary experi- mental results on the process Cs(6P3/2)1Cs(6P3/2) Cs(7P )1Cs(6S ) have recently been obtained @19# → J8 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 @20#. †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. ~1!#. 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 Lasers, 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- 1050-2947/96/54~2!/1372~13!/$10.0054 1372 © 1996 The American Physical Society 54 ENERGY-POOLING COLLISIONS IN CESIUM: . 1373 FIG. 1. ~a! Energy levels of cesium showing transitions studied in this work. Wavelengths are given in nm. ~b! Cesium atomic levels lying near twice the 6PJ level energies. 6PJ16PJ energies are represented by dashed lines. Energies are taken from Ref. @56#. 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 nlJ857P1/2 ,7P3/2, The energy-pooling process described by Eq. ~1! 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 nlJ8 which lie near twice rate equation model used to extract the energy-pooling rate the energy of the pumped resonance state @see Fig. 1~b!#. coefficients from the measured fluorescence ratios. It also Rate equations can be used to derive theoretical expressions discusses radiation trapping and related optical depth 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 @15#. The steady- of various sources of error. Finally, our conclusions are pre- state rate equation for the population in state nlJ8 following sented in Sec. V. pumping of 6PJ reads 1374 Z. J. JABBOUR et al. 54 k @n ~rY!#2 n ~rY! Factors such as the absolute detection efficiency and col- nlJ8 6PJ nlJ8 n˙ ~rY!505 2 , ~2! lection solid angle are experimentally difficult to determine. nlJ8 2 teff nlJ8 Therefore it is advantageous to measure fluorescence ratios. Specifically, we measure the ratio of fluorescence from the which has the solution state nlJ8 , populated through energy pooling, to fluorescence 1 2 eff observed on the directly pumped resonance transition; i.e., nnl ~rY!5 2 knl @n6P ~rY!# t , ~3! J8 J8 J nlJ8 on the 6P 6S transition J→ 1/2 eff nat Here, knl is the rate coefficient for process ~1!, and tnl is J8 J8 Inl n l l6P 6S «nl n l Gnl n l J8→ 8 8J9 J→ 1/2 J8→ 8 8J9 J8→ 8 8J9 the effective lifetime for atoms in state nlJ8 . Note that in the 5 nat I6P 6S lnl n8l8 «6P 6S G6P 6S absence of quenching collisions and radiation trapping, J→ 1/2 J8→ J9 J→ 1/2 J→ 1/2 (teff )21 is just the sum of the Einstein A coefficients for nlJ eff 2 3 8 Tnl n l knl tnl *@n6P ~rY!# d r transitions connecting state nl to all lower levels. However, J8→ 8 8J9 J8 J8 J J8 3 3 . at higher atom densities, radiation trapping will reduce the T6P 6S 2 *n6P ~rY!d r J→ 1/2 J effective radiative rate for transitions to the ground state. We ~5! will find that radiation trapping can also occur, under some circumstances, for transitions terminating on levels directly Finally, we can solve Eq. ~5! for the rate coefficient k populated by the laser. Note that the factor 2 introduced in nlJ8 Eq. 2 is due to the fact that the 6P atoms are identical. ~ ! J I /« 2 nlJ8 n8l8J9 nlJ8 n8l8J9 Therefore [n6P] /2 is proportional to the number of excited- k 5 → → nlJ atom pairs in the volume, as first pointed out in Ref. @21#. 8 S I6P 6S /«6P 6S D J 1/2 J 1/2 We are interested in the fluorescence corresponding to the → → Gnat transition nlJ n8l8J emitted by atoms in the particular lnl n8l8 6P 6S T6P 6S 2 8→ 9 J8→ J9 J→ 1/2 J→ 1/2 volume which is imaged onto the slits of our monochro- 3 nat eff l6P 6S G Tnl n l t J 1/2 nl n l J8 8 8J9 nlJ mator.