Z. Phys. D - Atoms, Moleculesand Clusters 22, 597-601 (1992)

Atoms, Molecules ze,,.o.r,, f~ir Physik D and Clusters © Springer-Verlag 1992

Excitation energy transfer in the L i - Cs collision: Li*(2P) + Cs(6S) Li(2S) + Cs*(5D) D. Veza 1, C. Vadla 1'2, and K. Niemax l 1 Institut fiir Spektrochemieund AngewandteSpektroskopie(tSAS), Bunsen-KirchhoffStrasse 11, W-4600 Dortmund t, Federal Republic of Germany 2 Institute of Physicsof the University,POB 304, Bijenicka46, YU-41001 Zagreb, Yugoslavia Received 1 July 1991; final version 9 September 1991

Abstract. The measurement of the collisional cross section for the process L i * ( 2 P ) + C s ( 6 S ) ~ L i ( 2 S ) +Cs*(5D) are reported. The technique of resonant Doppler-limited two-photon laser excitation with thermionic detection is applied. The population density of the Cs* 5 D state is probed by photoionization, and the signals of the Cs(6S) ~ Cs*(5D) and the Li(2S) ~ Li*(2P) transitions are compared. The value for cross section of 30/~2 is measured, with an accuracy of 45%. PACS: 34.50; 32.00.

1. Introduction Since many decades excitation energy transfer processes in low-energy atomic collisions between excited neutral atoms have been investigated. Studies of such interactions provide important checks on interatomic interaction potentials and collision models. On the other hand, the results of these investigations are found to be important in a variety of fields dealing with ionized gases and low-temperature plasmas (astrophysics, physics of the earth's atmosphere, chemical reactions, new laser systems, etc.). The data for the collision cross sections and rate constants can be used for determination of the population densities and other parameters of excited atomic systems. In general, these inelastic (or superelastic) processes can be schematically described by

(i) A(n) + B(m) ~ A(n) + B(m'). Among these processes collisions between excited (A*) and ground state atoms (B(O)) are the simplest. Here, the excitation transfer takes place within one atom

(ii) A*(n)+ B(O) --+A*(n')+ S(O), or from one collisional partner to the other

(iii) A* (n) + B (0) --* A (0) + B* (m').

More complicated collision processes which still belong to the same class of collisions are those in which two excited atoms collide and produce one highly excited atom (A**) and one atom in the ground state

(iv) A* (n) + B* (m) ~ A** (n') + B(O). The excitation exchange processes in collisions between alkali atoms are very convenient for experimental and theoretical investigations. Among the most investigated processes are the collisions involving atoms excited in the resonance state (first P level). Typical processes of scheme (ii) are intermultiplet excitation mixings between the fine structure levels of the resonance states of the alkali atoms. Most results in this field were published until 1975 and summarized in [1, 2]. Majority of the experiments from [1, 2J are performed using different types of cells for the generation of alkali vapors. Recently, the total or differential scattering cross-sections are rather often measured using the atomic beam technique, see e.g. [3] and references therein. The experimental and theoretical cross sections for excitation transfer, which are defined analogously to the gas-kinetics cross sections, differ considerably. In general, the calculated cross sections are much smaller than the experimental values. In more recent papers excitation transfers between the highly excited states have been studied in order to determine the dependence on energy and quantum numbers of the levels involved [4, 5, 6, 7]. In the case of process (iv), which is first reported by [8] and named energy pooling, there are no theoretical calculations which explain the large experimental excitation energy transfer cross sections. The problem of excitation transfer in low energy atomic collisions is usually treated in two steps. The first is the determination of the adiabatic quasimolecular potentials for the given atomic pair, and the second is the modelling of a non-adiabatic transfer process. The transitions should occure in a localized non-adiabatic region characterized by avoided crossings of potential curves. The large cross sections found for the excitation

598 energy transfer between the alkali atoms is believed to be due to strong long-range interaction forces. The long-range adiabatic potentials of one alkali atom in the first P state and the other in the ground state have been calculated and proved by line-shape measurements of the alkali resonance lines [9, 10, 11]. However, as mentioned above, the calculations of excitation energy transfer cross sections are in considerable disagreement with the experiments [12]. Disagreements can be found, in particular, in the systems where no avoided crossings of the adiabatic potential energy curves occur. We report on the measurements of the collision cross section for the excitation energy transfer in the L i - C s system. The investigated process belongs to class (iii) processes and is described by

(1)

Li* (2 P) + Cs (6 S) ~ Li (2 S) + Cs* (5 D).

As shown in [13], the long-range potentials for Li*(2P)+ Cs(6S) system are characterized by strong repulsive dipole-quadrupole interaction due to the relatively small energy difference between the Li 2 P and Cs 5 D levels (about 350 cm- 1). The potentials are of a simple form. Therefore, this system can be taken as suitable test for the modelling of the excitation transfer.

2. Excitation transfer between lithium and cesium

The data analysis in our experiment is based on the four-level model including the Li(2P1/2, 3/2) and Cs(5 D3/z. 5/2) states, with the relevant radiative and collisional rates as shown in Fig. 1. The main goal in the present study is the determination of the collisional transition rates Ri for process (1). These rates give rise to the energy transfer to Cs ground-state atoms, which are excited to the 5 D level. The rates R i represent the number

2P312 2Pl/2

,

Cl i D ,

",\ ',

'V, ',", \ \

\ N

' R 2 ' , R~, RI\

5D5~2

"R3\

~1 ÷ Sin12

Au AL'

AC~A~

,X

X

of transfer collisions per excited Li atom per second, and they are given by [14] : Ri = gLi-Cs (7.i N (Cs),

(2)

where gLi-Cs is the mean relative velocity of the L i - C s system, a~ the corresponding energy transfer cross section, and N(Cs) is the density of the Cs ground-state atoms. The mean relative velocity in (2) is Maxwellian and it is given by ~Li-Cs--'~(8 kT/M) 1/2, where M is the reduced mass of L i - Cs system. The process in the opposite direction, the excitation of the Li ground-state atoms in collision with the excited Cs atoms, is given analogously by rates of the form R~ = ~Li-Cs at N (Li). Since in present experiment the lithium number density N(Li) was much lower than density of cesium (about 106 times), these rates can be neglected in discussed case, but cross sections oi and a t are assumed to be of the same order of magnitude. Because of the same reason, all other collisional rates in this model refer only to the excitation energy transfers induced due to collisions between the particular excited species (Li* or Cs*) and ground-state Cs atoms. In order to determine the collisional rates Ri, the population densities of the Cs* (5 D) level generated through two different excitation channels, have to be compared. If one of the Cs 5D3/2,s/2 levels, e.g. the Cs 5D3/2 level, is optically excited by laser radition field then the steadystate population density of the Cs 5 D levels is described by ))](Cs 5Ds/2) = 0=XN~(Cs

5D3/2)

- - ( 1 / ' c + Y) N a ( C s 5 D 5 / 2 ) ,

N,(Cs 5D3/2) = 0 = P,I BCs(3/2) N(Cs) + YN~(Cs 5D5/2) -- (1/r + X) N~(Cs 5 D3/2).

2S'~t2

Li Cs Fig. 1. Partial term diagrams of the lithium and cesium atoms. The rates for intermultiplet mixing within Li 2P and Cs 5D levels are C, D and X, Y,respectively.The excitation transfer rates between the Li 2P and Cs 5D states are R~, AL~is the spontaneous emission coefficientof the Li 2 P doublet and the spontaneous emission coefficients for Cs 5D state are denoted by Ac~2

(4)

Here the N's denote the population densities of the relevant levels, the P.1 is the spectral density of the radiation field of the first step laser, the BC~(3/2) is the Einstein coefficient for the absorption transition Cs6S1/z --.5D3/2, and z is the lifetime of the Cs5D level. The intermultiptet coltisional mixing rates for the process Cs*(5D3/2)+Cs(6S1/2)--.Cs*(5Ds/2)+Cs(6S1/2) are denoted by X and Y. The sum of (3) and (4) gives the total population density of the directly (optically) excited Cs 5 D level N~(Cs 5 D) = N~(Cs 5 Ds/2 q- Na(Cs 5 D3/2) = P a l Bcs(3/2) N(Cs) r,

6P

(3)

(5)

which we call the reference population density. If one of the Li 2P3/2,1/2 levels, e.g. 2P1/2 level is excited, the steady state situation is described by the following set of rate equations 2~rb(Li 2P3/2) = 0 = C Nb(Li 2P1/2)

--(ALI+R3+R4+D)Nb(Li2P3/z),

(6)

~rb(Li 2Pa/2)=O=pb 1 uti(i/2) n ( L i ) + DN~(Li 2~/~)

--(ALI + RI + Rz + C) Nb(Li 2P1/z),

(7)

599

~ ( C s 5D5/2)=0=R4 Nb(Li 2P3/2)+ R2 Nb(Li 2P~/2) --(1/z + Y) Ub(Cs 53s/2) + XNb(Cs 5D3/2), (8) Nb(Cs 503/2~ = 0 = R3 Nb(Li 2 P3/2)+ Rt Nb(Li 2 P~/2) + YN~(Cs 5D5/2) -- (1/'c + X ) Nb(Cs 5 33/2).

(9) Here, C and D are the rates for the intermultiplet mixing process in Li*(2P) induced by collisions with Cs(6Sw2), e.g. Li*(2P1/z)+Cs(6S~/z)--*Li*(2P3/2)+Cs(6P~/2), the Pb~ denotes the spectral density of the radiation field of first step laser, BLi(1/2) is the Einstein coefficient for the Li 2S~/2-2P~/2 absorption and AL~is the spontaneous emission coefficient of the Li 2P doublet. From (8) and (9) the total population density of the collisionally excited Cs 5 D level is obtained Nb(Cs 5D)= ((R3 + R4) Nb(Li 2 P3/2) +(R1 +R2) Nb(Li 2 P1/2)) z.

(10)

The total collisional depopulation rates for the Li 2P1/2 and Li 2P3/z levels are R(1/2)=RI+R 2 and R(3/2) = R 3 + R 4 , respectively. If we assume that these rates are equal R = R (1/2)= R (3/2),

(11)

we obtain from (6), (7) and (10) a simple expression for the "sensitized" population density of the Cs 5 D doublet N~(Cs 5 D) = Pb~ BLi(1/2) N (Li) R z/A Li.

(12)

The ratio of the sensitized population density to the reference population density, nba = Nb(Cs 5 3)/Na(Cs 5D), is given by

nb,= (Pb1/P, ~) (BLi(1/2)/Bc~ (3/2)) •(N (Li)/N (Cs)) R/A Li.

(13)

The data for the Einstein B coefficients can be found in [15] and [16]. All other quantities in (13) are measured in this work. One may use the other optical excitation channels and apply the formula (12) with corresponding absorption coefficients ratios BLi/B c~. However, the data show no dependence on the chosen excitation channel confirming indirectly the assumption (11). Namely, if (11) is not correct, then the expression (12) would be different for the optical pumping of Li(251/2) Li(2 P3/2) or Li(2SI/2) -~ Li(2P3/2). The supposition (11) is based on the general property of the collisional transfer rates, which show a strong dependence on the energy difference between relevant levels for the particular interaction system [1]. Indeed, in our case the energy differences E(Li2Pj)-E(Cs5D) for J = l / 2 and J = 3 / 2 can be regarded as equal (see Fig. 1).

3. Experiment and data analysis The experimental apparatus is shown schematically in Fig. 2. A stainless-steel heat-pipe with quartz windows,

ring dye taserl

~

to recorder

recorder

ring dye [aser2

6G

+

',

pp.',

+

\- .... _f taser

,~ absorption to recorder

Fig. 2. Experimental arrangement

containing the L i - C s mixture (1:1 in solid state) and neon as the buffer gas, was heated in the middle part up to 520 K. The corresponding number densities of lithium and cesium vapors in the 9 cm long heated zone were approximately 101° and 1016 cm -3, respectively. The pressure of the noble gas was measured by a precise manometer (MKS Baratron). It was kept constant at 600 mTorr. Since the typical value for the partial metalvapor pressure was about 500 mTorr, the heat-pipe was running nearly in heat-pipe mode. With a built-in cathode filament (0.3 mm diameter molybdenum), the heatpipe served simultaneously as the thermionic diode detector for collisionally produced ions [17]. The optical excitation of the metal vapor was performed by two counter-propagating laser beams (diameters: 5 ram) passing through the heat-pipe along its axis. Both lasers were c w single-mode, frequency stabilized (line width about 1 MHz) ring dye-lasers (Spectra Physics 380D) pumped by two argon-ion lasers (Spectra Physics, Series 2000). The first laser (dye: DCM), used for the excitation of the ground-state atoms (either Cs to 5D or Li to 2P state), was scanned over the relevant transitions. The laser-beam absorption in the metal-vapor column was measured simultaneously by a photodiode ("ph.d." in Fig. 2) and used for determination of the Li and Cs number densities, using the method of curve of growth for optically thin lines. The 0.5 m confocal Fabry-Perot interferometer was used for dispersion calibration of the spectra. In the case ofCs 6S1/2 --* 5D3/2, 5/2 excitation ("forbidden" quadrupole lines) the power of the first laser was about 40 roW. It was proven that the power of the second laser was well below the limit of optical saturation. For the Li resonance line 2S1/2--,2P~/2, 3/2, the optical saturation was avoided by using neutral-density filters for the attenuation of the power of the first taser (about I mW). In order to probe the population density of the Cs 5 D state, the cesium atoms in the 5 D state were photoionized applying the second laser (dye: Rh 6 G, power: about 50 mW). The beam was chopped (7 Hz) and the thermionic signal produced was fed into a lock-in amptitier. The output was recorded by a strip-chart recorder.

600

I p ~ 2Pl/2.3/2

7'2 '~ 5D5,'2 503J2

SD~2 II-LL-

'l7`1a

k

6Sit2

25112

6Sl/2

Li

Cs Cs absorption: 6SI12[F= 3 ] -~ 511:312

Cs

Li absorption: 2Sv2~ 2Pv2

(vt

qC V1

thermionic signal so(x1)

Io

15Hz I

o)

,

ib

0

b)

Typical scans together with the corresponding pumping diagrams are shown in Fig. 3. In addition to the 2-photon thermionic signals, the absorption spectra were recorded. In the scan shown in Fig. 3a, the reference population density of the Cs 5D level was generated by using the Cs 6S1/2 --~5D3/2 excitation channel. The line shown is one of the two hfs-components of the Cs ground state (F = 3). The oscillator strength of this hfs-structure component is l a x 10 -7 [-15]. In the case Fig. 3b, the optical excitation channel Li 2 $1/2 -~ 2 P~/2 was used. The absorption measurement provide the data for Cs and Li number densities to be 8.5 x 1015 and 1.1 x 10 l° cm -3, respectively. The wavelength of the second laser was kept at fixed value (2 = 5909.47 A) which photoionize the Cs atoms in the 5D3/2 as well as in 5Ds/z level. The generated thermionic signals are proportional to the total population density of the Cs 5D levels. This is valid if the photoionization cross sections for this levels are equal, which was proved by detuning the second laser to longer wavelength which could photoionize only the atoms in the Cs 5D5/2 state. The ratio of this signal to the signal when both 5 D levels were ionized was found to be equal to the ratio of the corresponding statistical weights (3: 5). In Fig. 3 one can observe that the thermionic signals follow the shape of the absorption coefficient in the first excitation step. The resonant 2-photon lines are Doppler-limited, due to non-selectivity of the photoionisation process in respect to the different atomic velocity groups. The temperature of the metal vapor was estimated by measuring the line widths of the Doppler broadened Cs 6SI/2 -~ 5D3/z, 5/2 lines. From the line presented in Fig. 3, we obtained T = 510 K. The range of the Li and

Fig. 3. The spectra shown in a and b show simultaneously recorded thermionic signals due to the photoionization of the Cs 5D levels, the absorption on the Cs quadrupole transition, and the absorption on the Li resonance line. The spectra are taken at T = 510 K, A~ = 1.1 x 101° cm -3 and Nc~=8.5 x 1025 cm -3

Cs number densities, in which the measurements could be made, was limited by the minimum measurable absorption and by the optical thickness of the relevant lines. In order to avoid the trapping effects, the measurements were done at conditions which are characterized by the absorption coefficients of the considered lines lower than 0.1 cm-1, where according to the theoretical calculations [18] radiation trapping can be neglected. Therefore, the measurements were performed in a relatively small temperature range (500-520 K). The corresponding number density ranges for Cs and Li were 0.5 x10J6-1.5x1016cm -3, and 0.8xl01°-l.2xl01°cm -3, respectively. Since the integral thermionic signals s=~s(v) dv are proportional to the total population densities of the Cs 5D state, the collisional transfer rate R is given as

R = (sb/s,,) (P,,1/Pb,)(fc,/fLi)(N(Cs)/N(Li)) AL,.

(14)

Here, the oscillator strengths f are introduced instead of Einstein coefficients. The results of rate measurements show a linear dependence on the Cs number density and no dependence on the excitation channels. Introducing the data for R in (2), the corresponding cross section for the collisional excitation transfer process Li*(2P)+Cs(6S)~Li(2S)+Cs*(5D) is found to be 30 A 2 . The statistical error for a is about 20 O%. Including all systematic uncertainties, e.g., metal vapor column length and inhomogeneous distribution of noble gas and metal atoms over the column length, we estimate a total error of about 45%.

60t

4. Discussion and conclusion The transfer cross section of 30 ~t 2 found for the process El* (2 P) + Cs (6 S) ~ Li(2 S) + Cs* (5 D) is extraordinary large compared to the transfer cross sections measured in collision processes involving other dissimilar alkali atoms. These cross sections strongly depend on the energy differences between levels involved in the transfer process [1]. F o r example, the transfer cross sections obtained for K*(4P)+Rb(5S)-~K(4S)+Rb*(5P) and Rb* (5 P) + Cs (6 S) ~ Rb (5 S) + Cs* (6 P) are between 0.5 and 5 A 2. In particular, the system K* (4 P) + Rb (5 S) is formally very similar to the case investigated in this paper. First, the potential energy curves do not cross in the long-range region, as well as in L i - C s case. Second, it exhibits relatively strong repulsive long-range interaction [10] which may be compared to the strength of long-range interaction in L i - Cs case. The size of this interaction, dominated by the dipole-dipole force, is due to small energy differences between the K 4P~jz,3/2 and Rb 5P~/2, 3/2 states (168, 225, 409 and 466 cm-1, respectively). However, the transfer cross sections differ by about one order of magnitude. We suggest that shortrange interaction gives the crucial contribution to the transfer cross section in the L i - C s case. Preliminary theoretical calculations support this assumption. Because the L i - Cs system has to be represented in coupled approximation the corresponding long-range potentials have relatively simple form. Therefore, the system is an ideal test case for the further theoretical modelling of excitation energy transfer between dissimilar alkali atoms.

The authors whish to thank the Deutsche Forschungsgemeinschaft, the Bundesministerium ffir Forschung und Technologic and the Ministerium fiir Wissenschaft und Forschung (Nordrhein-Westfalen) for financial support.

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