52P12 -52P32 fine-structure mixing in potassium atoms induced by collisions with noble gases

J. Quant. Spectrosc. Radiat. Transfer Vol. 37, No. 2, pp. 157-164, 1987 Printed in Great Britain. All rights reserved

0022-4073/87 $3.00+0.00 Copyright © 1987PergamonJournals Ltd

52pI/2-52p3/2 FINE-STRUCTURE

MIXING IN POTASSIUM ATOMS INDUCED BY COLLISIONS WITH NOBLE GASES*

R. W. BERENDS,t W. KEDZIERSKI~ and L. KRAUSE Department of Physics, University of Windsor, Windsor, Ontario N9B 3P4, Canada (Received 28 April 1986)

Abstract--Cross sections for 52p~/2-52p3amixing in potassium induced in collisions with noble gas atoms were determined by methods of fluorescence spectroscopy. Mixtures of K vapour and a buffer gas were irradiated in a vapour cell with pulses of laser light and the resulting fluorescence spectrum was resolved with a scanning Fabry-Perot interferometer. Measurements of fluorescence intensities in relation to buffer gas pressures yielded the following cross sections Qu(52Pt/2--* 5:P3/2) and Q21 (52Pt:2~ 52P3/2) (in units of 10-~6cm), respectively:for He, 561 and 260; for Ne, 196 and 98; for Ar, 317 and 153; for Kr, 195 and 99; for Xe, 146 and 67.

INTRODUCTION Although experimental studies of collision-induced fine-structure mixing in alkali atoms have for m a n y years focussed on the alkali 2p resonance states,~ there have been several more recent reports of experiments dealing with inelastic collisions involving more highly excited alkali atoms. 2"3 2P1/2-2P3/2 mixing in potassium is induced in collisions with noble gas atoms and has been investigated in vapour cells in Ciurylo and Krause, 4 and CuveUier et al. 5 carried out a crossed-beam experiment in which they studied the fine-structure transition resulting from He collisions. Cross sections for transfer between the fine-structure components in the second alkali doublets, induced in collisions with noble gases, have also been determined for Rb 6 and Cs 7. The extensive theoretical and experimental study of the potassium 52p doublet, reported by Spielfiedel et al., s dealt with broadening and shift of the spectral lines caused by collisions with noble gases, though the authors also calculated the fine-structure mixing cross sections. In this investigation, we have studied 52pI/2-52p3/2 excitation transfer in K induced in collisions with ground-state noble-gas atoms. The cross sections for the forward and reverse processes were determined separately by selectively exciting each fine-structure component by light pulses from a laser and employing time-integration of both direct and sensitized fluorescence emitted from the vapour-gas mixture. THEORY The collisional excitation transfer process m a y be represented by K(52P3/2) + X ~ K ( 5 2 P l / 2 ) + X + A E ,

(1)

where X is a ground-state noble-gas a t o m and AE = 18 c m - ~ is the energy defect between the 2p fine-structure states, each of which was excited in turn by pulses from a laser. When the 2p1/2 state is radiatively excited, the time-evolution of the population densities of both states may be described by the rate equations d N l / d t = Sl - NI(r -i + Zi2 + Z l ) + N2Z21,

(2)

d N 2 / d t = N i Z i z - N2(z - | + Z21 + Z2),

(3)

*Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada. tHolder of an NSERC graduate scholarship. :l:On leave from the Pedagogical University, Kielce, Poland. 157

158

R.W. BEI~NDSet al.

where N] and N 2 are the population densities of the 2pI/2 and 2p3/2 substates, respectively, sl is the 2P]/2 radiative excitation rate, z = 133.3 ns is the radiative lifetime of the 52p state, 9 and Zab are the frequencies of inelastic collisions per excited atom, leading to the transfer a--*b. Zl and Z2 represent non-radiative depopulation of the fine-structure state by quenching collisions which result in excitation transfer to all states below the 52p state, including the ground state. When the 2P3/2 state is populated by laser excitation, the time-evolution of the two substates is described by the rate equations dN2/dt = s2 - N2(z-i + Z21 + Z2) + NiZl2, (4) d N t / d t = N 2 Z z l - Nl(2-

1 q_ Z i 2 + Z l ),

(5)

where s2 is the 2P3/2 radiative excitation rate. Although the population densities of the 2p states are time-dependent because of pulsed excitation, equations (3) and (5) can be integrated to give I° ~ l / N 2 = ( z - l + Z21 + Z2)/ZI2,

(6)

~72/./~71 = (,~ 1 + Z I 2 ..[_ ZI)/Z21.

(7)

In equation (6), A72 represents the time-integrated population produced by collisional transfer, whereas AT~ is due to radiative excitation; in equation (7), the reverse is the case. Assuming the measured fluorescence intensities to be proportional to the products of the appropriate populations and Einstein A coefficients, equations (6) and (7) may be expressed in terms of the time-integrated intensities of the two spectral components Zj 2 = rh(Ai/z/A3/2)( z -i + Z2 ' + Z2), (8) Z21 = th(A3/z/Al/2)( z ] + Z, 2 + ZI),

(9)

where nl and n z are the measured ratios of the fluorescence intensities: ql = •(4047 A)/I(4044/~,); r/2 = •(4044 •)/I(4047 A).

(10)

The component appearing in the denominator is in each case of the same wavelength as the exciting radiation. Since the A3/2 and A 1/2 coefficients are very nearly equal to one another I~ as are the frequencies of the two spectral components, their ratios were omitted from further consideration. The lifetimes • 1/2 and 2-3/2were taken as equal to one another (2-~/2= 23/2 -~- ,17 ~-- 133 + 3 ns). 9'12 It is also assumed that Z~ and Z2 may be neglected because quenching of alkali fluorescence by collisions with noble gases has been found to be too slight to be measurable even at much higher buffer gas pressures than those employed here. 6J3 Using these approximations equations (8) and (9) may be solved for Z,2 = 1/2- (712 "Jr ~1~2)/(1 -- ~1~2),

Z2I = 112- (rh +

rttq2)/(1 - q,rt2).

(11)

(12)

Equations (11) and (12) provide the connection between the measured fluorescence intensity ratios and the collision numbers Zab which, when representing the transfer a--*b, can be related to the corresponding total cross section Qab by analogy with the gas-kinetic cross section, Zab = N(X)Qab G,

(13)

where N ( X ) is the density of the noble gas atoms and v~ is the average relative speed of the colliding partners whose reduced mass is #. Here, Vr = (8 k T /lrl.t )l/2;

k is the Boltzmann constant and T the absolute temperature of the fluorescing vapour-gas mixture. In this way, by exciting the fluorescence with each component of the 52P doublet in turn and measuring the corresponding time-integrated fluorescence intensity ratios ql and r/2, it is possible to determine independently the cross sections QI2 and Qzl. According to the principle of detailed balancing, the cross sections should be in the ratio Qt2/ Q21 = (g2/gl ) exp ( - A E /k T),

where gl = 2 and g2 = 4 are the statistical weights of the 2Pi/2 and 2p3/2 states, respectively.

52P~/2-52P3/2fine-structuremixing

S2

T

FP

159

~-

Fig. 1. Schematicarrangement of the apparatus. N2L, nitrogen laser; DL, dye laser; PD photodiode; D, delay line; ~, vacuum and gas filling system; FP, Fabry-Perot interferometer; T, telescope; PM, photomultiplier tubes; S1, $2 shutters; AMP, amplifier-discriminator; GATE, gated pulse-inverter amplifier; LT, channel advance laser trigger; SC, shutter control.

D E S C R I P T I O N OF T H E A P P A R A T U S The arrangement o f the apparatus is shown schematically in Fig. 1. Potassium atoms mixed with a noble gas and contained in a fluorescence cell were irradiated with pulses from a N2 laser-pumped dye laser which produced a population of 52P1/~ of 52p3/2 states. The resulting fluorescence spectrum was monitored at right-angles to the direction of excitation and was resolved with a scanning F a b r y - P e r o t interferometer whose output was detected with a photomultiplier and accumulated in a multichannel scaler (MCS). The N2 laser which was built in-house, H emitted 10 ns-wide ( F W H M ) light pulses at a repetition rate of 35 Hz, which were applied transversely to a two-stage dye laser 14 operated with a nearly saturated solution of DPS dye in p-dioxane, contained in magnetically stirred cuvettes. The dye-laser output was condensed into an optical fibre and conveyed to the fluorescence cell where an appropriate termination produced a parallel beam in the cell, 2 mm in dia and passing 2 mm from the observation window. The resulting fluorescence was collected by a lens near the observation window, rendered parallel and directed onto the mirrors of a piezoelectrically scanned F a b r y - P e r o t interferometer (Burleigh 110) which was fitted with 2" (2/200) aluminized mirrors. With 94 + 2% reflectivity, the instrument had a finesse o f 30. The interferometer was scanned at 0.5 Hz and was stabilized with the aid of a Burleigh DAS10 stabilization system, using a H e - H e laser as a reference source. The interferometer output was collimated and focussed on the photocathode o f an ITT FW130 refrigerated photomultiplier, whose output pulses were amplified by an Ortec 9302 amplifier-discriminator, sent to an inverter-amplifier and collected in a 1024-channel MCS, whose memory was subdivided into 4 quarters. The accumulated spectrum was transferred for further analysis to a Commodore PET 2001 computer where the integrated intensities of the fluorescence peaks were determined, after corrections for noise counts and for pileup. 15,16 The quartz fluorescence cell had a square cross section (2.5 x 2.5 x 4.0 cm) and was fitted with a 1-cm long side arm protruding from the bottom. The body of the cell was enclosed in an oven heated by oil circulating from a Neslab Ultrathermostat and was maintained at 115 +_ 0.5°C. The

R. W. BERENDSet al.

160

Table 1. 52PI/2-52p3/2 fine-structuremixingcross sections(in 10-I° cm2) Collision partners

K-He K Ne K Ar K-Kr K-Xe

QQ12(2pI/2--+2P3/2) 561 + 84 156 196 _+29 75 317_+45 139 195 + 29 146_+21 166

Q21(2PI/2~2P3:2)

Q12/Q2~

260 _+39

2.2

98 ± 18

2.0

153_+22

2.1

99 + 18 67+ I1

2.0 2.1

Source

This work Ref. [8] This work Ref. [8] This work Ref. [8] This work This work Ref. [8]

side-arm was heated separately a n d was kept at 74°C to p r e v e n t c o n d e n s a t i o n o f p o t a s s i u m o n the windows. T h e t e m p e r a t u r e was m e a s u r e d with several c o p p e r - c o n s t a n t t h e r m o c o u p l e s located at v a r i o u s p o i n t s o n the cell a n d side-arm. T h e cell was c o n n e c t e d by a n a r r o w - b o r e tube a n d a greaseless stopcock to a v a c u u m a n d gas filling system from which buffer gases were a d m i t t e d as required. The gases (research grade) were supplied by the M a t h e s o n Co. G a s pressures which r a n g e d from 8 to 600 m T o r r were m e a s u r e d with a n M K S B a r a t r o n capacitance gauge. I n order to ensure the p r o p e r stability o f the s c a n n i n g interferometer, as well as the s c a n - t o - s c a n r e p r o d u c i b i l i t y required for signal averaging, the interferometer was locked to the o u t p u t from a H e - N e laser, which was s c a n n e d d u r i n g the initial 0.15 s o f each 2 s sweep a n d provided a reference for the D A S 1 0 stabilizer a n d the r a m p g e n e r a t o r c o n t r o l l i n g the piezoelectric element. T h e H e - N e laser light was c o n d u c t e d by a n optical fibre to the o b s e r v a t i o n w i n d o w o f the fluorescence cell where it was reflected, passed t h r o u g h the interferometer a n d directed by a 5% m i r r o r to a n auxiliary p h o t o m u l t i p l i e r whose signal was conveyed to the D A S - 1 0 unit. The H e - N e laser light

2 P3/2

(o)

Fig. 2. Interferogram of the 4047 ~/4044/~ fluorescence doublet in K with 200 mTorr Kr, arising from the 52Pi/2,3/2~4 2Sl: 2 transitions (2 orders) showing direct and sensitized fluorescencecomponents; (a) with laser-excitation of the 52P3:2state; (b) with laser-excitation of the 52P~:2 state.

He pressure

0

(mTorr)

~5

30

45

60

I

I

I

I

1.0

o

o

0.8

o ~2

0.6

o

o

o. 4

o

/

~

~

~o.2

0.4

~

- r/z

Ar /

o

0.2

0.0

[3

I

o

I

I

60

30

Ar

[3

I 120

90

pressure (mTorr)

Fig.3. Plotsof fluorescenceintensityratiost/, and ~/2vs He and Ar pressure. 0.8

~

o

~ O

0.6

0

o°

0.4

0

0

o

~

o

0.0 0.4

o

~c

0.2 ~ 8

oo

o.o 0

50

100

150

Gas pressure

i

200

[] i

250

(mTorr)

Fig. 4. Plots of fluorescence intensity ratios ~h and t/2 vs Ne, K r and Xe pressure. 161

162

R.W. BERENDSet al. He p r e s s u r e O 1.2

(mTorr)

15

30

45

I

~

I

60 I o

1.0

o

o

0.8 He

0.6

~ 0.4 L o.2

0.0 Z12~

-

0.2 ~ 0.0 0

I 30 Ar

I

I

I

60

90

120

pressure

(mTorr)

Fig. 5. Plots of collision numbers Zt2 and Z21 VSHe and Ar number of such spectra was recorded over a range of buffer gas pressures. The intensity ratios r/of sensitized-to-direct fluorescence, derived from these measurements, and the collision numbers Z obtained from the experimental daa in conjunction with equations (11) and (12), are plotted in Figs 3 ~ against the buffer gas pressures. As expected, the plots of the Z-numbers are linear. The cross sections Q which were calculated from all the data points and averaged, are compared in Table 1 with the theoretical values of Spielfiedel et al. 8 Our values are considered to be accurate within _ 15-20%, the main source of experimental error arising from the uncertainty in the measurements of gas pressures and from counting statistics, since the count rates were quite low to avoid pileup. The ratios QI2/Q21 of the cross sections, which were determined independently, are in better agreement with the value 1.9 predicted from the principle of detailed balancing than might be expected from the stated limits of error. No estimate is available for the accuracy of the theoretical values, though Spielfiedel et al. 8 in their paper quote a range of values obtained from their calculations and from those of others, which differ among each other by a few percent. It is apparent from Table 1 that, although there is agreement as to order of magnitude between the experimental and calculated values of the cross sections, the experimental values are larger except for the pressure. was p r e v e n t e d from interfering with the fluorescence detection system by two shutters, S~ p o s i t i o n e d in f r o n t o f the laser a n d $2 in f r o n t o f the m a i n p h o t o m u l t i p l i e r , whose o p e r a t i n g cycle was locked to the interferometer sweep by the trigger o u t p u t o f the r a m p generator. T o avoid interference f r o m scattered dye-laser light, the pulse inverter-amplifier was gated. The gate was triggered b y a p h o t o d i o d e which m o n i t o r e d the dye laser o u t p u t pulses. The variable data acceptance w i n d o w o f the inverter-amplifier extended from 8 ns after the t e r m i n a t i o n o f the laser pulse, t h r o u g h 1400 ns (~- 10r). Since the g a t e - o n time tg was short c o m p a r e d with z, it was still possible to a s s u m e that

f 10~N d t

=

f0 ~ N d t .

wJtg

A c o m p u t e r - s i m u l a t i o n confirmed the validity o f this a p p r o x i m a t i o n . W i t h the dye laser repetition rate of 35 p.p.s, a n d the interferometer s c a n n i n g frequency o f 0.5 Hz, the M C S c h a n n e l a d v a n c e was triggered at a rate o f 4 x 35 = 140 Hz. C o n s e q u e n t l y , with

52P,/2-52P3/2fine-structuremixing

163

256 memory channels (1/4) available to register the fluorescence spectrum, 4 interferometer sweeps covered all the MCS channels. RESULTS AND DISCUSSION Before each experimental run, the fluorescence cell was pumped down to 5 x 10-7Torr and isolated from the vacuum system. For a period at about 12 h, the main oven was kept at about 115°C and the side-arm at 15°C to ensure the condensation of all the potassium in the side-arm. The cell was again opened to the vacuum system and maintained for 1-2 h at 5 x 10 7 Torr with the side-arm at 74°C, while the N2 laser was turned on, stabilized, and tuned to 4044 or 4047 observing the fluorescence produced in an auxiliary cell containing potassium vapour. Finally, the cell was flushed with clean buffer gas, pumped down and filled with a quantity of the gas appropriate to begin the experiment. After a short time, during which the gas pressure in the cell reached equilibrium, the cell stopcock was closed. The fluorescence count rate was adjusted to produce 1-2 counts per MCS sweep (35 laser pulses) by varying the output power of the N2 laser and the degree of focussing of the exciting laser beam into the fibre optic cable which conveyed it to the fluorescence cell. The count rate was checked frequently and maintained constant by making adjustments to compensate for the deterioration of the laser dye. The tuning of the dye laser was periodically changed to alternate between 2Pl/2 and 2P3/2 excitation and the fluorescence signals emitted from the two states were accumulated in different quarters of the MCS memory. Figure 2 shows typical interferograms o f the fluorescence spectrum consisting of 2 components, one due to direct fluorescence and the other to sensitized fluorescence. A large Xe cross section. Nevertheless, the two sets of cross sections exhibit a similar overall trend, showing minima for Ne bracketed by relatively high He and Ar values. No fully satisfactory explanation can be offered for the decrease of the measured cross sections from Ar to Xe, since the opposite trend should be

1.O o

o

0.8 2

0.6

Ne

o

Z12 o []

[]

0.4

/oO

T

0

~ 0.2

°2I-

/

o

[]

o 0

[]

~ D

9o o

o

O0 0.2 ~

0.0

0

50

I 100

Gos pressure

I 150

I 200

1 250

(rnTorr)

Fig. 6. Plots of collision numbers Zu and Z~, vs Ne, Kr and Xe pressure.

164

R.W. BERENDSet al.

e x p e c t e d o n the basis o f the p o l a r i z a b i l i t i e s o f these a t o m s , t h o u g h p r e v i o u s e x p e r i m e n t s w i t h the s e c o n d a n d t h i r d P - d o u b l e t s in R b 6 a n d Cs 7'17 also p r o d u c e d cross sections w h i c h were n o t fully c o r r e l a t e d w i t h the p o l a r i z a b i l i t i e s o f the n o b l e gases. T h e fact t h a t the m i x i n g cross sections d o n o t i n c r e a s e m o n o t o n i c a l l y w i t h the p o l a r i z a b i l i t i e s , m i g h t be d u e to the effect o f v a r i a t i o n s in the relative v e l o c i t y o f the c o l l i d i n g pairs, f r o m K - H e to K - X e . REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

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