OPTOGALVANIC STUDY OF XENON RYDBERG STATES

HAL Id: jpa-00223307

https://hal.archives-ouvertes.fr/jpa-00223307

Submitted on 1 Jan 1983

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

OPTOGALVANIC STUDY OF XENON RYDBERG STATES

E. Giacobino, F. Biraben, P. Labastie

To cite this version:

E. Giacobino, F. Biraben, P. Labastie. OPTOGALVANIC STUDY OF XENON RYDBERG STATES.

Journal de Physique Colloques, 1983, 44 (C7), pp.C7-505-C7-511. �10.1051/jphyscol:1983750�. �jpa-

00223307�

page

~ 7 - 5 0 5

OPTOGALVANIC STUDY OF XENON RYDBERG STATES

E . Giacobino, F. Biraben and P. L a b a s t i e

Laboratoire de Spectroscopie Hertzienne de ZtE.N.S., Universite' Pierre e t Marie Curie,

4 ,

PZace Jussieu,

75230

Paris Cedex

05,

France

Rdsumd

-

Nous avons u t i l i s e une e x c i t a t i o n l a s e r conjointement avec une dbtec- tion-alvanique dans une ddcharge radiofrdquence pour d t u d i e r des niveaux de Rydberg n s e t nd du xdnon. Notre mLthode repose s u r une dscharge radiofrbquence e n t r e t e n u e p a r des d l e c t r o d e s e x t e r n e s e t une mesure de ltimpddance du plasma p a r des d l e c t r o d e s i n t e r n e s . C e t t e technique nous permet d ' e x t r a p o l e r f a c i l e m e n t nos r g s u l t a t s B i n t e n s i t 6 de ddcharge n u l l e .

5 5

Nous avons mesurb l e s d n e r g i e s des niveaux 5p n s (n = 14-27) e t 5p nd (n = 12

-

^25).

Ces s d r i e s s o n t peu p e r t u r b b e s e t peuvent d t r e r e p r b s e n t s e s p a r l a formule de Rydberg. Nous obtenons une n o u v e l l e v a l e u r de l a premisre l i m i t e d ' i o n i s a t i o n . Nous avons Lgalement g t u d i b l e s Slargissements e t d6placements e n p r e s s i o n des t r a n s i - t i o n s 6p ⁺ nd e t 6p ⁺ n s . Leurs v a l e u r s e t l a dLpendance en f o n c t i o n du nombre quantique p r i n c i p a l n o n t Ltd i n t e r p r b t d e s p a r un modsle t h s o r i q u e u t i l i s a n t l e s t h d o r i e s de Fermi e t dlOmont.

A b s t r a c t

-

We have used l a s e r e x c i t a t i o n t o g e t h e r w i t h o p t o g a l v a n i c d e t e c t i o n i n a radiofrequency d i s c h a r g e t o s t u d y n s and nd Rydberg l e v e l s of xenon. Our method involves R.F. e x c i t a t i o n of t h e d i s c h a r g e by e x t e r n a l e l e c t r o d e s , and measurement of t h e plasma impedance by m e a s o f two i n t e r n a l e l e c t r o d e s . This technique allows easy e x t r a p o l a t i o n of t h e r e s u l t s t o zero d i s c h a r g e i n t e n s i t y .

5 5

We have measured t h e e n e r g i e s of t h e 5p n s (n = 14

-

27) and 5p nd (n = 12 - 25) l e v e l s . These s e r i e s a r e l i t t l e p e r t u r b e d and can be very w e l l accounted f o r by Rydberg's formula. We have o b t a i n e d a new v a l u e of t h e f i r s t i o n i s a t i o n l i m i t . We have a l s o s t u d i e d t h e p r e s s u r e broadenings and s h i f t s of t h e 6p ⁺ nd and 6p ⁺ n s t r a n s i t i o n s . T h e i r v a l u e s and t h e i r dependence on t h e p r i n c i p a l quantum number have been i n t e r p r e t e d by a t h e o r e t i c a l c a l c u l a t i o n u s i n g Fermi and Omont models.

I

-

INTRODUCTION

I n t h i s paper, we d e s c r i b e a type of optogalvanic spectroscopy which i s i n some way i n t e r m e d i a t e between t h e two widely used methods which i n v o l v e e i t h e r d . c .

[ l ] [2] o r r a d i o f r e q u e n c y [3] [4] [S] e x c i t a t i o n and d e t e c t i o n . We use a radiofrequency d i s c h a r g e b u t t h e d e t e c t i o n i s performed by two e l e c t r o d e s l o c a t e d i n s i d e t h e c e l l t o measure t h e impedance of t h e d i s c h a r g e . Our method has two advantages. F i r s t , t h e radiofrequency e x c i t a t i o n allows us t o o b t a i n much lower d i s c h a r g e l e v e l s than d.c. e x c i t a t i o n , which d e c r e a s e s t h e s p u r i o u s phenomena due t o t h e d i s c h a r g e ( s h i f t and broadening of t h e l i n e s ) . On t h e o t h e r hand, t h e d i r e c t measurement of t h e i m - pedance of t h e d i s c h a r g e g i v e s us a measurement of t h e d i s c h a r g e i n t e n s i t y , which a l l o w s us t o e x t r a p o l a t e t h e r e s u l t s a t z e r o d i s c h a r g e i n t e n s i t y . We have used c h i s technique t o s t u d y t h e a b s o r p t i o n spectrum of xenon i n t h e range 5150-5450 8. We have observed t h a t t h e d i s c h a r g e p o p u l a t e s t h e s t a t e s of t h e 5p56p c o n f i g u r a t i o n

( s e e F i g u r e 1) w i t h a good e f f i c i e n c y . From t h e s e s t a t

5

S , t h e a b s o r p t i o n of one photon p e r m i t s t h e e x c i t a t i o n of t h e Rydberg l e v e l s 5p ns and 5p5nd. I n t h e f o l l o - wing we s h a l l denote t h e s e l e v e l s 6p, n s and nd r e s p e c t i v e l y . Although t h i s process

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983750

JOURNAL DE PHYSIQUE

i s n o t Doppler f r e e , t h e Doppler width i n xenon being s m a l l , t h e use of a CW s i n g l e - mode dye l a s e r h a s allowed us, on t h e one hand, t o measure t h e p o s i t i o n s of t h e l e v e l s with a g r e a t p r e c i s i o n , and on t h e o t h e r hand, t o s t u d y t h e s h i f t and broa- dening of t h e a b s o r p t i o n l i n e s w i t h p r e s s u r e .

F i g u r e 1

-

Energy l e v e l s of xenon

I1 - EXPERIMENTAL PROCEDURE

The experimental set-up i s shown i n F i g u r e 2 . We use a CW r i n g dye l a s e r o p e r a t i n g on a s i n g l e mode. The dye i s Cumarin 540 pumped by t h e 4880

A

l i n e of an argon i o n l a s e r . This l a s e r i s o p e r a t e d on a s i n g l e mode using a s o l i d non-coated Perot-Fabry e t a l o n and an air-spaced coated Perot-Fabry e t a l o n . Both e t a l o n s a r e servolocked, which allows a sweep of t h e s i n g l e mode without mode hops on a frequency range l a r g e r than 150 GHz [ 6 ] . The l a s e r frequency i s monitored by a monochromator

(accuracy 20 GHz) and by two Perot-Fabry e t a l o n s , 5 and 30 mm t h i c k ( f r e e s p e c t r a l ranges 30 and 5 GHz r e s p e c t i v e l y ) . The s p a c e r s of t h e 30 mm e t a l o n a r e made of c e r - v i t i n o r d e r t o d e c r e a s e the temperature d r i f t s and t h e e t a l o n i s p l a c e d i n an eva- cuated box. The Perot-Fabry e t a l o n h a s been c a l i b r a t e d i n t h e range 5150 - 5450 A by comparison w i t h t h e a b s o r p t i o n l i n e s of i o d i n e [ 7 ] . The p r e c i s i o n of a measure- ment i s 4 . 1 0 - ~ cm-'.

The experimental c e l l i s connected t o a pumping l i n e i n o r d e r t o vary t h e xenon p r e s s u r e ( t y p i c a l l y from 0.1 t o 0.4 T o r r ) . Two e x t e r n a l loops produce t h e r a d i o - frequency d i s c h a r g e . Two e l e c t r o d e s l o c a t e d i n s i d e t h e c e l l allow t h e measurement of t h e d i s c h a r g e : we apply a v o l t a g e V of t h e o r d e r of 10 V between t h e e l e c t r o d e s and t h e r e s u l t i n g c u r r e n t I i s measured u s i n g t h e r e s i s t a n c e R ( 1 kQ)

The l a s e r beam i s chopped a t a frequency of t h e o r d e r of l kHz and t h e v o l t a g e mea- sured through t h e r e s i s t a n c e R i s f e d i n t o a l6ck-in d e t e c t o r . For t h e most i n t e n s e l i n e t h e modulation r a t i o can r e a c h 20 %. We simultaneously r e c o r d t h e o u t p u t s i g n a l

t h e 18d [K] J s t a t e .

i n t e

t o r e c o r d e r

F i g u r e 2

-

Experimental set-up

To o b t a i n p r e c i s e d a t a from such a r e c o r d i n g , i t i s n e c e s s a r y t o take i n t o account t h e s h i f t and t h e broadening of t h e l i n e s with t h e p r e s s u r e and t h e d i s c h a r g e i n - t e n s i t y . Thus we have t o perform a double e x t r a p o l a t i o n a g a i n s t d i s c h a r g e i n t e n s i t y and p r e s s u r e . F i g u r e 4 shows t h e p o s i t i o n of t h e 6 p [ 5 / 2 ] 3 + 26s[3/212 t r a n s i t i o n a s a f u n c t i o n of t h e s e two parameters. This e x t r a p o l a t i o n a l s o y i e l d s t h e c o e f f i c i e n t s of t h e s h i f t and of t h e broadening w i t h p r e s s u r e .

F i g u r e 3 - Recording of t h e 6p 15/21 + 18d[K] t r a n s i t i o n

JOURNAL DE PHYSIQUE

e 0.42 Torr m 0.21 Torr

A 0.10 Torr

I

(MA) p r e s s u r e (Torr)

F i g u r e 4

-

Double e x t r a p o l a t i o n ( w i t h d i s c h a r g e i n t e n s i t y and with p r e s s u r e ) of t h e l i n e p o s i t i o n s f o r t h e 6p [ 5 / 2 ] + 26s [3/2] t r a n s i t i o n .

I11

-

SPECTROSCOPIC RESULTS

Using l a s e r e x c i t a t i o n from t h e v a r i o u s 6p l e v e l s , we have been a b l e t o observe t h e n s and nd s t a t e s . When t h e s i g n a l - t o - n o i s e r a t i o was good enough, we have performed t h e double e x t r a p o l a t i o n d e s c r i b e d b e f o r e . When t h e s i g n a l - t o - n o i s e r a t i o was n o t s u f f i c i e n t t o o p e r a t e i n t h i s way, we did t h e measurement f o r a very low d i s c h a r g e (with a c u r r e n t between t h e measure e l e c t r o d e s of 5 v A ) , t o minimize t h e s p u r i o u s e f f e c t s due t o t h e d i s c h a r g e , and f o r a p r e s s u r e of 0.2 Torr ( p r e s s u r e f o r which t h e s i g n a l - t o - n o i s e r a t i o i s optimized). Then we assumed t h a t t h e d i s c h a r g e e f f e c t i s n e g l i g i b l e and t h a t t h e p r e s s u r e s h i f t can be deduced from o t h e r s e r i e s . We have i d e n t i f i e d t h e l i n e s using ( i ) t h e c a l c u l a t i o n of t h e quantum d e f e c t s , which enabled us t o connect our measurements w i t h l e v e l s a l r e a d y t a b u l a t e d L81

( i i ) t h e c a l c u l a t i o n of t h e l i n e i n t e n s i t i e s assuming pure Racah coupling, which i s a f a i r l y good approximation.

The e n e r g i e s of t h e n s (n = 14

-

27) and nd (n = 12

-

25) s t a t e s a r e o b t a i n e d w i t h a p r e c i s i o n of 4 . 1 0 - ~ cm-'. They a r e l i s t e d i n r e f [g1

.

We s h a l l c o n c e n t r a t e h e r e on t h e quantum d e f e c t s . The quantum d e f e c t i s connected t o t h e i o n i z a t i o n li- m i t E and t o t h e energy of a l e v e l E by Rydberg's formula

p317 _-, - m n

E = E

+

^K

P3/2 n (n

-

v3/2) 2

To account f o r small p e r t u r b i n g e f f e c t s [ I O ] , we have assumed a s l i g h t l i n e a r va- r i a t i o n of t h e quantum d e f e c t w i t h energy

= v. + a ( ~

-

E ~ )

The v a l v e s o b t a i n e d f o r

Z3l2,

V. and a a r e l i s t e d i n Table I f o r t h e v a r i o u s s e r i e s . P3/2

The v a l u e s of EP1,? o b t a i n e d from t h e J = 1 s e r i e s show a r a t h e r l a r g e d i s p e r s i o n which shows thatJQLmore d e t a i l e d MQDT a n a l y s i s i s n e c e s s a r y i n t h a t c a s e .

Taking into account the results obtained for first ionisation limit

E-

E

=

97834.261 (l~f/2cm-i.

P3/2

The uncertainty comes from the statistical error and from the calibration of the Perot-Fabry etalon. This value is smaller than the values given by Moore [8] and by Grandin and Husoon [3] .

IV - COLLISION EFFECTS

We have measured the pressure shift and broadening of the following one-photon transitions

:

6p L5121 3

+

ndL71214 n

=

12 - ²⁵

6p [5/213

+

ns L3121 2 n

=

14 - 27 6p L5121 2

+

ns L3121 1 n

=

14 - ¹⁸

6p [3/21 1

+

ns 13/21 1 n

=

17 - 23

We have studied a pressure range from 0.1 to 0.4 Torr at room temperature (290 K).

We first eliminate the effect of collisions with charged particles by extrapolating the widths and positions of the lines to zero discharge intensity for each value of the pressure, as described in section 2.

It is then straightforward to determine the variation of the shift with pressure.

To obtain the broadening coefficient, we have to take into account the lineshape at zero pressure. We use natural xenon and the lines we study have an isotopic structure and a hyperfine structure. Then the lishape at zero pressure is a sum of Gaussian lines with the Doppler width. In our case, the Doppler width is 620 MHz.

The broadening due to the structure is difficult to evaluate precisely. Neverthe- less, this broadening can be assumed to be constant for the transitions of the same series 6p[KlJ

-t

nl. To simplify the ~rocessing of the experimental results, we have assumed that, for each series, the lineshape at zero pressure was approximately Gaussian with a constant full width at half maximum.

In the impact regime, the pressure broadening is Lorentzian. As we suppose that the lineshape at zero pressure is Gaussian, the observed lines are expected to have a Voigt profile which is well verified experimentally. The Lorentzian part of this profile is obtained by deconvolution.

The experimental data for the shift and broadening coefficients have been plotted

against the principal guantum numbers in Figure 5 for the ip5nd[7/2] 4 levels and

in Figure 6 for the 5p ns[3/2] 1 and 5p5ns [3/2] 2 levels. In all these cases, we have

observed a red shift with pressure.

JOURNAL DE PHYSIQUE

Figure 5

-

Broadening and s h i f t c o e f f i - F i g u r e 6

-

Broadening and s h i f t c o e f f i - c i e n t s p l o t t e d a g a i n s t t h e p r i n c i p a l c i e n t s p l o t t e d a g a i n s t p r i n c i p a l quan- quantum number n f o r t h e 6p [5/2] turn number n f o r ns[3/21 2

,

and f o r nd[7/2I4 t r a n s i t i o n s . The p o i n t s a r e ns [3/2] 1

.

The p o i n t s a r e experimen- experimental, t h e curves a r e t h e the- t a l , t h e c u r v e s a r e t h e o r e t i c a l . o r e t i c a l curves c a l c u l a t e d from

Omont's model ( 1 0 - ~ cm3 0.53 GHz

~ o r r - l a t 290 K)

The r e s u l t s have been i n t e r p r e t e d i n t h e frame of Fermi [ I l l and Omont [l21 t h e o r i e s . The i n t e r a c t i o n between an atom i n a Rydberg s t a t e A* and a p e r t u r b e r was f i r s t t h e o r e t i c a l l y s t u d i e d by Fermi. This type of c o l l i s i o n s i s e s s e n t i a l l y dominated by t h e i n t e r a c t i o n between t h e weakly bound e l e c t r o n e- w i t h B. For t h i s r e a s o n , t h e s h i f t and t h e broadening of t h e o p t i c a l t r a n s i t i o n s t o a Rydberg s t a t e does n o t depend, i n a f i r s t approximation, on t h e n a t u r e of t h e atom A b u t o n l y on t h e per- t u r b e r B. Thus Fermi's t h e o r y p r e d i c t s t h a t , i n t h e l i m i t of l a r g e quantum numbers n, t h e broadening of t h e l i n e goes t o z e r o and t h e s h i f t goes t o an asymptotic va- l u e 2vL, L being t h e s c a t t e r i n g l e n g t h of t h e e l e c t r o n f o r t h e rare-gas B (L=-6,5ao f o r xenon). This t h e o r y has been extended f o r i n t e r m e d i a t e n v a l u e s by Omont (1977).

The d l e v e l s show good agreement w i t h such a c a l c u l a t i o n whereas f o r t h e s l e v e l s t h e model has t o be r e f i n e d . This comes from t h e f a c t t h a t t h e quantum d e f e c t f o r t h e S l e v e l s i s c l o s e t o an i n t e g e r , and one cannot n e g l e c t s t r o n g c o l l i s i o n a l t r a n s f e r s t o t h e neighbouring hydrogen-like m u l t i p l e t . The use of a g e n e r a l i z e d Fermi p o t e n t i a l [l21 t o c a l c u l a t e t h i s e f f e c t [l31 y i e l d s t h e t h e o r e t i c a l curves shown which show f a i r agreement w i t h t h e experimental v a l u e s .

V

-

CONCLUSION

We s e e t h a t single-mode l a s e r e x c i t a t i o n t o g e t h e r w i t h o p t o g a l v a n i c d e t e c t i o n a l l o - wed us t o o b t a i n a l a r g e number of s p e c t r o s c o p i c r e s u l t s a s w e l l a s c o l l i s i o n a l d a t a . N e v e r t h e l e s s p r e c i s e measurements must t a k e t a k e i n t o account t h e s p u r i o u s e f f e c t s

measurements are possible only for rather low-lying levels (n < 30)

;

the lines being too much broadened by the discharge for higher levels.

REFERENCES

[l] P. CAMUS, M. DIEULIN and C. MORILLON, J. Physique Lett. 40 L513 (1979)

121 C. DELSART, J.C. KELLER and C. THOMAS, J. Phys. B At. Mol. Phys. 14 3355 (1981) [3] J.P. GRANDIN and H. HUSSON, J. Phys. B At. Mol. Phys. 14 433 (198n

[4] D.R. LYONS, A.L. SCHAWLOW and G.Y. YAN, Opt. Comm. 2 E ⁽¹⁹⁸¹⁾

[5] T. SUZUKI, Opt. Comm. 38 364 (1981)

[61 F. BIRABEN and P. LABASTIE, Opt. Comm. 5 49 (1982)

[7] S. GESTERKORN and P. LUC, Atlas du Spectre dfAbsorption de la Moldcule dfIode (Editions du C.N.R.S., 15 quai Anatole France 75700 PARIS) (1978) and

Rev. Phys. Appl. 14 791 (1979)

[8] C.E. MOORE, Atomic Energy Levels NSRDS-NBS 35 v01 I11 (Washigton DC U.S. Govt Printing Office) 1958

[g] P. LABASTIE, F. BIRABEN and E. GIACOBINO, J. Phys. B At. Mol. Phys. 15 ²⁵⁹⁵

(1982)

[l01 K.T. LU, Phys. Rev. 579 (1971) [Ill E. FERMI, Nuevo Cim. 157 (1934) 1121 A. OMONT, J. Physique 38 1343 (1977)

[l31 P. LABASTIE, E. G I A C O B ~ O and F. BIRABEN, J. Phys. B At. Mol. Phys. 2 ²⁶⁰⁵

(1982).