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IONIZATION DETECTION OF RYDBERG LINESHAPES IN STRONTIUM VAPOUR
PERTURBED BY FOREIGN GASES
D. Bruce, W. Duley
To cite this version:
D. Bruce, W. Duley. IONIZATION DETECTION OF RYDBERG LINESHAPES IN STRONTIUM
VAPOUR PERTURBED BY FOREIGN GASES. Journal de Physique Colloques, 1983, 44 (C7),
pp.C7-469-C7-477. �10.1051/jphyscol:1983746�. �jpa-00223303�
JOURNAL D€ PHYSIQUE
Colloque C7, supplement au nO1l, Tome 44, novembre 1983 page C7-469
I O N I Z A T I O N DETECTION OF RYDBERG LINESHAPES I N STRONTIUM VAPOUR PERTURBED BY FOREIGN GASES
D.M. Bruce and W.W. Duley
Department of Physics, York University, 4700 KeeZe S t r e e t , Downsview, Ontario M3J ZP3, Canada
R&sum&
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L ' e x c i t a t i o n S deux photons l a s e r 2 e t 6 u t i l i s g e pour o b t e n i r d e s p a r a m 5 t r e s de forme d e s p r o f i l s de r a i e pour d e s n i v e a u x Rydberg du S r p e r t u r b 6 s p a r d e s c o l l i s i o n s . Les Glar- g i s s e m e n t s e t l e s dgplacements d e s niveaux 5 s n s 1 s 0 e t 5snd 1~~( 7 _< n 5 52) en p r e s e n c e d e s gaz He, A r , Xe d d e s p r e s s i o n s a l - l a n t j u s q u ' 2 une atmosphPre, s o n t donngs e t compargs aux va- l e u r s t h g o r i q u e s . L ' o b s e r v a t i o n de s t r u c t u r e s s a t e l l i t e s pour l e s niveaux de Rydberg peu 6 l e v 6 s e s t a u s s i p r g s e n t g e .
A b s t r a c t
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Using l a s e r two-photon e x c i t a t i o n and i o n i z a t i o n d e t e c t i o n , we r e p o r t l i n e s h a p e p a r a m e t e r s f o r c o l l i s i o n a l l y p e r t u r b e d Rydberg l e v e l s of S r . With He, Ar, K r and Xe a s p e r t u r b e r g a s e s a t p r e s s u r e s up t o one atmosphere, t h e broad- e n i n g and s h i f t r a t e s o f 5 s n s and 5 s n d 1 ~ 2( 7 i n -L 5 2 ) a r e g i v e n and compared w i t h t h e o r e t i c a l p r e d i c t i o n s . The o b s e r v a t i o n o f s a t e l l i t e s t r u c t u r e s on low l y i n g Rydberg l e v e l s a r e a l s o p r e s e n t e d .I n t r o d u c t i o n
The e f f e c t s o f c o l l i s i o n a l p e r t u r b a t i o n s by f o r e i g n g a s e s on a t o m i c s p e c t r a l l i n e s c o n t i n u e s a s an a c t i v e a r e a of e x p e r i m e n t a l and t h e o r e t i c a l r e s e a r c h . These c o l l i s i o n a l p e r t u r b a t i o n s r e s u l t i n e x p e r i m e n t a l l y observed a b s o r p t i o n and e m i s s i o n s p e c t r a t h a t have l i n e s h a p e s which a r e asymmetric, broadened and s h i f t e d i n f r e q u e n c y r e l a t i v e t o t h e i r n a t u r a l p o s i t i o n s . I n o r d e r t o a c c o u n t f o r t h e s e observed f e a t u r e s v a r i o u s l i n e s h a p e t h e o r i e s have e v o l v e d . A t e s t of t h e t h e o r y r e q u i r e s t h a t a comparison b e made between a l i n e p r o f i l e computed u s i n g a unique i n t e r a c t i o n p o t e n t i a l and t h e c o r r e s p o n d i n 5 l i n e p r o f i l e t h a t i s e x p e r i m e n t a l l y o b s e r v e d .
T r a d i t i o n a l l y t h e a l k a l i m e t a l r e s o n a n c e l i n e s have produced t h e b u l k o f e x p e r i m e n t a l r e s u l t s a g a i n s t which t h e o r y can be t e s t e d f o r c o l l i - s i o n a l p e r t u r b e d t r a n s i t i o n s . There was a l s o e a r l y i n t e r e s t i n p e r - t u r b e d Rydberg l e v e l s w i t h o b s e r v a t i o n s of t h e p r i n c i 9 a l s e r i e s of Ma b e i n g p e r t u r b e d by r a r e g a s e s [ l ] . A t t h i s same time Fermi I21 de- v i s e d a s i m p l e model which s u c c e s s f u l l y accounted f o r t h e s h i f t and broadening of t h e Rydberg l e v e l s n e a r t h e s e r i e s l i m i t . H i s t h e o r y a l s o p r e d i c t e d t h a t t h e amount of s h i f t and broadening were independ- e n t of t h e s p e c i e s of Xydberg atom and was o n l y a f u n c t i o n of t h e t y p e of p e r t u r b e r . More r e c e n t l y F e r m i ' s t h e o r y h a s been r e f i n e d by Alekseev and Sobelman [ 3 ] Choudhury [ 4 ] and Omont [ 5 ] . The main r e s u l t of t h e s e r e f i n e m e n t s i s t h a t b r o a d e n i n g and s h i f t can now b e c a l c u l a - t e d f o r much lower s e r i e s members.
Also of c u r r e n t i n t e r e s t a r e l i n e y r o f i l e c a l c u l a t i o n s u s i n g t h e method of a u n i f i e d t h e o r y . T h i s t e c h n i q u e ?reduces complete l i n e - shape p r o f i l e s i n c l u d i n g t h e l i n e c o r e , t h e wings and a s s o c i a t e d s a t e l l i t e s . A l l a r d , Sahal-Brechot and B i r a u d [ 6 ] imglemented t h i s
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983746
JOURNAL DE PHYSIQUE
t e c h n i q u e t o c a l c u l a t e l i n e p r o f i l e s f o r t h e CS resonance l i n e s p e r t u r b e d by Xe. Kielkopf a l s o u s e d t h i s m e t h o d t o i n v e s t i g a t e some
low members of t h e p r i n c i p a l s e r i e s of CS [ 7 ] and Ba [ 8 ] which were p e r t u r b e d by Xe. The a c c u r a c y of t h e i r c a l c u l a t i o n s were t e s t e d by comparison of t h e r e s u i t s t o p r e v i o u s i y r e c o r d e d experiinelitai r e s u l t s . 47e r e p o r t h e r e t h e o b s e r v e d l i n e s h a p e p a r a m e t e r s o f c o l l i s i o n a l l y p e r t u r b e d Rydberg l e v e l s of S r . Rydberg s t a t e s were a c c e s s e d by two- photon a b s o r p t i o n and i o n i z a t i o n d e t e c t i o n was used t o r e c o r d t h e a b s o r p t i o n s i g n a l . The r a r e g a s e s used a s c o l l i s i o n a l p e r t u r b e r s i n c l u d e d He, A r , K r and Xe a t p r e s s u r e s up t o one atmosphere.
The two-photon a b s o r p t i o n spectrum of S r has been r e p o r t e d e a r l i e r by E s h e r i c k [ g ] . Observed t r a n s i t i o n s extended from t h e 5 s 2 ground s t a t e up t o 5 s n s l s o , 5snd ' D 2 and 5snd 3 ~ 1l e v e l s . The 5 s n 8
a b s o r p t i o n s e r i e s 1s p a r t i c u l a r l y s t r o n q d u e t o t h e n e a r resonance of t h e 5s5p l p l s t a t e w i t h t h e v i r t u a l i n t e r m e d i a t e s t a t e of t h e two- photon p r o c e s s . These s e t s o f t r a n s i t i o n s a r e r e f e r r e d t o a s d i r e c t t r a n s i t i o n s s i n c e an a l t e r n a t e p r o c e s s a l s o o c c u r s t h a t r e s u l t s i n t r a n s i t i o n s t o t h e same f i n a l s t a t e s . These a l t e r n a t e t r a n s i t i o n s r e s u l t when a f o r e i g n p e r t u r b e r g a s i s p r e s e n t a l o n g w i t h t h e S r vapour. R e f e r r e d t o a s h y b r i d t r a n s i t i o n s t h e y i n v o l v e a two-photon, two-step p r o c e s s where t h e f i r s t s t e p i s one-photon a b s o r p t i o n from t h e ground s t a t e i n t o t h e c o l l i s i o n a l l y p e r t u r b e d wing o f t h e 5s5p1p1 i n t e r m e d i a t e s t a t e . T h i s produces a p o p u l a t i o n i n t h e i n t e r m e d i a t e s t a t e . Atoms i n t h i s s t a t e a r e t h e n a b l e t o a b s o r b a second photon t o make a t r a n s i t i o n t o t h e 5 s n s 'S and 5snd 'DJ l e v e l s . Hybrid t r a n s i t i o n s appear a s a c o n v e n t i o n 3 one-photon spectrum w i t h a l i m i t a t 413 nm. P7hile d i r e c t t r a n s i t i o n s have h a l f t h e d i s p e r s i o n o f t h e h y b r i d t r a n s i t i o n s and proceed t o a l i m i t a t 435 nm.
Experimental
The work r e p o r t e d h e r e h a s made u s e of e s s e n t i a l l y t h e same e x p e r i - mental t e c h n i q u e t h a t we used p r e v i o u s l y f o r s t u d i e s on t h e c o l l i s i o n - a l l y ~ e r t u r b e d Rydberg s t a t e s of Rb [ 1 0 ] . A s b e f o r e t h e m e t a l vapour was c o n t a i n e d i n a s t a i n l e s s s t e e l c y l i n d r i c a l t u b e of a p p r o x i m a t e l y 2.5 cm d i a m e t e r and 30 cm l e n g t h . The e n d s o f t h e t u b e were s e a l e d w i t h w a t e r c o o l e d Pyrex windows. To o b t a l n t h e d e s i r e d p r e s s u r e o f S r vapour i n t h e t u b e t h e c e n t r a l r e g i o n was h e a t e d w i t h nichrome w i r e wound h e a t e r s s u p p l i e d by a v a r i a b l e v o l t a g e d - c . power s u p p l y . Temperature was monitored by a chromel-alumel thermocouple f i x e d c e n t r a l l y i n t h e h e a t e d r e g i o n of t h e t u b e . Temperatures c o u l d be m a i n t a i n e d w l t h i n i 5X. I n i t i a l l y a s m a l l sample o f S r m e t a l
( Q 1-2 gm) was p l a c e d i n t o t h e c e n t r e of t h e t u b e and t h i s was s u f f - i c i e n t f o r s e v e r a l weeks o f o p e r a t i o n . The u s u a l o p e r a t i n g tempera- t u r e o f t h e system was between 700-800:Z which produces a s a t u r a t e d S r vapour p r e s s u r e of a p p r o x i m a t e l y 0 . 3 t o 8 mTorr. By means o f a g a s h a n d l i n g system coupled t o t h e S r vapour c e l l t h e r a r e g a s p e r t u r b e r s p e c i e s c o u l d be a d m i t t e d a t a known p r e s s u r e . A t u n g s t e n r o d i s extended a l o n g t h e c e n t r a l a x i s of t h e c e l l and i t i s h e l d a t a b i a s of
+
9 v o l t s r e l a t i v e t o t h e s u r r o u n d i n g c e l l w a l l s . The r o dc o l l e c t e d t h e e l e c t r o n s from t h e i o n i z a t i o n p r o d u c t s which a r e pro- duced when an a b s o r p t i o n e v e n t t a k e s p l a c e . T h i s r e s u l t i n g s i g n a l i s c a p a c i t i v e l y c o u p l e d t o a g a t e d boxcar i n t e g a t o r f o r s i g n a l pro- c e s s i n g and t h e o u t p u t i s r e t a i n e d on a s t r i p - c h a r t r e c o r d e r .
The l a s e r s o u r c e employed was a NZ-pumped dye l a s e r system where t h e N2 l a s e r was a model UV 1 4 l l o l e c t i o n l a s e r c a p a b l e of p u l s e e n e r g i e s of 5 m j o u l e s a t r a t e s up t o 50 p . p . s . The dye l a s e r was i n t h e g r a z i n g i n c i d e n c e c o n f i g u r a t i o n w i t h an o u t p u t e n e r g y o f approximate- l y 0.5 mjoules and a l i n e w i d t h o f 0.2 cm-lat 440 nm.
F i g u r e 1
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Recorder t r a c e showing t h e b r o a d e n i n g and r e d s h i f t r e l a t i v e t o t h e r e f e r e n c e s c a n f o r t h e 16 'S l e v e l (on l e f t s i d e ) and t h e 1 5 l r 3 ~ l e v e l s . The p e r t u r b a t i o n s a r e due t o A r a t a d e n s i t y of 0.35 amagats and a t e m p e r a t u r e of 780K.E x p e r i m e n t a l p r o c e d u r e r e q u i r e d t h a t two of t h e above mentioned c e l l s be employed. One would c o n t a i n t h e p e r t u r b e r g a s e s a t d e n s i t i e s up t o 0.40 amagat ( h i g h p r e s s u r e c e l l ) w h i l e t h e o t h e r c o n t a i n e d o n l y v e r y low d e n s i t y o f He t o p r e v e n t t h e S r vapour from d i f f u s i n g t o t h e Pyrex windows ( r e f e r e n c e c e l l ) . The l a s e r beam was s p l i t i n t o two components and f o c u s s e d i n t o t h e c e n t r a l r e g i o n o f e a c h c e l l . By s c a n n i n g t h e l a s e r t h r o u g h an a b s o r p t i o n r e s o n a n c e a s i m u l t a n e o u s r e c o r d i n g was produced o f b o t h t h e broadened and s h i f t e d p e r t u r b e d t r a n s i t i o n a l o n g w i t h t h e r e f e r e n c e t r a n s i t i o n . T h i s p r o c e s s was c a r r i e d o u t i n t h e s p e c t r a l r e g i o n from 430 t o 520 nm which c o n t a r n s d i r e c t and h y b r l d two-photon t r a n s i t i o n s t o n l S , nlD and n3D l e v e l s f o r 6 I n S 52. The p e r t u r b e r g a s e s u s e d , He, A r , K r and Xe, were u s u a l l y a t d e n s i t i e s around 0.40 amagat b u t some lower d e n s i t i e s were a l s o employed i n o r d e r t h a t t h e l i n e a r i t y o f s h i f t and b r o a d e n i n g w i t h p e r t u r b e r d e n s i t y c o u l d be c o n f i r m e d .
C7-472 JOURNAL DE PHYSIQUE
The r e f e r e n c e s c a n p r o v i d e s b o t h t h e p o s i t i o n of t h e u n p e r t u r b e d t r a n s i t i o n and t h e i n s t r u m e n t a l w i d t h o f t h e e x c i t a t i o n r a d i a t i o n
(which i s p r i m a r i l y due t o t h e l a s e r l i n e w i d t h ) . The s h i f t of a c o l l i s i o n a l l y p e r t u r b e d t r a n s i t i o n i s simply measured by i t s s e p a r a - t i o n from t h e c o r r e s p o n d i n g t r a i l s i t i o i l o f iiie r e f e r e n c e s c a n . To d e t e r m i n e t h e F. W.H.II. of a broadened t r a n s i t i o n t h e i n s t r u m e n t a l l i n e w i d t h must be deconvolved from t h e o b s e r v e d l i n e w i d t h o f t h e p e r t u r b e d t r a n s i t i o n . T h i s o n l y becomes a f a c t o r when t h e broadened l i n e w i d t h a p p r o a c h e s t h a t o f t h e r e f e r e n c e l i n e w i d t h . When necessary an approximate deconvolved broadened l i n e w i d t h ( T B ) was c a l c u l a t e d from t h e o b s e r v e d l i n e w i d t h ( T O ) and i n s t r u m e n t a l l i n e w i d t h ( T L ) by r g = [ r O 2 - T I P ] % . T h i s method p r o v i d e s s u f f i c i e n t a c c u r a c y r e l a t i v e t o t h e measurement e r r o r s i n c u r r e d i n d e t e r m i n i n g T O and
r 1 .
A number o f s c a n s f o r e a c h p e r t u r b e r g a s were made o v e r t h e s p e c t r a l r a n g e i n d i c a t e d above. For e a c h t r a n s i t i o n t h e c a l c u l a t e d s h i f t and F.W.H.M. were a v e r a g e d and t h e mean v a l u e a l o n g w i t h i t s s t a t i s t i c a l e r r o r a r e r e p o r t e d .
F i g u r e 1 i l l u s t r a t e s a t y p i c a l s c a n t h r o u g h t h e 16 ' S , 15 I D and 1 5 3~ l e v e l s . The broadened t r a n s i t i o n s a r e s h i f t e d t o l o n g e r w a v e l e n g t h s due t o an A r d e n s i t y o f 0.35 amagats. The accompanying
r e f e r e n c e s c a n i n d i c a t e s t h e p o s i t i o n s o f t h e u n p e r t u r b e d t r a n s i t i o n s . X e s u l t s and D i s c u s s i o n
F i g u r e 2 p l o t s t h e a b s o l u t e v a l u e o f t h e a v e r a g e s h i f t r a t e s c a l - c u l a t e d f o r t h e n l ~ l e v e l s f o r t h e v a r i o u s p e r t u r b e r g a s e s . He p e r t u r b e r s produce a v i o l e t s h i f t g i v i n g p o s i t i v e s h i f t r a t e s w h i l e
t h e o t h e r p e r t u r b e r s g i v e r e d s h i f t s and n e g a t i v e s h i f t r a t e s . The s t a t i s t i c a l e r r o r s f o r t h e s h i f t r a t e s f o r a l l p e r t u r b e r g a s e s ranged U? t o a maximum o f 1 0 % w i t h t h e t y p i c a l e r r o r b e i n g approx- i m a t e l y 5 % . The r e s u l t s f o r t r a n s i t i o n s t o t h e n I S ( 7 r n L 20) and n 3~ ( 1 3 S n s 1 8 ) l e v e l s a r e n o t i n c l u d e d on t h i s f i g u r e s i n c e t h e i r v a l u e s , w i t h i n e x p e r i m e n t a l a c c u r a c y , a r e comparable t o t h e n 1~
s h i f t r a t e s . A much more l i m i t e d s e t o f h y b r i d t r a n s i t i o n s p e r t u r b e d by He and A r ( n ' S , 9 n S 1 4 ; n lD, 7 S n I 1 3 ; n 3 ~ n , = 8 , 9 ) a l s o have s h i f t r a t e s comparable t o t h o s e o b s e r v e d f o r d i r e c t t r a n s i t i o n s and a r e a l s o o m i t t e d from t h i s f i g u r e f o r t h e s a k e o f c l a r i t y . ( I t must b e remembered t h a t h y b r i d s h i f t r a t e s must be h a l v e d when con- p a r e d w i t h t h o s e o f d i r e c t t r a n s i t i o n s s i n c e t h e s i n g l e photon h y b r i d t r a n s i t i o n s have t w i c e t h e d i s p e r s i o n r e l a t i v e t o two-photon d i r e c t t r a n s i t i o n s ) . The o b s e r v e d r e l a t i o n s h i p between s h i f t r a t e and p r i n c i p a l quantum number n a s shown i n F i g u r e 2 i s c o n s i s t e n t w i t h t h e o r y . T h a t i s t h e s h i f t r a t e h a s a minimum v a l u e f o r s m a l l n and i n c r e a s e s m o n o t o n i c a l l y t o a l i m i t i n g v a l u e f o r l a r g e n . The d a t a f o r He and A r i n c l u d e s s u f f i c i e n t l y s m a l l n t o o b s e r v e t h e d e c r e a s i n g s h i f t r a t e s w h i l e f o r K r and Xe t h e s h i f t r a t e s f o r t h e l o w e s t o b s e r v e d n have a l r e a d y a t t a i n e d t h e i r l i m i t i n g v a l u e s . S i n c e a l l p r e v i o u s l y measured s h i f t r a t e s of h i g h Rydberg s t a t e s have o n l y i n v o l v e d t h e a l k a l i m e t a l s t h e n a comparison o f t h e s e
r e s u l t s w i t h p r e v i o u s e x p e r i m e n t a l l y o b s e r v e d a l k a l i m e t a l d a t a would c o n f i r m t h e a p p l i c a b i l i t y of F e r m i ' s t h e o r y t o a group o t h e r t h a n t h e a l k a l i m e t a l s . P r e v i o u s l y we measured t h e s h i f t r a t e s f o r t h e n 2~ l e v e l s of Rb p e r t u r b e d by He and A r f o r 8 r n S 35 [10]. The l i m i t i n g r a t e f o r He and A r p e r t u r b e d Rb t r a n s i t i o n s a r e 2.8 t 0.3 and 5.0 1 0.4 cm-l/amagat r e s p e c t i v e l y w h i l e f o r S r t h e c o r r e s p o n d i n 5 r a t e s a r e 2.65
+
0.15 and 5.35*
0.40 cm-l/amagat. The most r e c e n t d a t a f o r K r and Xe p e r t u r b e d t r a n s i t i o n s a r e g i v e n by B r i l l e t and G a l l a g h e r [ l 1 1 where t h e y r e p o r t s h i f t r a t e s f o r s e l e c t e d 2~ and 2 D l e v e l s u s i n g two-photon a b s o r p t i o n t e c h n i q u e s . For 30 2 ~ which , i s t h e h i g h e s t l y i n g l e v e l r e p o r t e d , t h e s h i f t r a t e s a r e 10 - 4+
0.5and 20.9
+
0 . 9 cm-'/amagat f o r K r and Xe r e s p e c t i v e l y . The corresgond-- i n g S r r a t e s which we have measured a r e 9.9 2 0 . 3 and 21.0+
1 . 0cm-l/amagat. The c o n s i s t e n c y of t h e s e r e s u l t s f o r S r and Rb i n d i c a t e t h a t F e r m i ' s assumption [ 2 ] t h a t t h e r a t e o f s h i f t i s i n d e p e n d e n t of t h e s p e c i e s of Rydberg atom and depends o n l y upon t h e p e r t u r b i n g s p e c i e s i s c o r r e c t . I t i s a l s o e x p e c t e d t h a t s h i f t r a t e s a r e n o t a s s e n s i t i v e a s t h e b r o a d e n i n g r a t e s t o t h e t y p e of Rydberg atom s i n c e t k p o l a r i z a t i o n i n t e r a c t i o n component c o n t r i b u t e s o n l y 1 0 % t o t h e t o t a l s h i f t r a t e f o r He, K r and Xe and 20% f o r A r ( s e e t a b l e 11, r e f . 5 ) .
F i g u r e 2 - The s h i f t r a t e s f o r He, A r , K r and Xe on 5snd a r e g i v e n i n u n i t s o f cm-l/amaGat. The e n e r g y u n i t s a r e measured a t t h e l a s e r f r e q u e n c y .
I t s h o u l d a l s o be n o t e d t h a t t h e i n t e r m e d i a t e s t a t e , 5s5p ' p 1 , which c o n t r i b u t e s t o t h e h y b r i d t r a n s i t i o n s s n o u l d n o t be s i g n i f i c a n t i n a f f e c t i n g t h e o b s e r v e d s h i f t o f t h e upper s t a t e s i n c e He, A r and Xe p e r t u r b e s produce a s h i f t of t h e 5 l p l l e v e l of o n l y 0 . 0 3 , 0.27 and 0 . 1 1 cm- /amagat [ 1 2 ] .
f
F i g u r e 3 r e p r e s e n t s t h e c a l c u l a t e d b r o a d e n i n g r a t e s (FWHM) f o r He and and A r p e r t u r b e r s . E r r o r l i m i t s r a n g e from a maximum o f 0.35 cm-l/
amagat f o r t h e l o w e s t l y i n g l e v e l s t o a minimum of 0.25 cmdl/amagat f o r t h e upper l e v e l s of t h e s e r i e s . The b r o a d e n i n g r a t e s f o r K r and Xe were d e t e r m i n e d f o r o n l y a few nlD l e v e l s n e a r t h e upper l i m i t and it was found t h a t t h e y m a i n t a i n e d r e l a t i v e l y c o n s t a n t v a l u e s i n t h i s r e g i o n . The c a l c u l a t e d r a t e s f o r K r and ::e a r e 2.0
+
0.2 and5.5
+
1 . 0 cm-l/amagat r e s p e c t i v e l y . A s f o r t h e c a s e o f s h i f t r a t e s a s m a l l e r s e l e c t i o n o f n l S and n 3 ~ l e v e l s were o b s e r v e d and t h e s e have b r o a d e n i n g r a t e s s i m i l a r t o t h o s e c a l c u l a t e d f o r t h e n l l e v e l s . ~ Comparing t h e He and A r r e s u l t s w i t h t h e p r e v i o u s n2D s e r i e s b r o a d e n i n g r a t e s of Bruce e t a l . [ l 0 1 a g a i n shows t h a t t h e r e i s goodagreement t h r o u g h o u t t h e range o f o b s e r v e d l e v e l s .
JOURNAL DE PHYSIQUE
n 'D LEVEL
F i g u r e 3 - The b r o a d e n i n g r a t e s f o r He and A r on t h e S r Rydberg s e r i e s 5snd 1~ a r e g i v e n i n u n i t s of cm-l/amagat. The b r o a d e n i n g i s measured a s t h e F.iJ.H.11. a t t h e l a s e r f r e q u e n c y . The f u l l c i r c l e s and s q u a r e s a r e t h e e x p e r i m e n t a l p o i n t s and t h e s o l i d and dashed l i n e s a r e t h e c a l c u l a t e d v a l u e s .
B r i l l e t and G a l l a g h e r [ l 1 1 g i v e b r o a d e n i n g r a t e s f o r Rr and Xe on t h e 30 2~ l e v e l of ?Rb o f 1 . 6 5 ? 0.07 and 4 . 5 k 0 . 4 cm-l/amagat. The r e a s o n a b l e agreement between b r o a d e n i n g r a t e s f o r S r and P& f o r t h e s e f o u r r a r e g a s e s c o n f i r m s t h e v a l i d i t y o f F e r m i ' s a s s u r q t i o n t h a t c o l l i s i o n a l p e r t u r b a t i o n s on Zydberg l e v e l s a r e i n d e p e n d e n t of t h e e x c i t e d s p e c i e s . The b r o a d e n i n g r a t e s a r e a more r i g o r o u s t e s t of t h i s a s s u m g t i o n t h a n a r e t h e s h i f t r a t e s because t h e b r o a d e n i n g f o r l a r g e n i s dominated by t h e p o l a r i z a t i o n component of t h e Fermi potent- i a l . S i n c e t h e p o l a r i z a t i o n p o t e n t i a l i s a r r i v e d a t by r e p l a c i n g t h e a t o m i c c o r e o f t h e e x c i t e d Rydberg atom by a p o s i t i v e p o i n t c h a r g e t h e n i t i s t h i s ? a r t of t h e model t h a t would be most s e n s i t i v e t o t h e s p e c i e s o f Rydberg atom. From t h e abcve d a t a i t a p p e a r s , however, t h a t F e r r ~ i ' s a s s u m p t i o n i s v a l i d w i t h i n t h e a c c u r a c y a v a i l a b l e i i ? t k s e e x p e r i m e n t s .
I n c l u d e d on f i g u r e 3 a r e t h e c a l c u l a t e d b r o a d e n i n g r a t e s f o r He and A r a t a t e m p e r a t u r e of 725K. The c a l c u l a t i o n s shown, which e x t e n d t o low n v a l u e s , a r e d e r i v e d from e q u a t i o n s 4.15 and 4.17 of r e f e r e n c e 5 . The t o t a l c a l c u l a t e d b r o a d e n i n g r e s u l t s f r o n two t e r m s , one from t h e p o L a r i z a t i o n p o t e n t i a l and t h e o t h e r from t h e e l a s t i c s c a t t e r i n g o f t h e Rydberg e l e c t r o n . For l a r g e n t h e p o l a r i z a t i o n term dominates and s i n c e i t i s independent.of n t h e n a ixinimum b r o a d e n i n g r a t e i s approached f o r l a r g e n . A t s m a l l e r n t h e e l a s t i c s c a t t e r i n g of t h e Rydberg e l e c t r o n p r e d o m i n a t e s and i s r e f l e c t e d i n t h e l a r g e r b r o a d e n i n g r a t e s . T h i s i s t h e term n o t i n c l u d e d i n F e r m i ' s [ 2 ] o r i g i n a l t r e a t m e n t and hence r e s t r i c t e d h i s a n a l y s i s t o o n l y l a r g e 11, i . e . n 1 2 0 . Another f a c t o r which c a n i n f l u e n c e t h e b r o a d e n i n g i s t h e i n e l a s t i c s c a t t e r i n g o f t h e Rydberg e l e c t r o n by t h e p e r t u r b e r g a s e s . As t h e Rydberg l e v e l s have d e c r e a s i n g e n e r g y s e p a r a t i o n ( A E ) f o r i n c r e a s i n g n , t h e n t h e r e becomes i n c r e a s i n g p r o b a b i l i t y t h a t an e l e c t r o n - p e r t u r b e r g a s i n t e r - a c t i o n w i l l i n d u c e a t r a n s i t i o n . Omont [ 5 ] d e t e r m i n e d t h a t t h i s
a d i a b a t i c c o n d i t i o n s i s s a t i s f i e d r'or n v a l u e s such t h a t n2 B < < An, where An = 1 and O i s t h e a v e r a g e k i n e t i c c o l l i s i o n v e l o c i t y of t h e p e r t u r b e r gas
(O
i s i n atomic u n i t s ) . For l a r g e r n where i n e l a s t i c s c a t t e r i n t h e n becomes r e l e v a n t , Alelcseev and Sobelman [ 3 ] g i v ers,
= (8Lq/a)iSp a s t h e a d d i t i v e c o n t r i b n t i o i l t o t h e b r o a d e n i n g r a t e due t o inelastic c o l l i s i o n s (wherer s c
i s t h e F . W . H . M . , L i s t h e e l e c t r o n s c a t t e r i n g l e n g t h on t h e r a r e gas p e r t u r b e r and tJp i s t h e p e r t u r b e r d e n s i t y ) . The e f f e c t of t h i s term i s i n c l u d e d i n t h e c a l - c u l a t e d b r o a d e n i n g r a t e s f o r t h e l a r g e r n v a l u e s and shown i n f i g u r e 3 a s t h e s h o r t e r l i n e s . Even by t h e i n c l u s i o n o f t h i s i n e l a s t i cc o l l i s i o n term t h e observed b r o a d e n i n g r a t e s exceed t h o s e t h a t a r e c a l c u l a t e d . I t i s unlilcely t h a t t h i s d i f f e r e n c e c o u l d be due t o s e l f - b r o a d e n i n g because of t h e S r vapour p r e s s u r e which does n o t exceed a few mTorr. A t t h i s vapour p r e s s u e t h e amount o f s e l f - b r o a d e n i n g would be i n t h e o r d e r o f 1 0 ~ ~a c c o r d i n g t o r a t e s observed f o r Rb and CS [ 1 3 , 1 4 1 . T h i s i s i n s i g n i f i c a n t r e l a t i v e t o t h e f o r e i g n gas broadening.
F i g u r e 4
-
a e c o r d e r t r a c e of t h e s a t e l l i t e s observed on t h e h i g h energy s i d e o f t h e d i r e c t 5 s 2 s I S l e v e l f o r an A r d e n s i t y o f 0.35 amagats and a t e m p e r a t u r e of 775K.F i g u r e 1 i l l u s t r a t e s t h e g e n e r a l l i n e s h a p e observed f o r a l l l e v e l s w i t h n 2 1 2 . They a p p e a r a s b e i n g a p p r o x i m a t e l y L o r e n t z i a n - s h a p e d broadened t r a n s i t i o n s and remain s y m m e t r i c a l . T h i s i s n o t t h e c a s e f o r lower l y i n g s e r i e s numbers where t h e s e b r o a d e r l i n e s become asymmetrical and develop wings on t h e v i o l e t o r r e d s i d e f o r He and A r p e r t u r b e r s a t d e n s i t i e s a s low a s 0.2 amagats. O t h e r f e a t u r e s t h a t a p p e a r a r e a r a t h e r d i f f u s e r e d s h o u l d e r on t h e 7 l ~ t r a n s i t i o n and a p a i r o f w e l l r e s o l v e d s a t e l l i t e s on t h e h i g h f r e q u e n c y s i d e o f t h e 8 l ~ t r a n s i t i o n . An e x p e r i m e n t a l t r a c e of t h e s e s a t e l l i t e s a p p e a r s i n f i g u r e 4 where on t h e l e f t s i d e of t h e diagram t h e A r broadened 8 l 5 l e v e l i s s e e n accompanied by t h e r e f e r e n c e s i g n a l . These s a t e l l i t e s were o b s e r v e d f o r b o t h He and A r a t d e n s i t i e s between 0.3 and 0.4 amagats. Over t h i s p r e s s u r e range t h e r e was no measurable s h i f t i n t h e p o s i t i o n of e i t h e r s a t e l l i t e . For He(Ar) t h e p o s i t i o n of t h e c l o s e s t s a t e l l i t e r e l a t i v e t o t h e 8lS r e f e r e n c e l i n e was 13
+
1 cm-l( 9 . 0
+
1 cm-l) and f o r t h e f u r t h e s t 34+
2 cm-l (30+
2 cm-l). A t r a c e of t h e c l o s e s t s a t e l l i t e u s i n g an expanded v e r t i c a l s c a l e i s g i v e n i n f i g u r e 5. The measured F.W.H.M. i s a p p r o x i m a t e l y 7.5 cm-l.JOURNAL DE PHYSIQUE
F i g u r e 5
-
A v e r t i c a l l y expanded t r a c e of t h e s a t e l l i t e c l o s e s t t o t h e 8 l ~ t r a n s i t i o n s e e n i n f i g u r e 4 . The v e r t i c a l s c a l e t o t h e r i g h t o f t h e p o i n t i n d i c a t e d i s i n c r e a s e d by a f a c t o r o f t e n . The p e r t u r b e r gas i s A r a t 0.35 amagats and a t a t e m p e r a t u r e of 775K.No f u r t h e r a n a l y s i s on t h e s e s a t e l l i t e s o r l i n e s h a p e s h a s y e t been a t t e m p t e d b u t t h e s e , r e s u l t s i n d i c a t e t h a t t h i s e x p e r i m e n t a l system h a s t h e p o t e n t i a l e o p r o v i d e more d a t a f o r l i n e s h a p e measurements, p a r t i c u l a r l y w i t h $he h e a v i e r r a r e g a s e s . C u r r e n t u n i f i e d t h e o r i e s o f c o l l i s i o n a l l i n e p r o f i l e s e n a b l e c a l c u l a t i o n s t o be made o f t h e complete l i n e s h a p e , i n c l u d i n g s a t e l l i t e s . Thus any a v a i l a b l e e x p e r i - mental p r o f i l e s would a s s i s t i n d e t e r m i n i n g t h e v a l i d i t y o f t h e t h e o r e t i c a l model o r t h e chosen p o t e n t i a l s used by t h a t model. A s an example o f t h i s t e c h n i q u e Kielkopf h a s c a l c u l a t e d s p e c t r a f o r b o t h CS [ 7 ] and Ba [ 8 ] p r i n c i p a l s e r i e s members f o r 7 i n 5 11 ( p e r t u r b e d by Xe)
.
These s p e c t r a i n c l u d e b o t h w e l l d e f i n e d s a t e l l i t e s t o t h e r e d o f t h e CS l i n e s and s h o u l d e r s on t h e r e d wings o f t h e Ba l i n e s . I n summary, we have r e p o r t e d s h i f t and b r o a d e n i n g r a t e s f o r a l a r g er a n g e of Rydberg l e v e l s o f S r p e r t u r b e d by H e , A r , Xr and X e .
T h e o r e t i c a l c a l c u l a t i o n s u s i n g c u r r e n t t h e o r y have b e e n performed f o r t h e b r o a d e n i n g r a t e s o f l e v e l s w i t h i n t e r m e d i a t e and h i g h n. I n g e n e r a l t h e agreement between t h e s e r e s u l t s a r e s a t i s f a c t o r y e x c e p t a t n i g h n where t h e e x p e r i m e n t a i v a i u e s a r e c o n s i s t e n t i y i a r g e r t h a n t h o s e c a l c u l a t e d . I t i s a l s o shown t h a t t h i s t y p e of e x p e r i m e n t i s c a p a b l e of p r o d u c i n g h i g h r e s o l u t i o n l i n e s h a p e p r o f i l e s f o r low Rydberg s t a t e s .
T h i s r e s e a r c h was s u p p o r t e d by a g r a n t from t h e N a t u r a l S c i e n c e s and E n g i n e e r i n g R e s e a r c h C o u n c i l o f Canada.
R e f e r e n c e s
[ l
1
~ G c h t b a u e r , C. and S c h u l z , P - , Z . Physilc97
(1935) 699.[2 ] Fermi, E., Nuovo Cimento
11,
(1934) 1 5 7 .[ 3 ] A l e k s e e v , V.A. and Sobelman, I . I . , Sov. Phys. JETP
12
(1966) 882.[4 l Choudhury, 14.H.
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Atom. Molec. Phys.
1
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[ 8
1
K i e l k o p f , J . F . , J . Phys. B: Atom. Kolec. Phys. (1978) 25.[9 ] E s h e r i c k , P., Phys. Rev. &A (1977) 1920.
DO] Bruce, D.M., M i r z a , M . Y . and Duley, X . W . , O p t i c s Cornrn.
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D 1 1
B r i l l e t , W.L. and G a l l a g h e r , A . , Phys. Rev. A s (1980) 1012.P21 LJang, S.Y. and C h ' e n , S.Y., J . Q u a n t . S p e c t r o s c . R a d i a t . T r a n s f e r 22 (1979) 87.
B31 ~ a t G Y . and S t o i c h e f f , B.P., J. Opt. Soc. Am. 66 (1976) 490.
p 4 ] M a z i n g , M.A. and S e r a p i n a s , P.D., Sov. Phys.
