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DOPPLER-FREE TWO-PHOTON LASER SPECTROSCOPY OF RYDBERG STATES IN
ALKALINE-EARTH ELEMENTS WITH THERMIONIC DETECTION
R. Beigang, A. Timmermann
To cite this version:
R. Beigang, A. Timmermann. DOPPLER-FREE TWO-PHOTON LASER SPECTROSCOPY OF RYDBERG STATES IN ALKALINE-EARTH ELEMENTS WITH THERMIONIC DETECTION.
Journal de Physique Colloques, 1983, 44 (C7), pp.C7-137-C7-148. �10.1051/jphyscol:1983712�. �jpa-
00223269�
JOURNAL DE PHYSIQUE
Colloque C7, suppl6ment au n O 1 l , Tome 44, novembre 1983 page C7-137
DOPPLER-FREE TWO-PHOTON LASER SPECTROSCOPY OF RYDBERG STATES IN ALKALINE-EARTH ELEMENTS WITH THERMIONIC DETECTION
R. Beigang and A . Timmermann
I n s t . f . Atom und FestkBrpernhysik, FU Berlin, 1000 Berlin 33, F.R. G.
R6sumS
-
La s p e c t r o s c o p i e 3 deux-photons s a n s e f f e t Doppler a 6 t $ u t i l i s S e pour G t u d i e r les S n e r g i e s d e s n i v e a u x , l e s dsplace-.ments i s o t o p i q u e s e t l e s s t r u c t u r e s h y p e r f i n e s d e s s 6 r i e s de Rydberg msns e t msnd d e s 6lGments a l c a l i n o - t e r r e u x Mg (m=3), Ca
(m=4)
,
S r (m=5) e t Ba (m=6) e n t r e l e s nombres q u a n t i q u e s p r i n c i - paux n=3 e t 150. Le m6lange s i n g u l e t - t r i p l e t dQ aux i n t e r a c t i o n s de c o n f i g u r a t i o n s e t l e s e f f e t s h y p e r f i n s i n d u i t s o n t &t& d s t e c - t 6 s . L ' u t i l i s a t i o n d ' u n anneau de d i o d e s thermo-ionique a permis de r s a l i s e r d e s mesures 3 h a u t e r s s o l u t i o n j u s q u ' a u x nombres q u a n t i q u e s p r i n c i p a u x n % 160.A b s t r a c t
-
D o p p l e r - f r e e two-photon s p e c t r o s c o p y was a p p l i e d t o i n v e s t i g a t e l e v e l e n e r g i e s , i s o t o p e s h i f t s and h y p e r f i n e s t r u c - t u r e s of msns and msnd Rydberg s e r i e s o f a l k a l i n e e a r t h e l e m e n t s Mg (m=3),
Ca ( m = 4 ),
S r (m=5) and Ba (m=6) between p r i n c i p a l quantum numbers n=3 and 150. A s a r e s u l t c o n f i g u r a t i o n i n t e r a c - t i o n s , s i n g l e t - t r i p l e t mixing and h y p e r f i n e - i n d u c e d e f f e c t s were d e t e c t e d . The u s e of a t h e r m i o n i c r i n g d i o d e a l l o w e d f o r h i g h r e s o l u t i o n measurements up t o p r i n c i p a l quantum numbers n Q 160.I . INTRODUCTION
The a l k a l i n e e a r t h e l e m e n t s c a n form two t y p e s of Rydbera s e r i e s con- v e r g i n g t o d i f f e r e n t i o n i z a t i o n l i m i t s . I n t h e main s e r i e s o n l y one v a l e n c e e l e c t r o n i s e x c i t e d whereas t h e second e l e c t r o n remains i n t h e l o w e s t p o s s i b l e c o n f i g u r a t i o n r e s u l t i n g i n Rydberg s e r i e s msnl (1 = s , p , d ,
. . .
) w i t h t h e m s 2~ i o n i z a t i o n l i m i t . I f b o t h e l e c t r o n s a r e e x c i t e d t h e doubly exciteA/&ydberg s e r i e s m ' l ' n l converge w i t h i n - c r e a s i n g n t o t h e l i m i t s m ' l ' 2 ~ J of t h e c o r r e s p o n d i n g i o n which a r e always h i g h e r i n e n e r g y compared t o t h e i o n i z a t i o n l i m i t of t h e main s e r i e s . Few members of t h e s e s e r i e s may l i e below t h e f i r s t l i m i t and c a u s e p e r t u r b a t i o n s of t h e r e g u l a r s e r i e s due t o c o n f i g u r a t i o n mixing which i n t u r n can l e a d t o s i n g l e t - t r i p l e t mixing. The d e t e r m i n a t i o n of l e v e l e n e r g i e s a n a l y s e d by Multi-Channel--Quantum-Defect-Theory (MQDT) / l - 5 / , l i f e t i m e s /6-9/, S t a r k - s h i f t s / 6 / , and g - f a c t o r /10/ measure- ments were s u c c e s s f u l l y employed i n t h e p a s t t o i n v e s t i g a t e c o n f i g u r a - t i o n i n t e r a c t i o n s and s i n g l e t - t r i p l e t mixing.Another q u a n t i t y which i s v e r y s e n s i t i v e t o t h e t y p e of c o u p l i n g between t h e two v a l e n c e e l e c t r o n s and t o c o n f i g u r a t i o n mixing i s t h e h y p e r f i n e s t r u c t u r e . Using t h e h y p e r f i n e s t r u c t u r e a s t h e probe even weak p e r t u r b a t i o n s a r e o b s e r v a b l e w h i c b c a n n o t b e d e t e c t e d from o t h e r measurements. I n c h a p t e r I11 we w i l l p r e s e n t some s e l e c t e d r e s u l t s t o
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983712
C7-138 JOURNAL DE PHYSIQUE
d e m o n s t r a t e t h e h i g h s e n s i t i v i t y of t h i s method.
I n s t e a d of u s i n g t h e h y p e r f i n e s t r u c t u r e merely a s a p r o b e , t h e hyper- f i n e i n t e r a c t i o n o f t h e lower m s v a l e n c e e l e c t r o n i t s e l f can c a u s e c o n s i d e r a b l e p e r t u r b a t i o n s . T h i s was a l r e a d y p o i n t e d o u t b y L i a o e t 21.
/11/ i n t h e c a s e of 3 ~ e where t h e h y p e r f i n e i n t e r a c t i o n o f t h e I s open- s h e l l e l e c t r o n g i v e s r i s e t o a s i g n i f i c a n t m o d i f i c a t i o n of t h e hyper- f i n e s t r u c t u r e of t h e n 3 ~ s t a t e s . Hyperf ine-induced e f f e c t s dominate i f t h e energy s e p a r a t i o n between n e i g h b o r i n g l e v e l s i s comparable t o o r s m a l l e r t h a n t h e F e r m i - c o n t a c t t e r m of t h e m s v a l e n c e e l e c t r o n . T h i s i s s y s t e m a t i c a l l y t h e c a s e f o r Rydberg s e r i e s : With i n c r e a s i n g p r i n c i p a l quantum number n t h e s i n g l e t - t r i p l e t s e p a r a t i o n d e c r e a s e s w i t h 1 / n * 3 whereas t h e F e r m i - c o n t a c t t e r m remains c o n s t a n t i n f i r s t o r d e r n e g l e c t i n g s c r e e n i n g e f f e c t s . The h y p e r f i n e - i n d u c e d s i n g l e t - t r i p l e t mixing r e s u l t s i n a n--dependent l e v e l s h i f t and a v a r i a t i o n of t h e t r a n s i t i o n p r o b a b i l i t y . Examples f o r b o t h e f f e c t s w i l l b e g i v e n i n c h a p t e r I V .
F i n a l l y , w i t h i n c r e a s i n g n t h e energy s e p a r a t i o n between c o n s e c u t i v e p r i n c i p a l quantum numbers n becomes comparable t o t h e F e r m i - c o n t a c t energy and l e v e l s w i t h d i f f e r e n t n b u t t h e same t o t a l a n g u l a r momenta F w i l l i n t e r a c t . F i r s t examples of t h i s hyperf ine--induced n-mixing w i l l a l s o be p r e s e n t e d i n c h a p t e r I V . I n o r d e r t o measure t h e s e i n t e r - a c t i o n s h i g h r e s o l u t i o n s p e c t r a above p r i n c i p a l quantum numbers
n 100 a r e r e q u i r e d . I n t h i s energy r a n g e even s m a l l f i e l d s c a u s e s t r o n g p e r t u r b a t i o n s a s t h e p o l a r i z a b i l i t y of t h e Rydberg atoms i n - c r e a s e s p r o p o r t i o n a l w i t h n7. P a r t i c u l a r c a r e h a s t o be t a k e n t o a v o i d s t r a y e l e c t r i c f i e l d s i n t h e t h e r m i o n i c d i o d e . T h e r e f o r e we have de- veloped a new t h e r m i o n i c r i n g d i o d e which a l l o w s f o r h i g h r e s o l u t i o n measurements up t o p r i n c i p a l quantum numbers n % 160. A s t h i s d i o d e i s of p a r t i c u l a r importance f o r t h e measurements c l o s e t o t h e i o n i z a t i o n l i m i t i t w i l l b e d e s c r i b e d i n d e t a i l i n s e c t i o n 11.
11. EXPERIMENTAL
I n o r d e r t o overcome t h e Doppler b r o a d e n i n g and t o a c h i e v e h i g h re-.
s o l u t i o n , a Doppler-free e x p e r i m e n t a l s e t u p was used i n combination w i t h a narrow-band cw dye l a s e r . The h i g h r e s o l u t i o n i s n e c e s s a r y a s t h e s e p a r a t i o n between d i f f e r e n t i s o t o p e s and h y p e r f i n e components i s of t h e o r d e r of 10 t o 500 MHz. Two-photon s p e c t r o s c o p y i s p a r t i c u l a r l y w e l l s u i t e d f o r t h e i n v e s t i g a t i o n s o f h i g h Rydberg s t a t e s i n Car S r , and Ba, s i n c e t h e energy d i f f e r e n c e between t h e ground s t a t e and t h e Rydberg s t a t e s can be b r i d g e d by two photons of a n energy a c c e s s i b l e w i t h cw dye l a s e r s . The o u t p u t power n e c e s s a r y f o r two-photon t r a n s i - t i o n s i s o b t a i n a b l e w i t h r i n g l a s e r systems. These l a s e r systems a r e i d e a l t o o l s e s p e c i a l l y f o r h i g h - r e s o l u t i o n two-photon s p e c t r o s c o p y due t o t h e h i g h single-mode o u t p u t power and narrow bandwidth.
The measurements r e p o r t e d h e r e were c a r r i e d o u t w i t h a commercial r i n g dye l a s e r i n t h e wavelength r e g i o n between 406 and 4 8 0 nm, which was covered by t h r e e d i f f e r e n t dyes. For t h e s p e c t r o s c o p y of Ca, S r , and Ba, S t i l b e n e 1 , S t i l b e n e 3 , and Coumarine 102 were u s e d , r e s p e c t i v e l y . A l l t h e s e dyes were pumped w i t h t h e uv l i n e s o f an ~ r + i o n l a s e r pro- v i d i n g a maximum pump power o f 3.6 W.
The dye l a s e r was f r e q u e n c y s t a b i l i z e d t o an e x t e r n a l Fabry-Perot r e - f e r e n c e c a v i t y r e s u l t i n g i n a l i n e w i d t h of a b o u t 1 MBz. The t o t a l con- t i n u o u s single-mode t u n i n g r a n g e e x t e n d e d o v e r 30 GHz, more t h a n s u f - f i c i e n t t o measure a l l h y p e r f i n e components and i s o t o p e s o f one Rydberg s t a t e i n a s i n g l e s c a n .
RING LASER 1
F i g . 1
-
E x p e r i m e n t a l s e t u p f o r D o p p l e r - f r e e two-photon s p e c t r o - SCOPYABSOLUTE WAVE -
LENGTH CALIBRATION
RELATIVE FREOUENCY MEASUREMENT
R = 200
TO LOCK I N
1
D o p p l e r - f r e e s i g n a l s were o b t a i n e d by a p p l y i n g t h e u s u a l geometry f o r h i g h - r e s o l u t i o n two-photon s p e c t r o s c o p y a s s k e t c h e d i n F i g . 1. The m e t a l vapor was produced i n a s t a i n l e s s s t e e l h o t p i p e h e a t e d t o a t e m p e r a t u r e which c o r r e s p o n d s t o a vapor p r e s s u r e of a p p r o x i m a t e l y 2 5 mTorr. To o b t a i n t h e power d e n s i t y n e c e s s a r y f o r t h e two-photon pro-.
c e s s t h e l a s e r beam was f o c u s e d i n t o t h e c e n t e r of t h e p i p e and r e - f l e c t e d back v i a a s p h e r i c a l rr.irror. The e x c i t e d Rydberg atoms were t h e n d e t e c t e d by a space-charge l i m i t e d t h e r m i o n i c d i o d e w i t h s u b s t a n - t i a l q a i n f o r d e t e c t i o n o f i o n i z a t i o n . T h i s d e t e c t i o n method h a s proven t o b e i n p a r t i c u l a r w e l l s u i t e d f o r t h e s p e c t r o s c o p y of h i g h Rydberg s t a t e s i n a c e l l geometry. The s e n s i t i v i t y i n c r e a s e s w i t h i n c r e a s i n g p r i n c i p a l quantum number n and t h e r e f o r e p a r t l y compensates f o r t h e d e c r e a s i n g t r a n s i t i o n p r o b a b i l i t y . The p r i n c i p l e and optimum o p e r a t i o n c o n d i t i o n s have been d e s c r i b e d i n d e t a i l e l s e w h e r e / 1 2 , 1 3 / . Here we want t o f o c u s on p a r t i c u l a r problems c o n n e c t e d w i t h t h e e x c i t a t i o n and d e t e c t i o n of v e r y h i g h Rydberg s t a t e s ( p r i n c i p a l quantum numbers n > 1 0 0 ) . The p o l a r i z a b i l i t y o f t h e e x c i t e d Rydberg atoms i n c r e a s e s d r a s t i c a l l y ( S n 7 ) and even s m a l l e l e c t r i c f i e l d s may c a u s e l i n e broadening and l i n e s h i f t s . For t h i s r e a s o n t h e t h e r m i o n i c d i o d e i s u s u a l l y d e v i d e d by a n e t a l g r i d i n an e x c i t a t i o n and a d e t e c t i o n chamber t o p r o v i d e a f i e l d f r e e r e g i o n below t h e g r i d . The e l e t r i c f i e l d from t h e s p a c e c h a r g e s produced by t h e h e a t e d w i r e i n t h e d e t e c - t i o n chamber i s t h u s s h i e l d e d from t h e e x c i t a t i o n zone. The e x c i t e d Rydberg atoms d i f f u s e t h r o u g h t h e g r i d i n t o t h e d e t e c t i o n chamber t o produce an i o n i z a t i o n s i g n a l . Using t h i s s h i e l d i n g Rydberg s t a t e s of Rb up t o p r i n c i p a l quantum numbers n=138 were d e t e c t e d / 1 4 / .
I n t h e c a s e of t h e a l k a l i n e e a r t h e l e m e n t s , however, t h i s t y p e of s h i e l d i n g f a i l s . Due t o t h e h i g h t e m p e r a t u r e ( T % 600
...
800 OC) neces-s a r y t o produce a s u f f i c i e n t vapor p r e s s u r e a l l m e t a l p a r t s i n t h e h o t zone of t h e p i p e w i l l produce s p a c e c h a r g e s . T h i s a l s o h o l d s f o r t h e s h i e l d i n g g r i d i t s e l f and t h e m e t a l w a l l s . T h e r e f o r e it i s n e a r l y i m - - p o s s i b l e t o p r o v i d e a f i e l d f r e e and r e p r o d u c i b l e e x c i t a t i o n of t h e
JOURNAL DE PHYSIQUE
Rydberg atoms.
A s a consequence s p e c t r a above p r i n c i p a l quantum numbers n 85 a r e s t r o n g l y p e r t u r b e d by t h e S t a r k e f f e c t . I n F i g . 2 a t y p i c a l example of a Doppier-free e x c i t a t i o n spectrum of S r a t n=100 i s shown u s i n 9 a s h i e l d e d d i o d e w i t h no a d d i t i o n a l v o l t a g e a c r o s s t h e p i p e . The f o u r s t a b l e S r i s o t o p e s c a n n o t b e r e s o l v e d a l t h o u g h t h e i r e n e r g y s e p a r a t i o n i s i n t h e o r d e r of 100 t o 200 MHz.
The t h e r m i o n i c r i n g d i o d e we want t o d e s c r i b e h e r e c o n s i d e r a b l y re-- duces t h e i n f l u e n c e of e l e c t r i c s t r a y f i e l d s and i n c r e a s e s t h e d e t e c - t i o n s e n s i t i v i t y due t o a n improved d e t e c t i o n g e o n e t r y . A s a conse- quence t h e r i n g d i o d e a l l o w s f o r h i g h - r e s o l u t i o n s p e c t r o s c o p y of Ryd- b e r g atoms up t o p r i n c i p a l quantum numbers n 160. The new d i o d e i s based on a h i g h l y symmetric arrangement of t h e s p a c e c h a r g e s and t h u s compensating f o r t h e r e s u l t i n g e l e c t r i c f i e l d i n f i r s t o r d e r . The p r i n c i p l e i s shown a s a n i n s e r t i n F i g . 2. The r i n g d i o d e b a s i c a l l y c o n s i s t s of 8 t o 1 2 t u n g s t e n w i r e s a r r a n g e d l o n g i t u d i n a l l y on a r a d i u s of a b o u t 1 cm around t h e a x i s of t h e m e t a l p i p e . The e x c i t a t i o n by t h e l a s e r beam t a k e s p l a c e e x a c t l y i n t h e c e n t e r of t h e p i p e . Although t h e r e a r e s p a c e c h a r g e s from t h e w i r e s i n t h e i n n e r p a r t of t h e p i p e t h e r e s u l t i n g f i e l d a t t h e c e n t e r i s z e r o i n f i r s t o r d e r due t o t h e r a d i a l symmetry. A s m a l l n e g a t i v e v o l t a g e ( 0 . 1
-
1 V ) between w i r e s and p i p e r e d u c e s t h e s p a c e c h a r g e s and i n c r e a s e s t h e i o n i z a t i o n s i g n a l . The v o l t a g e may be a d j u s t e d s o t h a t t h e i n f l u e n c e o f S t a r k e f f e c t be- comes z e r o . T h i s c a n be checked by t h e w i d t h of t h e two-photon s i q n a l s and by t h e a p p e a r a n c e of S t a r k - i n d u c e d t r a n s i t i o n s t o I P and I Fs t a t e s o f t h e even 8 8 ~ r i s o t o p e w i t h a h i g h n a t u r a l abunAancy ( % 3 8 ~ % ) . We have u s e d t h e Stark-induced s i g n a l a s t h e probe and a d j u s t e d t h e v o l t a g e t o a v a l u e s o t h a t t h e admixture was l e s s t h a n 0 . 2 % which a l s o g u a r a n t e e s a n e g l i g i b l e S t a r k s h i f t . I n t h e upper p a r t of F i g . 2 an e x c i t a t i o n s p e c t r a u s i n g a r i n g d i o d e i s shown. The improvement compared t o t h e s h i e l d e d d i o d e i s o b v i o u s .
F i g . 2 . -lTwo-photon e x c i t a t i o n s p e c t r a of 5s99d D2 and 5 ~ 1 0 0 s IS l e v e l s of S r . The i s o t o p e s a r e marked b y O t h e i r mass number.
Upper p a r t : D e t e c t i o n w i t h a r i n g d i o d e . Lower p a r t : D e t e c t i o n w i t h a s h i e l d e d
d i o d e .
Rel. Frequency (GHz)
111. CONFIGURATION INTERACTIONS
B e f o r e we p r e s e n t s e l e c t e d examples of h y p e r f i n e s t r u c t u r e measure- ments we want t o d e m o n s t r a t e t h e u s e of p r e c i s e l e v e l e n e r g y d e t e r - . m i n a t i o n f o r d e t e c t i o n of c o n f i g u r a t i o n i n t e r a c t i o n s i n Rydberg s e r i e s w i t h no h y p e r f i n e s t r u c t u r e . The l e v e l e n e r g i e s of members of t h e
5 s n s IS Rydberg s e r i e s o f S r w e r e measured between p r i n c i p a l quantum numbers0l0
5
n<
80 w i t h an a b s o l u t e a c c u r a c y of2
30 MHz u s i n g a n eva- c u a t e d wavemeter / 1 5 / . The wavemeter was of t h e Michelson t y p e w i t h an o p t i c a l arrangement s i m i l a r t o t h e one d e s c r i b e d i n Ref. / 1 6 / . The e n e r g y En of a Rydberg s t a t e-
i s u s u a l l y d e s c r i b e d byand it i s c o n v e n i e n t t o d e s c r i b e 6 by L a n g e r ' s f o r m u l a , which i s de- r i v e d from second o r d e r p e r t u r b a t i o n t h e o r y /17/:
where 6 i s t h e quantum d e f e c t and
E. i s t h e i o n i z a t i o n l i m i t and RSr t h e Rydberg c o n s t a n t f o r Sr(RSr=
1 bgn736. 627 cm'l )
.
Weak p e r t u r b a t i o n s a r e i n c l u d e d i n e q . ( 2 ) u s i n g a d d i t i o n a l c o n s t a n t s cli c o r r e s p o n d i n g t o t e r m v a l u e s Ti of p e r t u r b i n g e n e r g y l e v e l s .The So s e r i e s c a n b e d e s c r i b e d w i t h e q . ( 2 ) . Using a l e a s t s q u a r e f i t p r o c e d u r e t h e c o n s t a n t s a , b , c , d , a l and t h e i o n i z a t i o n l i m i t were d e t e r - mined. To e x c l u d e e r r o r s due t o p r e s s u r e s h i f t s o r o t h e r u n c e r t a i n t i e s a t h i g h n v a l u e s o n l y l e v e l e n e r g i e s from n = 10 t o 34 were u s e d f o r t h e f i t . F i g . 3 shows t h e e x p e r i m e n t a l d a t a and t h e t h e o r e t i c a l c u r v e f o r t h e quantum d e t e c t 6 u s i n g t h e f o l l o w i n g p a r a m e t e r s : a = 3.26897, b = -1.23508 X 10- cmi C = 4.87532 X 108A0 cm2, d = -7.005 X 10-14 cm3
,
a = 3.6059 X 10- cm-l, and E . ( S r ) = 45 932.1982 cm-l.
~ c c o r d i n g t o p r e v i o u s measurements t R 8 r e s h o u l d b e no p e r t u r b e r above n = 1 0 / 3 / . Due t o t h e a c c u r a c y of t h i s e x p e r i m e n t , however, a weak i n - f l u e n c e of t h e 4d2 3 ~ o s t a t e a t 4 4 525.82 cm-l i s c l e a r l y o b s e r v e d .
F i g . 3
-
P l o t of t h e 3.269-
quantum d e f e c t 6 v e r s u s
t h e p r i n c i p a l quantum 10
number n f o r 'S s t a t e s .
+
The s o l i d l i n e
4s
c a l c u - l a t e d from L a n g e r ' sformula w i t h t h e param- o e t e r s g i v e n i n t h e t e x t . I
Z
2
Q 3. 266L
110 10 26 3L
PRINCIPAL QUANTUM NUMBER n
C7-142 JOURNAL DE PHYSIQUE
T h i s s t a t e h a s t o be i n c l u d e d i n t h e f i t t o o b t a i n an agreement w i t h t h e e x p e r i m e n t a l d a t a which i s w i t h i n o u r e r r o r b a r s of
+
0.001 cm-l c o r r e s p o n d i n g t o an a c c u r a c y of 2 X 10-8.Compared t o l e v e l e n e r g i e s t h e h y p e r f i n e s t r u c t u r e is a much more s e n s i t i v e probe f o r s t a t e mixing. The measurement of t h e v a r i a t i o n of t h e h y p e r f i n e s p l i t t i n g due t o c o n f i g u r a t i o n i n t e r a c t i o n s a l l o w s f o r a q u a n t i t a t i v e d e t e r m i n a t i o n o f t h e amount of a d m i x t u r e . I n t h e f o l l o w i n g w e w i l l p r e s e n t t h r e e examples where t h e h y p e r f i n e s p l i t t i n g
s e r v e s a s an a i d f o r o b s e r v i n g c o n f i g u r a t i o n i n t e r a c t i o n s . I n a l l c a s e s t h e Fermi-contact t e r m a i s s t i l l s m a l l compared t o s i n g l e t - t r i p l e t s e p a r a t i o n o r spin-orb!% i n t e r a c t i o n .
The 5snd I r 3 D 2 Rydberg s e r i e s of S r were measured between p r i n c i a 1 quantum numbers 9
5
n5
70 / 1 8 / . The h y p e r f i n e s p l i t t i n g of t h e 'D s e r i e s i n c r e a s e s when g o i n g from n=9 t o n=15. Between n=15 and 16 ghe s i g n o f t h e h y p e r f i n e s p l i t t i n g changes and d e c r e a s e s a g a i n u n t i l i t l e v e l s o f f a t n 30. T h i s r e s o n a n c e b e h a v i o r of t h e h y p e r f i n e s p l i t t - i n g c o n s t a n t A i s summarized i n F i g . 4b. The v a r i a t i o n o f t h e hyper- f i n e s p l i t t i n g i s caused by a s t r o n g s i n g l e t - t r i p l e t mixing around n=15,16 which was r e p o r t e d by E s h e r i c k / 3 / a s determined from a MQDT a n a l y s i s . The i n t e r a c t i o n w i t h t h e doubly e x c i t e d 4d6s 1 1 3 ~ s t a t e s g i v e s r i s e t o t h e mixing w i t h a maximum around n=15 where t 6 e admix- t u r e i s v e r y c l o s e t o p u r e ( j j ) - c o u p l i n g . Using t h e i n t e r m e d i a t e coup- l i n g scheme /19/ and n e g l e c t i n g any d i r e c t c o n t r i b u t i o n s of t h e ex- c i t e d nd e l e c t r o n t h e admixture c o e f f i c i e n t s a and B can b e d e t e r m i n e d q u a n t i t a t i v e l y :where
1 . . .
> O s t a n d s f o r p u r e LS- coupled w a v e f u n c t i o n s .F i g . 4
-
a ) Amount of admix- t u r e of s i n g l e t i n t o t r i p l e t s t a t e s . b ) Observed hyper- f i n e o u p l i n g c o n s t a n t A f o r 5snd 'D2 and 3 ~ 2 s t a t e s a s a f u n c t l o n of n .m*
Q 2 0
.MOOT
ADMIXTURE PER
-
STATE
04:a,n_
Sr 5sz-5s nd , ,-
a X
10 20 30 L0
PRINCIPAL QUANTUM NUMBER n
N o r m a l i z a t i o n r e q u i r e s t h a t ci2+a2+y2 = 1 . From a measurement of t h e h y p e r f i n e s t r u c t u r e of b o t h ID2 and 3 ~ 2 l e v e l s t h e admixture of t r i p - l e t c h a r a c t e r i n t o t h e s i n g l e t s e r i e s 1s o b t a i n e d . The r e s u l t i s com- p a r e d w i t h t h e MQDT a n a l y s i s from E s h e r i c k / 3 / i n F i g . 3a. I n t h e r e g i o n above p r i n c i p a l uantum n u ~ b e r s n > 30 o n l y 2 % admixture of 5snd 3 ~ 2 i n t o t h e 5snd ?D2 s e r i e s a r e neeaed t o e x p l a i n t h e o b s e r v e d h y p e r f i n e s t r u c t u r e d e m o n s t r a t i n g t h e s e n s i t i v i t y t o s t a t e mixing.
A more i n s t r u c t i v e example f o r t h e h i g h s e n s i t i v i t y i s t h e s i n g l e t - t r i p l e t mixing i n t h e 4snd I D 2 s e r i e s o f Ca /20/. I t a l s o s t a n d s f o r t h e s e n s i t i v i t y of t h e r m i o n i c d e t e c t i o n of Rydberq s t a t e s i n combina- t i o n w i t h two-photon s p e c t r o s c o p y . The o n l y i s o t o p e w i t h a n u c l e a r s p i n , 4 3 ~ a (1=7/2), h a s an abundancy of 0.135 % and t h e r e f o r e a v e r y s e n s i t i v e d e t e c t i o n method i s r e q u i r e d i n o r d e r t o r e s o l v e t h e hyper- f i n e s t r u c t u r e .
T y p i c a l e x c i t a t i o n s p e c t r a a r e shown i n F i g . 5. A two-photon t r a n s i - t i o n t o t h e 4 ~ 1 0 s IS, Rydberg s t a t e i s shown i n t h e upper p a r t . With t h e e x c e p t i o n of 4 6 ~ a a l l s t a b l e i s o t o p e s a r e r e s o l v e d w i t h a h i g h s i g n a l - t o - n o i s e r a t i o . The i n t e n s i t y of t h e i o n i z a t i o n s i g n a l s i s d i r e c t l y p r o p o r t i o n a l t o t h e i s o t o p e abundancy i n t h e n a t u r a l m i x t u r e . The s i g n a l of t h e 4 3 ~ a ( I = 7 / 2 ) i s s p l i t i n t o f i v e h y p e r f i n e components f o r a 4s12d I D s t a t e , a s can be s e e n i n t h e lower p a r t of F i g . 5 . A l l components w i t & t o t a l a n g u l a r momenta F=3/2 t o 11/2 a r e r e s o l v e d and t h e h y p e r f i n e c o u p l i n g c o n s t a n t A c a n b e d e t e r m i n e d e a s i l y . T h i s was done up t o t h e p r i n c i p a l quantum number n=42.
The n-dependence o f t h e e x p e r i m e n t a l l y o b s e r v e d h y p e r f i n e c o u p l i n g c o n s t a n t A i s shown i n F i g . 6 . The i n c r e a s e of A around n=8 and n=15 i d d i c a t e s a l o c a l i z e d s i n g l e t - t r i p l e t mixing which i s caused by t h e
F i g . 5.
-
D o p p l e r - f r e e two-photone x c i t a t i o n s from t h e 4 ~ 1 0 s l ~ . l e v e l (upper p a r t ) a n d , on an
e n l a r g e d s c a l e , i n t o t h e 4s12d ' D s t a t e f o r t h e i s o t o p e s 42ca, 43ca:
and 4 4 ~ a ( l o w e r p a r t ) For t h e 4s12d I D 2 , s t a t e , t h e d 3 ~ a s i g n a l i s s p l i t l n t o f i v e h y p e r f i n e com- ponent S.
Rel. Frequency IMHzI
JOURNAL DE PHYSIQUE
F i g . 6
-
n-dependence of t h e e x p e r i - m e n t a l l y ob- s e r v e d hyper- f i n e c o u p l i n g c o n s t a n t A f o r 4snd ' D ~ s t a t e s of 4 3 ~ a .
3556 ID2 and 3d2 I D 2 p e r t u r b i n g s t a t e s , r e s p e c t i v e l y . The maximum ad- m i x t u r e a t n=15 i s a b o u t 5 % whereas most o t h e r s t a t e s have a d m i x t u r e s f a r below 1 % . Such s m a l l a d m i x t u r e s can s a f e l y by determined d e t e c t - i n g v a r i a t i o n s of t h e h y p e r f i n e s p l i t t i n g s . I t s h o u l d b e mentioned t h a t no s i n g l e t - t r i p l e t mixing was o b s e r v e d i n e a r l i e r measurements u s i n g p u l s e d dye l a s e r s and a MQDT a n a l y s i s / 2 / .
A s i m i l a r r e s o n a n c e - l i k e b e h a v i o r was a l s o o b s e r v e d f o r t h e 6snd I r 3 D 2 s e r i e s of Ba / 2 1 / . Using t h e a d m i x t u r e c o e f f i c i e n t s d e t e r m i n e d from h y p e r f i n e s t r u c t u r e measurements a s a d d i t i o n a l i n f o r m a t i o n f o r a MQDT a n a l y s i s t h e s i n g l e t - t r i p l e t mixing of 5snd 1 ~ 2 and 3 ~ 2 s e r i e s was r e - produced c o r r e c t l y / 2 2 / .
Rydberg s e r i e s o f t h e l i g h t a l k a l i n e - e a r t h e l e m e n t s Be and Mg a r e p r e - dominantly p e r t u r b e d by t h e doubly e x c i t e d c o n f i g u r a t i o n mp2 (m=2 f o r Be and m=3 f o r Mg). I n p a r t i c u l a r low members o f t h e msnd Rydberg s e r i e s c o n t a i n a c o n s i d e r a b l e amount of mP2 1 ~ 2 c h a r a c t e r / 2 3 / . The admixture s h o u l d have an i n f l u e n c e on t h e h y p e r f i n e s t r u c t u r e which i n t u r n can be used t o d e t e r m i n e t h e mixing c o e f f i c i e n t s A s an example we have measured t h e h y p e r f i n e s t r u c t u r e of t h e 3s3d i ~ 2 s t a t e of 25.9
( n u c l e a r s p i n I = 7 / 2 ) . F i g . 7 shows t h e e x p e r i m e n t a l l y d e t e r m i n e d hyper- f i n e s p l i t t i n g . The spectrum was o b t a i n e d by means of a f r e q u e n c y o f f - s e t l o c k i n g systems /21/ w i t h an a c c u r a c y of b e t t e r t h a n
+
150 kHz f o r t h e d e t e r m i n a t i o n of e n e r g y s e p a r a t i o n s . A- and B - f a c t o r s were d e t e r - mined t o A = -5.14 MHz and B = 8.38 MHz. The magnetic h y p e r f i n e s t r u c - t u r e which i s z e r o f o r s t a t e s w i t h u r e LS-coupling i s p a r t l y caused by t h e admixture of a b o u t 20 % 3p2 'D2-character i n t o t h e 3s3d 1 ~ ~ s t a t e ( A , % -3 MHz). The d i r e c t contribution o f t h e e x c i t e d 3d e l e c t r o n g i v e s r i s e t o a c o n t r i b u t i o n of A Q, -0.5 MHz and t h e r e m a i n i n g p a r t can be a t t r i b u t e d t o a s m a l l s i n g f e t - t r i p l e t mixing ( < 0.1 O/oo), For a d e t a i l e d a n a l y s i s of s i n g l e t - t r i p l e t mixing h i g h e r members of t h e 3snd ID2 s e r i e s and t h e c o r r e s p o n d i n g 3 ~ 2 l e v e l s have t o b e measured.F i g . 7
-
H y p e r f i n e s t r u c - t u r e of t h e 3s3d ID* s t a t e Of 2 5 ~ g .0 c 50 100 150
Rel. Frequency (MHz)
I V . HYPERFINE-INDUCED PERTURBATIONS
Hyperfine-induced s i n g l e t - t r i p l e t mixing i n t w o - e l e c t r o n systems g i v e s r i s e t o s i g n i f i c a n t m o d i f i c a t i o n s o f h y p e r f i n e s t r u c t u r e and i s o t o p e s h i f t s /11,25-28/. A s t h e amount of s i n g l e t - t r i p l e t mixing i n c r e a s e s r a p i d l y w i t h i n c r e a s i n g p r i n c i p a l quantum number n , s i n g l e t - t r i p l e t mixing i s o f c r i t i c a l importance, i n p a r t i c u l a r f o r t h e c h a r a c t e r of h i g h Rydberg s t a t e s . The i n f l u e n c e of t h i s h y p e r f i n e i n t e r a c t i o n i n h i g h Rydberg s t a t e s (10
5
n5
70) o f a l k a l i n e - e a r t h e l e m e n t s was ob-ved r e c e n t l y f o r t h e odd mass i s o t o p e s 4 3 ~ a / 2 9 / , g 7 s r /29/ and a 2 9 3 0 An i n s t r u c t i v e example i s t h e h y p e r f i n e - i n d u c e d l e v e l s h i f t o f t h e 5 s n s Rydberg s e r i e s o f S r due t o t h e f a c t t h a t t h i s s e r i e s i s n o t p e r t u r b e d by a d d i t i o n a l c o n f i g u r a t i o n i n t e r a c t i o n s . T y p i c a l e x c i t a t i o n s p e c t r a a r e shown i n F i g . 8 , The l a r g e s h i f t of t h e odd i s o t o p e 8 7 ~ r w i t h r e s p e c t t o t h e even o n e s i s e v i d e n t . For a c a l - c u l a t i o n of t h e l e v e l s h i f t t h e p e r t u r b e d w a v e f u n c t i o n s have t o be t a k e n a s a l i n e a r combination o f p u r e LS-coupled s i n g l e t and t r i p l e t wavef u n c t i o n s :
where
1 . . .
> O s t a n d s f o r p u r e LS-coypied w a v e f u n c t i o n s . D i a g o n a l i z a t i o n of t h e Hamiltonian H = H + a s ' I r e s u l t s i n t h e p e r t u r b e d l e v e l e n e r g i e s of s i n g l e t and? r i p l g g
s t a t e s /29/. The agreement w i t h ex- p e r i m e n t i n d i c a t e s t h a t t h e r e a r e no o t h e r p e r t u r b a t i o n s i n t h e e n e r g y r a n g e i n v e s t i g a t e d .Hyperfine-induced s t a t e mixing d o e s n o t o n l y l e a d t o l e v e l s h i f t s , b u t a l s o t o changes i n t r a n s i t i o n p r o b a b i l i t i e s . Due t o t h e f a c t t h a t J i s no l o n g e r a good quantum number s t a t e s c a n b e e x c i t e d which normally c o u l d n o t b e r e a c h e d by two-photon e x c i t a t i o n . For example, s t a t e s of t h e 5sns 3 ~ 1 s e r i e s i n S r w i t h 50
<
n5
125 were p o p u l a t e d by Doppler- f r e e two-photon t r a n s i t i o n s from t h e 5 s 2 I S ground s t a t e , b e c a u s e of t h e added t r a n s i t i o n s t r e n g t h t o t h e admixe8 5 s n s I s o s t a t e s /31/.JOURNAL DE PHYSIQUE
Fig. 8
-
Shift of the 5s''so -
5sns S two-photon absor tion line ofOthe odd isotope 8%r for three selected principal quantum numbers n.
I I
I l 1 I 1
0
I400 800 1200
Rel. Frequency (MHzI
Both effects, level shifts and "forbidden" transitions are shown in Fig. 9 in the case of the hyperfine spectra of 5s91d 1~~ and 3 ~ 2 states of Sr. The hyperfine-induced level shift of both hyperflne multiplets is obvious. The large admixture of singlet character into
the 3 ~ 2 wavefunctions of 87sr results in a high transition probability
Fig. 9
-
Two-photon excitation spec rum of the 5s91d D2''' states of Sr. The isotopes are labelledby their mass number.
-
CIc or
.
-
0
c
0.
-
C
.
E -
C
-
01000 2000 3000 LOO0 5000
Rel. Frequency (M H z
)to the "forbidden" 3 ~ 2 levels. Transitions to the 3 ~ 1 and 3D2 fine structure levels were not observed as the hyperfine ~nteractxon of the ID2 level is predominantly restricted to the 3 ~ 2 state. Calculations show that only about 10 % singlet character is admixed in all hyper- fine components of 3 ~ 1 and 3D3 levels. The transition probability to the D2 states of the even lsotopes is due to a residual singlet-trip- 3 let mixing ( z 2 % ) caused by spin-orbit-interaction, which is not a function of the principal quantum number n.
Finally we want to demonstrate a hyperfine-induced interaction between hyperfine levels from different principal quantum numbers n. For an illustration of this effect the excitation spectra of 5s112d ID2 and 5s113d lr3D levels of Sr are shown in Fig. 10. The expected energy separation getween the two hyperfine multiplets of ID (n=112) and 3
(n=113) states due to the hyperfine-induced level shigt within the D2 same n (for comparison see Fig. 9) is almost zero. Due to this degener- acy levels with equal F interact and repel1 each other. The new per- turbed wavefunctions can be taken again as a linear combination of the two interacting levels (see equ.(4)):
The mixed wavefunctions are symmetric and antisymmetric combinations of two wavefunctions which are composed of nearly equal amounts of singlet character. Therefore the singlet admixture in the antisymmetric wavefunction is close to zero, whereas the symmetric wavefunction con- tains almost pure singlet character. As only states with singlet character can be excited from the I S ground state the intensity ratio between ID2 and 3 ~ 2 levels should reBlect the admixture. This is clear-- ly demonstrated in Fig. 10 where the signal of the 5s113d 3 ~ 2 hyper- fine multiplet has a much higher intensity compared to the 5s112d 1 ~ 2 state. We expect this hyperfine-induced n-mixing to be a general be- havior of high Rydberg states in two-electron systems.
Fig. 10
-
Two-photon excita- tion spectrum of 5snd 1 3 ~ 2(n=112,113) states of Sr.
The spectrum was recorded using a thermionic ring diode as described in sec- tion 11. The transition to the 5s113p Ip1 state is in- duced by a residual Stark effect (admixture
<
0.5 % ) .I I
0 1 2 3 L 5
Rel. Frequency I G H z )
JOURNAL DE PHYSIQUE
REFERENCES
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52,
2 0 4 ( 1 9 8 1 ) 1 3 K , N i e m a x , A c t a P h y s i c a P o l o n i c a ,E,
5 1 7 ( 1 9 8 2 )1 4 B . P . S t o i c h e f f , L a s e r S p e c t r o s c o p y V , S p r i n g e r V e r l a g , B e r l i n , 2 9 9 ( 1 9 8 1 )
1 5 R. B e i g a n g , K. L u c k e , A. T i m m e r m a n n , P . J . W e s t , and D. F r o l i c h , O p t . C o m m u n .
42,
1 9 ( 1 9 8 2 )1 6 X i a H u i - R o n g , V . S . B e n s o n , a n d T.W. H a n s c h , L a s e r F o c u s ,
3,
M a r c h ( 1 9 8 1 )
1 7 W.R.S. G a r t o n , 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 .
2,
3 3 5 ( 1 9 6 2 ) 1 8 R . B e i g a n g , E . M a t t h i a s a n d A. T i m m e r m a n n , P h y s . R e v . L e t t .47,
3 2 6 ( 1 9 8 1 ) and P h y s . R e v . L e t t .
48,
2 9 0 ( 1 9 8 2 )1 9 A. L u r i o , M. M a n d e l , and R . N o v i c k , P h y s . R e v .
126,
1 7 5 8 ( 1 9 6 2 ) 2 0 R. B e i g a n g , K . L u c k e , and A. T i m m e r m a n n , P h y s . R e v .g ,
5 8 7( 1 9 8 3 )
2 1 H . R i n n e b e r g , J. N e u k a m m e r , P h y s . R e v . L e t t . 4 9 , 1 2 4 ( 1 9 8 2 ) 2 2 H. R i n n e b e r g , J . N e u k a m m e r , P h y s . R e v .
g ,
1 7 9 ( 1 9 8 3 ) 2 3 C . F r o e s e - F i s c h e r , C a n . J . P h y s .53,
1 8 4 ( 1 9 7 5 )2 4 H. G e r h a r d t , F . J e s c h o n n e k , W. M a k a t , F . S c h n e i d e r , A . T i m r n e r m a n n , R . W e n z , a n d P . J . W e s t , A p p l . P h y s .
c,
3 6 1 ( 1 9 8 0 )2 5 F. B i r a b e n , E - de C l e r c q , E. G i a c o b i n o , and G. G r y n b e r g , J . P h y s . B: A t . M o l . P h y s . 1 3 , L 6 8 5 ( 1 9 8 0 )
2 6 R.R. F r e e m a n , P . ~ T ~ i a o , R. P a n o c k , L.M. H u m p h r e y , P h y s . R e v .
g ,
1 5 1 0 ( 1 9 8 0 )2 7 E . de C l e r c q , F . B i r a b e n , E . G i a c o b i n o , G . G r y n b e r g , and J . B a u c h e , J . P h y s . B: A t . M o l . P h y s .
14,
L 1 8 3 ( 1 9 8 1 )2 8 L . B a r b i e r , R . J . C h a m p e a u , J . P h y s . ( P a r i s ) 4 1 , 9 4 7 ( 1 9 8 0 ) 2 9 R. B e i g a n g and A. T i m m e r m a n n , P h y s . R e v . ~ 2 5 , 1 4 9 6 ( 1 9 8 2 ) 3 0 H. R i n n e b e r g , J . N e u k a m m e r , a n d E . M a t t h i a s , Z . P h y s .
E ,
1 11 1 9 8 2 )
3 1 R. B e i g a n q and A . T i m m e r m a n n , P h y s . R e v .
