LASER SPECTROSCOPY OF HIGH RYDBERG STATES OF LIGHT ALKALINE-EARTH ELEMENTS : Be AND Mg

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LASER SPECTROSCOPY OF HIGH RYDBERG STATES OF LIGHT ALKALINE-EARTH ELEMENTS :

Be AND Mg

R. Beigang, D. Schmidt, P. West

To cite this version:

R. Beigang, D. Schmidt, P. West. LASER SPECTROSCOPY OF HIGH RYDBERG STATES OF

LIGHT ALKALINE-EARTH ELEMENTS : Be AND Mg. Journal de Physique Colloques, 1983, 44

(C7), pp.C7-229-C7-237. �10.1051/jphyscol:1983719�. �jpa-00223276�

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LASER SPECTROSCOPY O F H I G H RYDBERG STATES OF LIGHT ALKALINE-EARTH ELEMENTS: Be AND My

R. Beigang, D. Schmidt and P . J . West

I n s t . f . Atom- und Festkb'rperphysik, FU Berlin, 1000 Berlin 33, F.R. G.

R6sum6

-

Les s 6 r i e s de Rydberg d e s c o n f i g u r a t i o n s 6 l e c t r o n i q u e s msns e t msnd o n t 6 t d 6 t u d i 6 e s 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 p a u x 10

5

n

5

70 pour Be (m=2) e t Mg (m=3). Les 6 t a t s de Rydberg o n t 6 t 6 p e u p l d s

a

l ' a i d e d ' u n e e x c i t a t i o n en 6chelon ou d ' u n e t r a n s i t i o n d i r e c t e

a

deux photons avec d e s l a s e r s 2 colorant p u l s 6 s d o u b l e s e n f r e q u e n c e (235 nm 2 A < 330 nm)

.

Les atomes de Rydberg e x c i t 6 s o n t 6 t 6 d 6 t e c t 6 s a v e c une d i o d e t h e r - mo-ionique f o n c t i o n n a n t e n r6gime d e c h a r g e d ' e s p a c e . L ' a n a l y s e 2 l ' a i d e de l a t h 6 o r i e du d 6 f a u t q u a n t i q u e 21 p l u s i e u r s v o i e s d e s s 6 r i e s de Rydberg d a n s Be e t Mg a c o n d u i t 2 l a d6termi- n a t i o n d e s m6langes d e s 6 t a t s mp2 1 ~ 2 a v e c ceux d e l a s 6 r i e msnd ID2.

A b s t r a c t

-

Rydberg s e r i e s of msns and msnd c o n f i g u r a t i o n s o f Be(m=2) and My (m=3) were i n v e s t i g a t e d between p r i n c i p a l quantum numbers 10

5

n

5

70. The Rydberg s t a t e s were p o p u l a t e d u s i n g s t e p w i s e e x c i t a t i o n o r d i r e c t two-photon t r a n s i t i o n s w i t h frequency doubled l i g h t (235 nm

5

A < 330 nm) from p u l s e d dye l a s e r s . The e x c i t e d Rydberg atoms were d e t e c t e d w i t h a s p a c e c h a r g e l i m i t e d t h e r m i o n i c d i o d e . An a n a l y s i s of t h e Rydberg s e r i e s b o t h i n Be and M g by means of m u l t i - c h a n n e l quantum- d e f e c t t h e o r y (MQDT) r e s u l t s i n t h e d e t e r m i n a t i o n of mp2 1 ~ 2 a d m i x t u r e s i n msnd 1 ~ 2 s t a t e s .

I. INTRODUCTION

E x t e n s i v 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 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 Ca, S r and Ba have been c a r r i e d o u t o v e r t h e p a s t y e a r s u s i n g v a r i o u s s p e c t r o s c o p i c methods ( s e e e . g . / l - 5 / ) . The a n a l y s i s of even and odd p a r i t y Rydberg s e r i e s by means o f an e x t e n d e d Rydberg-Ritz formula o r a more s o p h i s t i c a t e d m u l t i - c h a n n e l quantum-defect t h e o r y

(MQDT) r e s u l t e d i n t h e d e t e r m i n a 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 , s i n g l e t - t r i p l e t mixing and a c c u r a t e i o n i z a t i o n l i m i t s . I n t h e c a s e of t h e l i g h t a l k a l i n e - e a r t h elements Mg and Be t h e !nowledge of h i g h Ryd- b e r g s t a t e s i s i n c o m p l e t e . For Mg o n l y t h e 3s3p s e r i e s i s known up t o h i g h p r i n c i p a l quantum numbers /6/ whereas a l l P d t h e r s e r i e s l i k e 3 s n s , 3snd and 3snf a r e n o t t a b u l a t e d f o r quantum numbers h i g h e r t h a n 25. I n Be no 2 s n l Rydberg s t a t e was e v e r measured above n=12. The knowledge of t h e s e s t a t e s , however, i s d e s i r a b l e e . g . f o r a s t r o p h y s i - c i s t s and a t o m i c t h e o r i s t s b e c a u s e Be and My a r e t h e l i g h t e s t a l k a l i n e - e a r t h e l e m e n t s and a b i n i t i o c a l c u l a t i o n s of e n e r g y l e v e l s and wave f u n c t i o n s seem f e a s i b l e .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983719

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JOURNAL DE PHYSIQUE

The d e t e r m i n a t i o n of complete Rydberg s e r i e s a l s o a l l o w s f o r t h e i n - v e s t i g a 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 between d i f f e r e n t s e r i e s . Although t h e s t r e n g t h of p e r t u r b a t i o n s d e c r e a s e s w i t h d e c r e a s i n g atomic w e i g h t r . B e and Mg e x h i b i t marked d e v i a t i o n s from t h e r e g u l a r b e h a v i o r of Rydberg s e r i e s . I n c o n t r a s t t o Car S r , and Ba where t h e Rydberg s e r i e s a r e mainly p e r t u r b e d by doubly e x c i t e d s t a t e s o r i g i n a t i n g from t h e open d - s h e l l , t h e dominating p e r t u r b e r i n Be and Mg i s t h e mp2 con- f i g u r a t i o n . I n p a r t i c u l a r t h e msnd I D s e r i e s i s s t r o n g l y p e r t u r b e d by t h e mp2 I D l e v e l . A MQDT a n a l y s i s w i ? l b e p r e s e n t e d which d e t e r m i n e s t h e a d m i x t u r e s of t h i s s t a t e i n t o t h e 1 ~ ~ s e r i e s . 2

11. EXPERIMENTAL

From t h e m s 2 'S ground s t a t e an energy gap of 7 5 000 cm-' and 6 1 000 cm-l h a s t o b e g r i d g e d t o e x c i t e h i g h l y i n g Rydberg l e v e l s f o r Be and Mgr r e s p e c t i v e l y . The r e l e v a n t p a r t of t h e e n e r g y l e v e l diagrams i s

shown s c h e m a t i c a l l y i n F i g s . l a and b . I n t h e c a s e of Mg a d i r e c t two- photon e x c i t a t i o n was chosen t o p o p u l a t e even p a r i t y msns and msnd Rydberg s t a t e s . For Be t h e vapor d e n s i t y a c h i e v e d i n t h e s e e x p e r i m e n t s was t o o low t o a l l o w f o r t h e d e t e c t i o n of two-photon t r a n s i t i o n s .

T h e r e f o r e t h e Rydberg s t a t e s were e x c i t e d w i t h s t e p w i s e t r a n s i t i o n s v i a t h e 2s2p I P ? i n t e r m e d i a t e l e v e l . I n b o t h c a s e s t h e r e q u i r e d uv r a d i a - t i o n was p r o v i d e d by f r e q u e n c y doubled l i g h t of p u l s e d dye l a s e r s . The dye l a s e r s were pumped w i t h t h e second o r t h i r d harmonic of a Nd:YAG l a s e r p r o d u c i n g peak powers up t o s e v e r a l 10 k W a t a l i n e w i d t h of a b o u t

F i g . l a P a r t of t h e e n e r g y l e v e l diagram of Be i l l u s t r a t - i n g s t e p w i s e e x c i t a t i o n of 2 s n s and 2snd Rydberg s t a t e s .

F i g . I b P a r t of t h e energy l e v e l diagram o f Mg w i t h d i r e c t two- photon t r a n s i t i o n s t o 3 s n s and 3snd Rydberg s t a t e s .

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60 600 cm-' up t o t h e i o n i z a t i o n l i m i t of Mg u s i n g two-photon t r a n s i - t i o n s . For Be a second dye l a s e r was n e c e s s a r y f o r t h e f i r s t s t e p t o t h e 2s2p l p l i n t e r m e d i a t e l e v e l : A s t i l b e n e 3 dye l a s e r was f r e q u e n c y doubled a t a f i x e d f r e q u e n c y i n a KB5 c r y s t a l producing 234.9 nm r a d i a - t i o n w i t h a peak power of s e v e r a l kW. A s e c o n d f r e q u e n c y doubled

Rhodamine 6G l a s e r was t h e n t u n e d t o promote t h e e x i t e d Be atoms t o h i g h Rydberg s t a t e s . A s c h e m a t i c diagram of t h e e x p e r i m e n t a l s e t up i s shown i n F i g . 2. 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 p i p e which was h e a t e d t o t e m p e r a t u r e s between 500 OC and 1200 OC. The t y p i c a l vapor p r e s s u r e used f o r t h e e x p e r i m e n t s was 50 t o 150 mTorr i n t h e c a s e o f M g . A b u f f e r g a s o f Ne a t 2-4 T o r r p r o t e c t e d t h e c e l l windows. A t t h e maximum t e m p e r a t u r e o b t a i n a b l e w i t h t h e s i m p l e h o t p i p e oven t h e Be v a p o r p r e s s u r e was l i m i t e d t o v a l u e s below 1 mTorr. There- 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 f o r t h e e x c i t e d Rydberg atoms was r e q u i r e d . We have used t h e r m i o n i c d e t e c t i o n w i t h a space-charge l i m i t e d d i o d e . The d i o d e was formed by a s t a i n l e s s s t e e l w i r e i n s e r t e d i n t h e c e n t e r of t h e p i p e and n e g a t i v e l y b i a s e d (-0.5.

..-

²^{V )} t h r o u g h a l o a d r e s i s t o r (10

...

^{l 0}^kR).The s e n s i t i v i t y of t h e t h e r m i o n i c d i o d e i n c r e a s e s w i t h d e c r e a s i n g e n e r g y d i f f e r e n c e t o t h e i o n i z a t i o n l i m i t , t h u s p a r t l y compensating 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 s e n s i t i v i t y may be i l l u s t r a t e d by t h e d e t e c t i o n of a ~ p i n ~ f o r b i d d e n t r a n s i t i o n i n B e . Prom t h e 2s2 I S ground s t a t e t h e 2s2p PI l e v e l was excited and d e t e c t e d w i t h t h e thegmionic d i o d e a l t h o u g h t h i s s t a t e i s more t h a n 50 COO cm-l below t h e i o n i z a t i o n l i m i t . With t h i s t r a n s i t i o n a s t h e f i r s t s t e p i t s h o u l d be p o s s i b l e t o p o p u l a t e and i n v e s t i g a t e a l s o t h e c o r r e s p o n d i n g t r i p l e t s e r i e s i n Be.

A l l s p e c t r a were c a l i b r a t e d by means of Rb and CS r e f e r e n c e p i p e s .

[ ~ e ; Mg

Diode+ Thermionic

Marker Diode Diode

Cavi t y

U KDP

l

Dye Laser tunable

F i g . 2 E x p e r i m e n t a l s e t up. The f i x e d dye l a s e r i s o n l y used f o r t h e s t e p w i s e e x c i t a t i o n o f B e Rydberg s t a t e s .

I/ 1/

/

v

U

v v , 2 v /

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JOURNAL DE PHYSIQUE

Using known t r a n s i t i o n wavelengths t h e l e v e l e n e r g i e s i n B e and Mgwre determined w i t h an a c c u r a c y of a b o u t 3 . 1 0 - ~ . ~ o i n t e r p o l a t e between ad- j a c e n t c a l i b r a t i o n l i n e s we used t h e t r a n s m i s s i o n peaks of a Fabry- P e r o t i n t e r f e r m o m e t e r w i t h a f r e e s p e c t r a l r a n g e of 0.5 cm-l i n t h e v i s i b l e .

111. F33SULTS AND DISCUSSION B e r y l l i u m

A t y p i c a l e x c i t a t i o n spectrum o f 2snd ID2 Rydberg s t a t e s 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 s shown i n F i g . 3. The I D s e r i e s w a s r e s o l v e d u p t o p r i n c i p a l quantum numbers n ?. 70. Due t o t h e lower t r a n s i t i o n p r o b a b i l - 2 i t y t o 2 s n s I s o s t a t e s t h i s s e r i e s was o n l y r e c o r d e d up t o n % 40. From t h e e x p e r i m e n t a l l y determined l e v e l e n e r g i e s En t h e quantum d e f e c t 6 was determined u s i n g t h e Rydberg-Ritz formula

E n = E . _{I o n}

- -

(n-6) ²

where E , i s t h e i o n i z a t i o n l i m i t and R t h e Rydberg c o n s t a n t f o r Be.

The res?i?P i s shown i n F i g . 4 . I t t u r n s o u t t h a t t h e 2 s n s I s o s e r i e s i s

I 1 l I I

I

75 130 75 160 Be Energy [cm-']

F i g . 3 Stepwise e x c i t a t i o n spectrum o f 2snd 1 ~ 2 Rydberg s t a t e s o f Be.

The upper t r a c e d i s p l a y s t h e r e f e r e n c e s i g n a l o b t a i n e d from a Rb p i p e .

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quantum number n . C l o s e d c i r c l e s and r e c t a n g l e s a r e own measurements. Energy l e v e l s f o r n

5

10 a r e t a k e n from Ref. / 7 / .

~ O O o O D O O ~ ~ w

O

2 sns 'so

10 20 30

Principal Quantum Number n

n o t p e r t u r b e d by o t h e r s e r i e s r e s u l t i n g i n a n a l m o s t c o n s t a n t quantum d e f e c t . The same h o l d s f o r t h e 1 ~ 2 s e r i e s f o r h i g h p r i n c i p a l quantum numbers. Using o n l y e n e r g y l e v e l s w i t h n

2

15 t h e i o n i z a t i o n l i m i t was d e t e r m i n e d t o Eion = 75 192.64 ( 6 ) cm-'. I n t h e r e g i o n o f low p r i n c i p a l quantum numbers n t h e 2snd series i s h e a v i l y p e r t u r b e d d u e t o a n i n t e r a c t i o n w i t h t h e 2p2 ID l e v e l . I n o r d e r t o d e t e r m i n e t h e amount o f 2p2 a d m i x t u r e i n t h e 2snd 1 ~ 2 series we h a v e p e r f o r m e d a two-channel MQDT a n a l y s i s w i t h t h e 2pnp s e r l e s a s s e c o n d c h a n n e l . Using MQDT param- e t e r a s l i s t e d i n T a b l e I t h e 2snd 1 ~ 2 series was f i t t e d w i t h t h i s s i m p l e two-channel model. The a d m i x t u r e a s a f u n c t i o n o f p r i n c i p a l

T a b l e I

MQDT-Parameter Be, D 2 bound s t a t e s .

2 s n d 2 PnP

--p .

Is = 75192.64 cm-" I = 107125.22 cm-'

P

p, = 0.96471

v,2

= 0.54006

The MQDT p a r a m e t e r s i n T a b l e s I a n d I1 a r e d e f i n e d i n R e f . / 9 / e . g .

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JOURNAI- DE PHYSIQUE

quantum number n i s shown i n F i g . 5. The l o w e s t bound ID2 s t a t e con- t a i n s a l m o s t e q u a l amounts o f 2s3d ( 5 7 % ) and

zp2

⁽⁴³^{% )}c h a r a c t e r . T h i s s t a t e w a s c l a s s i f i e d b e f o r e a s 2p2 'D2 / 7 / . Although a c l e a r c l a s s i f i c a t i o n w i t h a s i n g l e c o n f i g u r a t i o n i s q u e s t i o n a b l e , a s a l - ready c l a i m e d by Lu / 1 0 / , t h e l a b e l 2s3d I D 2 seems more a p p r o p r i a t e f o r t h i s s t a t e a c c o r d i n g t o t h e MQDT analysis.

2 1 F i g . 5 Admixture of 2p D2 c h a r a c t e r i n t o t h e 2snd D2 s e r i e s o f Be.

Principal Quantum Number n

Magnesium

I n Mg t h e 3snd 'D2 s e r i e s was r e s o l v e d up t o p r i n c i p a l quantum numbers n = 4 5 . The o t h e r even p a r i t y Rydberg s e r i e s which c o u l d b e e x c i t e d v i a two photons from t h e ground s t a t e , t h e 3sns I S s e r i e s , h a s a t r a n s i - t i o n p r o b a b i l i t y of one o r d e r of magnitude smayler t h a n t h e I D s e r i e s . T h e r e f o r e o n l y s t a t e s w i t h maximum p r i n c i p a l quantum number n=20 were r e c o r d e d . The d i f f e r e n c e i n t r a n s i t i o n p r o b a b i l i t y i s i l l u s t r a t e d i n F i g . 6 . The p l o t o f t h e auantum d e f e c t 6 a s a f u n c t i o n of n a g a i n c l e a r l y shows t h a t b o t h

fs0

and ID2 s e r i e s a r e n o t p e r t u r b e d above nz15

( F i g . 7 ) comparable t o Be. Below n 10 t h e 3snd ID2 s e r i e s i n t e r a c t s w i t h t h e 3p2 1 ~ 2 l e v e l . The l e v e l e n e r g i e s c a n b e f l t t e d w i t h a two- c h a n n e l MQDT a n a l y s i s u s i n g t h e 3pnp s e r i e s a s second c h a n n e l . The MQDT p a r a m e t e r a r e l i s t e d i n Table I I . D $ h e dominant a d m i x t u r e s o c c u r i n t h e low 3snd s t a t e s w i t h a maximum of 12 % i n t h e 3s3d 1 ~ 2 s t a t e whereas f o r higheE2 I D s t a t e s t h e admixture d e c r e a s e s r a p i d l y a s shown i n F i g . 8. The r e s u l t 8 a r e i n q u a l i t i t a t i v e agreement w i t h MCHF c a l c u - l a t i o n s o f F r o e s e - F i s c h e r /8/ w i t h a c a l c u l a t e d maximum a d m i x t u r e of 21-7 % f o r t h e 3s3d 1 ~ ~ s t a t e , however.

The b e h a v i o r of Be and Mg Rydberg s e r i e s i s v e r y s i m i l a r w i t h r e s p e c t t o t h e p e r t u r b a t i o n s by t h e mp2 c o n f i g u r a t i o n . The s t r e n g t h of i n t e r - a c t i o n d e c r e a s e s when g o i n g from Be t o Mg. T h i s t r e n d c o n t i n u e s i n t h e

h e a v i e r a l k a l i n e - e a r t h e l e m e n t s where 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 w i t h mp2 t e r m c a u s e o n l y l o c a l i z e d p e r t u r b a t i o n s .

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Fig. 6 Two-photon excitation spectrum of Mg. The middle trace shows the transmission fringes of the Fabry-Perot interferometer.

Fig. 7 Plot of the quantum

defect 6 versus principal 3sns

ISo

quantum number n.

1.5

C

U 0, LC

L3 0,

E

3

:

* b + * t

- : ~

-E

0.6-

a

ooo-

S

⁰

o 3snd

0.L-

-

0

0.2 ^I ^t ^I ^J

10 20 3 0

Principal Quantum Number

n

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JOURNAL D€ PHYSIQUE

Table I1

MQDT-Parameter Mg, 1 ~ 2 bound states.

3 snd 3 P ~ P

Principal Quantum Number n

Fig. 8 Admixture of 3p2 1 ~ 2 character in the 3snd series of Mg.

This work was supported by the Deutsche Forschungsgemeinschaft, S f b 161.

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3 9 , 1520 ( 1 9 7 7 )

/ 2 /

TA.

B o r g s t r o m a n d J . R . Rubbmark, J. P h y s . B: A t . Mol. Phys.

10,

3607 ( 1 9 7 7 )

/ 3 / M. Aymar, P. Camus, M. D i e u l i n , and C . M o r i l l o n , Phys. Rev.

e,

2173 ( 1 9 7 8 )

/4/ M. Aymar, P . G r a f s t r o r n , C . L e v i n s o n , H. Lundberg, a n d S . Svan- b e r , J . Phys. B: A t . Mol. Phys. 1 5 , 877 ( 1 9 8 2 )

/ 5 / T.F. G a l l a g h e r , W. S a n d n e r , K . A . S a f i n y a , Phys. Rev.

G,

²⁹⁶⁹

1 1 9 8 1 )

.

.,

/ 6 / C.M. Brown, R.H. N a b e r , S.G. T i l f o r d , a n d M.L. G i n t e r , Appl.

Opt. 1 2 , 1858 ( 1 9 7 3 )

/ 7 / L . ~ o h a n s s o n , P h y s i c a S c r i p t a

10,

236 ( 1 9 7 4 ) / 8 / C . F r o e s e - F i s c h e r , Can. J . P h y s . 5 3 , 184 ( 1 9 7 5 )

/ 9 / R . B e i g a n g a n d D. S c h m i d t , ~ h ~ s i c a - s c r i ~ t a

27,

172 ( 1 9 8 3 ) / 1 0 / K.T. Lu, J . Opt. Soc. Am.

c,

706 ( 1 9 7 4 )