HIGH RESOLUTION OPTOGALVANIC SPECTROSCOPY AS A USEFUL TOOL IN THE DETERMINATION OF ATOMIC HYPERFINE PARAMETERS AND ISOTOPIC SHIFTS

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HIGH RESOLUTION OPTOGALVANIC

SPECTROSCOPY AS A USEFUL TOOL IN THE DETERMINATION OF ATOMIC HYPERFINE

PARAMETERS AND ISOTOPIC SHIFTS

H.-O. Behrens, G. Guthöhrlein

To cite this version:

H.-O. Behrens, G. Guthöhrlein. HIGH RESOLUTION OPTOGALVANIC SPECTROSCOPY AS A USEFUL TOOL IN THE DETERMINATION OF ATOMIC HYPERFINE PARAMETERS AND ISOTOPIC SHIFTS. Journal de Physique Colloques, 1983, 44 (C7), pp.C7-149-C7-168.

�10.1051/jphyscol:1983713�. �jpa-00223270�

JOURNAI- DE PHYSIQUE

Colloque C7, suppl6ment au n o l l , Tome 44, novernbre 1983 page C7-149

HIGH RESOLUTION OPTOGALVANIC SPECTROSCOPY AS A USEFUL TOOL IN THE DETERMINATION OF ATOMIC HYPERFINE PARAMETERS AND ISOTOPIC SHIFTS

H.-0. Behrens and G.H. G u t h i j h r l e i n

HochschuZe der Bundeswehr Hamburg, Fachbereich EZektrotechnik, HoZstenhofweg 85, 2000 Hamburg 70, F.R.G.

R6sum6 - Nous pri5sentons un sommaire d e s t r a v a u x que nous avons e x 6 c u t d s pen- d a n t l e s deux annQes p r 6 c Q d e n t e s e n s p e c t r o s c o p i e o p t o - g a l v a n i q u e . En u t i l i - s a n t u n l a s e r h c o l o r a n t monomode c o n t i n u a v e c b a l a y a g e d e f r Q q u e n c e e t u n e larnpe h c a t h o d e c r e u s e m o d i f i d e du t y p e S c h i i l e r , r e f r o i d i e B l ' a z o t e l i q u i d e , nous avons e x c i t e e t a n a l y s Q l e s s p e c t r e s d e p l u s i e u r s Q l d m e n t s i n t r o d u i t s d a n s l a c a t h o d e . Des d t u d e s d e s p r o f i l s s p e c t r a u x d e s r a i e s l i m i t 6 s p a r l a l a r g e u r Doppler d ' u n e p a r t , e t d e s 6 t u d e s d e s t r u c t u r e s h y p e r f i n e s s a n s e f f e t Doppler d ' a u t r e p a r t , s o n t p r d s e n t B e s e t c o m p a r 6 e s pour l e s s p e c t r e s d e Mn I, CO I e t La I. Les c o n s t a n t e s d e c o u p l a g e s h y p e r f i n s e t d e d6placements i s o - t o p i q u e s o n t 6 t 6 d 6 t e r m i n 6 e s pour l e s s p e c t r e s d e Yb I , Eu I e t Eu 11.

A b s t r a c t

-

A s u r v e y i s g i v e n c o n c e r n i n g t h e work on o p t o g a l v a n i c s p e c t r o s - copy i n o u r l a b o r a t o r y done d u r i n g t h e l a s t two y e a r s . U s e h a s b e e n made of a single-mode cw d y e - l a s e r a s t u n a b l e l i g h t s o u r c e and l i q u i d n i t r o g e n c o o l e d m o d i f i e d Schiiler-type hollow-cathodes f o r g e n e r a t i n g atoms b e l o n g i n g t o t h e

l e v e l s u n d e r i n v e s t i g a t i o n and s e r v i n g a s o p t o g a l v a n i c e f f e c t s o u r c e s . Toge- t h e r some s t u d i e s on l i n e - s h a p e s D o p p l e r - l i m i t e d and D o p p l e r - f r e e h y p e r f i n e - s t r u c t u r e s t u d i e s i n t h e s p e c t r a o f Mn I, CO I and La I a r e p r e s e n t e d . Hyper- f i n e c o u p l i n g c o n s t a n t s and i s o t o p i c s h i f t s were d e t e r m i n e d i n t h e s p e c t r a of Yb I , Eu I and Eu 11.

I - INTRODUCTION

The aim of our work i s t h e evaluation of both hyperfine-coupling constants and isotopic s h i f t s of high-lying a t o m i c levels by use of t h e optogalvanic e f f e c t which should be ap- plied especially in t h e s e cases in which classical o p t i c a l spectroscopy fails d u e t o resolu- tion limitation by t h e Doppler e f f e c t .

Part of t h e work (Mn I) h a s been done in default of hyperfine d a t a t o be used by astro- nomers. O t h e r investigations (CO I , L a I, Yb I , Eu I and Eu 11) a r e part of more o r less detailed research programs in t h e c o n t e x t of e i t h e r thesis or m a s t e r s degree activities c a r r i e d out in our laboratory.

I1

-

EXPERIMENTAL ARRANGEMENT

Fig. 1 shows a s c h e m e of t h e experimental arrangement. An ion-laser pumped single-mode c w dye-laser served a s light source. This laser could be scanned over a frequency-range o f up t o 30 GHz. A few percent of t h e laser light w e r e f e d via beam-splitter BSI and mirror M t o a frequency-marking spherical fabry-perot i n t e r f e r o m e t e r being embedded in a t e m - p e r a t u r e stabilized box. As dyes e i t h e r rhodamine 6G or stilbene 1 1 were used.

In t h e c a s e of Doppler-limited measurements t h e laser beam was fed via t h e mirrors M3, M4 and M2 ( b e a n - s p l i t t e r BS being removed) i n t o t h e hollow-cathode discharge. Intenslty modulation of t h e laser light 'was achieved on t h e frequency f 2 b the chopper wheel. Y

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1983713

JOURNAL DE PHYSIQUE

C W Both reference fre-

A r - I o n - L a s e r Dye-Laser quency and via capa-

citor C ac-coupled optogalvanic signal a r e guided t o a lock- in amplifier whose output i s simultane- P D.

'4 ously digitized and

displayed together with t h e frequency marks

f r e q e n c y c a l l b r a t i o n on a xy y -plotter.

1 2 In t h e c a s e of t h e

O p p e r Doppler-free measure-

ments beam-splitter BSZ (as shown in Fig. 1) is inserted the inside t h e hollow- cathode downstream propagating laser beam now being modulated on t h e frequency f l whereas t h e Iock-in is detecting t h e sum of t h e t w o modulation frequencies f 1 + ~ 2 - The hollow-cathode constructed axial-sym- metric around t h e di- rection of t h e counter propagating laser beams consists o f a

4 (grounded) cathode cylinder K i-d. 3 mm, length up t o 40 mm with symmetricallv positioned anodes A (only one of them is drawn in Fig. 1).

Further shown a r e Fig. 1 - Scheme of t h e experimental set-up power-supply, ballast

BSI and BS2 a r e beam-splitters; M1, M2, M3 and M4 resistor R, coupling a r e mirrors; P.D. means photodiode capacitor C and t h e

chopper wheel. Not shown in t h e drawing is a s a f e t y circuit containing fast diodes t o prevent t h e lock-in am- plifier input from damage caused by f a s t temporary short circuits due t o irregular sputte- ring in t h e hollow-cathode. Details of t h e hollow-cathode construction including cooling assembly will be published elsewhere.

The cathode itself was made of either t h e metal under investigation (e.g. in t h e case of cobalt) or a n alloy containing a n appreciable amount of t h e element under study (e.g. man- ganese). In some cases (La I, Yb I, Eu I and Eu 11) we rolled a metallic cylinder using a metallic foil and inserted this cylinder into a hollow-cathode made of pure aluminium o r copper.

It should be noted t h a t also not shown in Fig. 1 is t h e vacuum-system suited for evacu- ating and filling of t h e hollow-cathodes with inert gases (neon, argon or krypton).

111

-

LINE SHAPE n U D I E S

Before extracting spectroscopic information out of our optogalvanic measurements w e exa- mined very carefully t h e line profiles and t h e symmetry properties of quasi-monochromatic signals.

I n 1 X 5 7 1 n m

upper trace : a;€ s p ~ c t r u m lover t r a c p : d e v l a t l o n curve to

t e s t ?ausslon p r o f i l e s

Fig. 2 - Line shape studies (Doppler-limited OG-spectrum).

Least squares fitting with gaussian profiles. (Details S. t e x t )

The upper t r a c e of Fig. 2 displays t h e ( ~ o ~ p l e r - l i m i t e d ) OG spectrum of t h e In I line A = 571 nm 8p

2~i12 -

6s Z ~ l 1 2 . The ordinate scale

represents t h e OG- signal intensity in arbitrary units, t h e abscissa is a linear frequency scale. The completely resolved doublet s t r u c t u r e (separation about 8.4 GHz) reflects the hyperfine split- ting of t h e lower fin s t r u c t u r e s t a t e

'i

6s

-

A least squares fit- ting procedure taking a s f r e e parameters the half-width, line centers and intensi- ties of t w o gaussian functions added t o a constant background was applied t o some 3.500 digitized d a t a points and for conve- nience t h e deviation between t h e best cal- culated spectrum and t h e measurement is shown a s lower t r a c e in Fig. 2. The oscil- latory behaviour sym- metrical t o t h e line c e n t r e of both hyper- fine components indi- c a t e s clearly t h a t there is a significant deviation of t h e t r u e line shape from a gaussian shape.

Owing t o this experi- ence w e made a new approach using now a

"modified Lorentzian"

line shape, i.e.

Fig. 3 - Line shape studies (Doppler-limited OG-spectrum).

Least squares fitting with "modified Lorentzian" profiles.

(Further details in t h e t e x t )

C7-152 JOURNAL DE PHYSIQUE

The result obtained by introducing this shape-function into t h e least squares procedure is shown in Fig. 3 (upper t r a c e being t h e s a m e a s in Fig. 2, lower t r a c e again deviation between bestfitted function and measurement). The deviations now coming down t o t h e noise indicates t h e good symmetry properties of our OG-signals.

The "modified Lorentzian" line shape is a rather fast numerical way t o compute line c e n t r e and line shape but t h e physical meaning of t h e shape parameters a , 6 and y is hard t o interprete. Therefore a third approach was made t o understand our (Doppler- limited) line shape. We determined by least squares the best Voigt-function by parametri- zation of both t h e Doppler-width and t h e Lorentzian width of t h e two constituents of the convolution.

Fig. 4 shows t h e result of this procedure o n t h e example of t h e G a I 6p 2 ~ 0 2 112

-

h = 641,401 nm low frequency hyperfine component. Here again the lower t r a c e displays t h e difference bet- ween measurement

L- and bestfitted

Voigt-profile. The difference is down

0 0

Ga I A 6 4 1 , 4 0 1 nm t o the noise. The

u p p e r t r a c e . ratio of gaussian

width t o Lorentzian O G E - s p e c t r u m + best f l t t e d amounts t o v o i g t f u n c t i o n

l o w e r t r a c e : d e v i a t i o n s b5tween m e a s u r e m e n t drld b e s t

FREQUENCY ( R E L . U N I T S )

7.82 t h e Lorentzian width following from t h e fit being 120 MHz in this example. The f a c t t h a t this homoge- neous part of t h e Voigt -profile lies one order of mag- nitude above t h e natural linewidth in this transition is thought t o be due t o collision broade- ning of t h e gallium a t o m s in t h e hollow- cathode plasma.

For reason of brev- ity detailed and even more complex investigations of t h e line shape functions in t h e Doppler-free OG-spectra will be omitted here. These will be published elsewhere in t h e near future.

Fig. 4 - Line shape studies (Doppler-limited OG-spectrum).

T h e best Voigt-function is obtained by a least squares fitting procedure. (Further details in t h e t e x t )

IV

-

HYPEWINE SCRUCTURE INVESTIGATIONS 1. _Manganese

T h e r e is a very well known triplet of fine s t r u c t u r e transitions in t h e manganese atom:

upper level lower level A (nm)

-, -

These lines a r e well suited f o r differential analyses of s t e l l a r abundances. E s p e c i a l l y if a s t r o n o m e r s a r e interested on weak-lined s t a r s t h e y have t o t a k e i n t o account t h e curves of growth. By proceeding in t h i s way t h e y have t o know e x a c t l y t h e hyperfine s t r u c t u r e of t h e lines if t h e t o t a l splitting i s comparable t o t h e Doppler width. As Beynon / l / pointed out unfortunately t h e r e was nothin known about t h e hyperfine s t r u c t u r e of t h e common upper fine s t r u c t u r e level e 'STI2 while very precise values of

-, -

t h e hyperfine interaction constants A and B were determined by H a ~ d r i c h , Steudel and Walther /2/ and also by Luc and Gerstenkorn /3/ for a l l of t h e z P O levels.

By reason of t h i s deficiency we decided t o measure t h e hyperfine s t r u c t u r e of t h e s e t h r e e lines. Part of our results i.e. t h e measurements on t h e

transition A = 601.3498 nm a r e presented here.

Fig. 5 represents t h e hyperfine level s c h e m e of both upper and lower f i n e s t r u c t u r e level t o g e t h e r with t h e allowed e l e c t r i c dipole transitions (upper s e c t i o n ) and t h e resulting t h e o r e t i c a l hyperfine s p e c t r u m (lower section). As usual t h e length of t h e vertical bars

Fig. 5 - Hyperfine level s c h e m e of e S 6 and z 6~ O fine s t r u c t u r e s t a t e (upper section) and h ~ p e r f i n e 3/2 s t r u c t u r e of t h e line.

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Fig. 6 - Doppler-free OG-spectrum of theX = 601.3498 nm Mn I line (upper t r a c e ) , theoretical hyperfine spectrum according t o Fig. 5 (middle t r a c e ) and frequency marks of t h e output of t h e spherical fabry-perot interferometer (lowest trace). The frequency difference between adjacent transmission peaks of t h e interferometer corresponds t o 149 MHz

The signal marked by a s t a r in the OG-spectrum corresponds t o a crossover resonance.

has been adjusted t o t h e relative intensities of the hyperfine components. (In drawing t h e hyperfine level scheme of t h e upper fine structure s t a t e t h e r e has been anticipated our final result). Fig. 6 shows a single scan (measuring t i m e 10 minutes) of a Doppler-free (intermodulated) OG-signal. For reason of clearity t h e r e a r e inserted positions and inten- sities of t h e hyperfine components already shown a t t h e bottom of Fig. 5 and brought he- re t o t h e right frequency-scale. The component in t h e OG-spectrum marked by a n aster- isk is due t o a cross-over resonance signal. At t h e bottom of Fig. 6 a r e plotted t h e si- multaneously measured transmission peaks of t h e f requency-marking spherical fabry-perot interferometer whose free-spectral-range amounts 149 MHz in this case.

Similar measurements of t h e hyperfine structures of t h e other two lines were done.

The evaluation of all measurements together with t h e possibility of a consistency test yielded a s final results:

A(e 6 = 805.1(20) MHz

B(e ' s ~ , ~ ) = 0 MHz within our limits of err01

The results presented here on the hyperfine structure of some CO I lines are part of the thesis of J. Ibrahim-Riid and will be published in detail later on. Table I gives a sketch of the transition types under investigation a s concerns this spectrum.

Fig. 7 shows a Table I

-

Listing of observed CO I transitions Doppler-limited

~ ( n m ) upper level lower level measurement of

the h = 641.78nm

641.78 7

3d 4s 4p z , 2 ~ 0 3d 4s a P 8 2 CO I line. All six

312 112 hyperf ine cornpo-

599.18 7

36 4s 4p z 'DK 8 2 nents are well re-

3d 4s a DgI2 solved. The best

41 1.054 7 2 o 8 2 fitted position of

3d 4s 4p z FgI2 3d 4s a FSl2 each component

411.8 7 2 o 8 2 as well a s twice

3d 4s 4p z 3d 4s a FgI2 the F-quantum

412.13 3d 4s 4p 7 z 2

~i~~

^3d 8 ^{4s a} 2 number of the upper (FO) and

591.5 7 2 2

3d8 4p y 2 ~ ; / 2 3d 4s a Grl2 the lower (FU) hyperfine level a r e given in the three last rows at the bottom of

A

^{Fig. 7}

^.

ca h 6 4 1 . 7 8 n m

I \

As done in Fie. 7

for the A = 641.78

l i

nm line. Fiz- 8

' 1

^,

S. displays the ana-

,.L ¹

^{CO the logous the fine I sixteen A} components line. = d a t a 599.18nm Five hyper- for of a r e fairly well

. -"M-

---

---&U

L,

i

-,, __, .., resolved. Further

0 CB b .n 0 1 o s. 0 ,7 a *'l

FREQIIENCY comments given

. - - -- - . -- -. .

: l ---- - in the d e s c r i p t i ~ n

: . , G

- . -. - ^.-.-p _ _ -. . of Fig. 7 a r e al-

,.,G L h

. . . - - -- - - - --- - - ^--p. so valid here.

Fig. 7 - OG-spectrum (Doppler-limited) and bestfit of CO I A = 641.78 nm

Fig. 8

-

OG-spectrum (Doppler-limited) and bestfit of CoI A = 599.18 nm

JOURNAL DE PHYSIQUE

Fig. 9 - Doppler-limited (upper trace) and Doppler-free (lower trace) OG-spectrum of the CO I line A = 411.054 nm (for details see text).

Fig. 9 shows a comparison between Doppler-limited (upper trace) and Doppler-free (lower trace) OG-spectrum of the CO I line1 = 411.054 nm. The "triplet" structure detectable already in the upper trace has its origin in a certain grouping of hyperfine components. If A F is calculated a s F-quantum number of the upper minus F-quantum number of the lower hyperfine level of each hyperfine component then the following holds: The transitions with AF = -1 l i e a t the low frequency side, those with AF = 0 which a r e the strongest if the J values of upper and lower fine structure level a r e equal lie in the middle part of the hyperfine structure, and those with A F =

+

1 lie a t the high frequency side. This feature is often observed in the hyperfine structure of complex spectra if the magnetic dipole interaction constants A are dominant and of equal order of magnitude for both fine structure levels.

Fig. 10 shows a further comparison between Doppler-limited (upper trace) and Doppler- f ree (lower trace) OG-spect rum of the CO I line A = 412.13 nm.

Looking a t the hyperfine structures displayed in Figs. 9 and 10 clears up that only the Doppler-free OG-spectra enable us t o determine the hyperfine interaction constants of each of the involved fine structure levels. The preliminary results of the evaluation of the spectra presented in Figs. 7, 8, 9 and 10 a r e summarized in Table 11.

Table I1 - Preliminary values of hyperfine parameters arising from the evaluation

of the OG-spectra presented in Figs. 7, 8, 9 and l 0 (* eval. in progr.) in MHz

level a P 2 2 0 2 0

112 a "5/2 a "512 a "7/2

"

^{";/2 '512 ":/2 G9/2}

A 586.4(5) 1,376.9(10) 977.7(35) 390.0(5) 1,367.2(10) 466.1(5) 848.6(27) 492.0(5)

d o p p l e r l i m i t e d and d o s p l e r - f r e e spectrum of CO I h 4 1 2 . 1 3 nm

Fig. 10

-

Doppler-limited (upper t r a c e ) a.nd Doppler-free (lower t r a c e ) OG-spectrum of t h e CO I line X = 412.13 nm

.

3. Lanthanum

Lanthanum was selected a s a well suited element for OG-studies mainly due t o two reasons: ( 1 ) t h e r e exist very precise hyperfine d a t a even for relatively high lying levels of t h e lowest even configuration (5d

+

6 s ) ) obtained by t h e a t o m i c beam resonance meth- od ( A B M R ) by Ting /4/ and Childs and Goodman /5/ which should be extended t o higher lying even levels not attainable by ABMR, (2) moreover t h e OG-spectroscopy promised further extensions of t h e hyperfine analysis of t h e odd configurations of La I of t h e type (5d

+

6s)' 6p by this way completing analyses done also by Childs and Goodman /7/

using the ABMR-Laser-lnduced-Fluorescence method.

Fig. 11 gives part of t h e fine structure level scheme of t h e Lanthanum atom containing only t h e transitions and thereby involved levels studied by us.

Three of them may be presented here:

3.1. L a I 5d 6p y 2 2 o _{. , -}

-

^{5d 6s a} 2 2 _{- , -} ^{X = 582.2 n m .}

Fig. 1 2 gives t h e hyperfine level schemes of t h e upper and lower fine structure level together with t h e allowed transitions and t h e corresponding theoretical hyperfine spectrum of t h e line (lower part).

Fig. 13 shows a Doppler-limited OG-spectrum of this line and Fig. 1 4 shows a Doppler- f r e e OG-spectrum of t h e s a m e line. Comparison of Figs. 12, 13 and 14 clarifies t h a t the Doppler-free OG-spectrum reveals almost a l l of t h e hyperfine components. Besides there a r e the additional (as compared with t h e "true" theoretical hyperfine s t r u c t u r e ) crossing- signals marked by an asterisk which account for a "true" doublet-group of hyperfine com- ponents is growing a triplet, a "true" triplet-group of hyperfine components i s growing a s e x t e t , a well known f e a t u r e of saturation spectroscopy.

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tonflgurat Ion

Fig. 11 - Sketch of t h e fine structure level scheme of t h e La I spectrum.

Only t h e investigated transitions a r e shown

2 0 2

'-'-

^{La I 5d2 6p y G7,'}

-

i d 6s a 2 ~ 9 , 2 L 580.8 nm

.

Fig. 15 corresponds t o Fig. 12 t h e situation being changed caused by t h e new lower level.

Fig. 16 gives a n example of a Doppler-limited OG-spectrum of this line.

-,

Fig. 1 7 shows level scheme and theoretical hiperfine s t r u c t u r e f o r this line.

Fig. 18 shows a Doppler-limited OG-spectrum and

Fig. 19 shows a Doppler-free OG-spectrum of this line. I t should be mentioned that all six hyperfine components a r e resolved in this case.

Table 111 summarizes t h e d a t a evaluated of all lanthanum OG-studies done by us. Also tabulated for comparison a r e t h e available d a t a from other authors.

-

^f

Frequency

Fig. 12 - Hyperfine level schemes of upper and lower fine structure level of the La 1 line X = 582.2 nrn (upper part) and theoretical hyperfine structure of the line.

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p = 0,43 mbar A r I = 6 0 mA

K

Fig. 13 - Doppler-limited OG-spectrum of the La I line A = 582.2 n m .

L a 1 h 5 8 2 , Z nrn p = 0,4 m b a r IF 85 mA

Fig. 14

-

Doppler-free OG-spectrum of the La I line A = 582.2 nm

.

FREQUENCY --.--c£

Fig. 15 - H ~ p e r f i n e level schemes and theoretical hfs of t h e La I line h = 580.8 nm

.

-

^L

Fig. 16 - Doppler-limited OG-spectrum of t h e L a I line X = 580.8 nm

.

JOURNAL DE PHYSIQUE

Table I11 -

Summary o f La I - r e s u l t s

P'REQUENCY ---cf

Fig. 17

-

Hyperfine level s c h e m e s and t h e o r e t i c a l h f s of t h e La I line A = 587.8 nm

.

l e v e l

2 2

5 d 6 s a G 7/2

2 2

5 d 6 s a G 9/2

2 2

5 d 6 s a F 7/2

2 2

5 d 6 s b D3/2

2 2 0

5d 6 ~ Y

2 2

5 d 6 p x D 5/2 2 0

5d6s6p X P 1/2

B / ~ Z t h i s work

-24(15)

228 (84)

4 1 ( 7 )

- 1 0 , 7 ( 8 )

74 (19)

33 (61

0

o t h e r p u b l i c a t i o n s

- - -

- -

-

-

* - - -

40,677 ( 1 2 3 ) [ 51

- 1 1 , 3 ( 3 , 6 ) t 5 1

- -

- - - -- -

- - -

-

-

- -

- - t h i s work

-289,113 (23)

553,135 ( 5 5 )

-195,06 ( 3 5 )

-419,23 (12)

7 3 , 9 3 5 (76)

9 6 , 6 2 4 ( 9 )

-384,93 ( 3 0 ) A/MHZ

o t h e r p u b l i c a t i o n s - 2 9 4 ( 3 ) [ 6 ]

-

-

- -

-

^{- -}

-197,066 ( 6 ) [5]

- 4 2 4 , 7 ( 1 , 4 ) [ S ]

- - -

- -

- -

---

- - -

- -

- -

- E Fig. 18 - Doppler-limited OG-spectrum of t h e La I line A = 587.8 nm

.

p = 0,46 m b a r I = 6 0 mA

K

Fig. 19

-

Doppler-free OG-spectrum of the La 1 line X = 587.8 nm

.

C7-164 JOURNAL DE PHYSIQUE

V

-

HYPERFINE STRUCTURE AND ISOTOPIC SHIFT DETERMINATIONS 1. Ytterbium

The fine structure of t h e neutral Ytterbium spectrum is characterized by the existence of two level systems "A1' and "B" with few interconnecting transitions:

q f ~ l l : 4f14 nl n ' l t ItBu: 4f13 nl n'll n t l l t l

As a first application of the OG-spectroscopy we selected a transition within system "B":

.

^- ₁

having a high lying metastable level a s lower level a t 30,524.714 cm-

.

The energy of t h e upper level is 47,911.48 cm-' (term designations and level energies originate from Meggers and Tech /8/ ).

In preparing t h e hollow-cathode for t h e Ytterbium investigations we used a pure metallic foil of t h e natural lanthanoid. The relative abundances of the seven stable ytterbium iso- topes a r e collected in Table IV.

Table IV - Mass numbers and relative abundances of the seven stable ytterbium isotopes

168 170 171 172 173 174 176 nuclid

0.14 3.03 14.31 21.82 16.13 31.84 12.73 rel. abundance in % There a r e two stable isotopes with a n odd number of nucleons 17'yb and 1 7 3 ~ b . The corresponding nuclear spin quantum numbers and nuclear magnetic moments a r e I = 1/2 and pI = 0.491889(8) n.m. for the 171yb isotpe,

I = 5/2 and pI = -0.67744(3) n-m. for the 1 7 3 ~ b isotope, the nuclear moment data being derived by Olschewski and Otten /9,10/

.

The OG-spectrum of t h e transition of interest is shown in Fig. 20

.

The upper trace is Doppler-limited while t h e lower t r a c e represents t h e Doppler-free measurement, which reveals clearly not only t h e isotopic shift but also the hyperfine structure of both odd- numbered isotopes. The strongest (diagonal) hyperfine components a and b of Yb-171 and a',b1,c',d',e' and f ' of Yb-173 a r e fairly well resolved. A careful evaluation of six high resolution spectra yielded the following results:

174 172

( l ) Isotopic shifts: ( ~ b ) - ( Yb) =

-

1,294.7(10) MHz Relative isotope positions:

170yb: -1.28; 171 Yb: -0.82; 17'yb: 0;

1 7 3 ~ b : +0.44; 1 7 4 ~ b :

+

1; 1 7 6 ~ b : +L95 (2) Hyperfine data:

The differences of t h e hyperfine coupling constants A and B of upper (labeled by "U") and lower (labeled by "I") level were deduced to: l7'Au

-

^{171A1 =} 664.12(17) MHz 1 7 3 ~

-

1 7 3 ~ 1 = -183.460(27) MHz

173Bu - 1 7 3 ~ 1 =

-

94.1(30) MHn

U

It was possible t o calculate t h e hyperfine anomaly h '

The isotopic data concerning the relative isotopic positions a r e in excellent agreement with results published by Broadhurst e t a1 /11/ a s measured on other transitions.

For the line we measured there existed only one experimental value determined by

classical optical interference spectroscopy using enriched isotopes or even mixtures of them

Fig. 20

-

Upper trace: Doppler-limited OG-spectrum of t h e Yb I line X = 574.992 nm Middle trace: Doppler-f ree OG-spect rum of t h e s a m e line

bottom trace: Transmission peaks of t h e frequency marking fabry-perot.

given by Ahmad, Machado and Saksena 1121

.

These authors give a value for t h e isotopic shift between Yb-172 and Yb-176 which deviates only 3.6 MHz from our result.

As concerns t h e hyperfine anomaly one has t o compare with the new value of ^h = - 0-382(19) for the 3 ~ 1 s t a t e of Yb determined by Clark, Cage e t a1 1131

.

Looking a t our limits of e r r o r t h e agreement is thought t o be rather good.

2. Europium

T o point out t h e versatility of OG-spectroscopy we carried out some experiments in t h e s p e c t r a of neutral and even singly ionized europium.

The sensitivity of t h e method is demonstrated in Fig. 21

.

There i s given a n example of a Doppler-limited OG-spectrum of t h e Eu I line X = 579.272 nm which connects t h e

7 7

41 5d 6p y 'Dgl2 level a t 36,889.62 cm-' with t h e 4f 5d 6s b level a t 19,631.26

-1 ^{- ,} - - , -

cm

.

Looking a t t h e intensity tables this Eu I line turns out t o be of a rather interme- diate t o faint intensity (e.g. Meggers e t a1 /14/ a t t r i b u t e a relative intensity value of 15 and Harrisons 1151 a r c intensity amounts 30 for this line). Nevertheless a s Fig. 21 demon- s t r a t e s t h e signal-to-noise ratio of t h e OG-spectrum is quite good. The two prominent maxima of t h e p a t t e r n originate from a n overlap of a group of hyperfine components of

t h e isotope 151Eu with one or several groups of hyperfine components of the i s ~ t o ~ e l ~ ~ E u

JOURNAL DE PHYSIQUE

Fig. 21

-

Upper trace: Doppler-limited OG-spectrum of t h e Eu I line X = 579.272 nm Lower trace: Transmission peaks of t h e frequency marking fabry-perot.

respectively. The hyperfine structure of the upper s t a t e being unresolved we a r e able t o deduce t h e hyperfine coupling constants AL and BL

qf

t h e line for both isotopes according t o the definition of Brix /16/ ans besides the so topic shift. The preliminary results are: 151

AL = - 344.8(5) MHz " ' B ~ =

-

136(15) MHz l S 3 ~ , = - 154.6(5) MHz 1 5 3 ~ L =

-

345(20) MHz

The ability of the OG-spectroscopy even in t h e case of t h e complex hyperfine structures of t h e ionic spectra of t h e rare-earth elements is demonstrated by two examples:

(1) one of the resonant transitions of t h e Eu I1 - spectrum

7 8 0 7 8 0 9 0

4f ( 6pIl2 (3/2, 1/21 -. 4f ( 6s S4 X = 420.505 nm

Fig. 22 shows a Doppler-limited OG-spectrum of this line whose hyperfine structure was earlier analysed by one of us (G.G.) /17/ using enriched isotopes and a double fabry-perot interferometer. This line was used t o test our apparatus and method.

(2) t h e Eu I1 transition

7 8 0 7 8 0 9 o

4f ( 6p3/2 (7/2, 3/21 + 4f ( 5d D2 X = 581.9 nm

Here a chance t o determine precise isotopic shift d a t a in Eu I1 became evident a f t e r

Fig. 22 - Doppler-limited OG-spectrum of t h e Eu I1 line A = 420.505 nm

publication of a paper by Arnesen e t a1 /18/

.

These authors have measured by collinear laser-ion beam technique t h e hyperfine s t r u c t u r e of each of t h e stable europium isotopes in t h e transition a r r a v

7 8 0 7 8 0

4f ( sYI2) 6pgI2 (7/2; 3/21 3,4

-

^{4f (} S7/2) 5d 9 ~ 2

9 9 f

The h v ~ e r f i n e _,

.

c o u ~ l i n g constants A and B of all t h e involved levels now being known t o ⁰ good precision w e supposed t o be able t o measure the isotopic shifts of this transition a r r a y even in t h e Doppler-limited OG-spectra. Our procedure is outlined on Fig. 23 in t h e example of the X = 581.9 nm Eu I1 line. The upper t r a c e of Fig. 23 represents the Doppler-limited OG-spectrum of this line. Below t h e spectrum a r e drawn all hyperfine components for both isotopes. T h e Eu-153 components a r e marked by crosses. For e a c h of t h e two isotopes t h e hyperfine pattern has been calculated using t h e d a t a of Arnesen e t al. The Eu-151 s t r u c t u r e c a n be f i t t e d t o t h e d a t a looking a t t h e first two groups of hyperfine components a t t h e low frequency side. Thereafter one only has t o search for t h e bestfit-position of t h e centre-of-gravity of t h e Eu-153 isotope. This has been done before drawing Fig. 23

.

The resulting isotopic shift amounts

+

1,190 MHz in this case.

V1 - CONCLUSIONS

It has been demonstrated t h a t t h e OG-spectroscopy is a powerful tool for providing d a t a of even complex s p e c t r a a s concerns hyperfine coupling constants and isotopic shifts.

Part of t h e work presented here a s well a s work still going on is financially supported by t h e sponsorship of t h e Deutsche Forschungsgemeinschaft which is gratefully acknowledged.

JOURNAL DE PHYSIQUE

C T

Fig. 23 - Doppler-limited OG-spectrum of t h e Eu I1 line X = 581.9 nm (f-details S-text)

/ l / BEYNON T.G.R., Astr. Astrophys. 61 (1977)853.

/2/ HANDRICH E., STEUDEL A. and wTLTHER H., Phys-Letters A29(1969)486.

/3/ LUC P. and GERSTENKORN S., Astr. Astrophys. ~ ( 1 9 7 2 ) 2 0 9 . - /4/ TING Y., Phys. Rev. 108(1957)295.

/5/ CHILDS W.J. and GOODMAN L.S., Phys. Rev. %3(1971)25.

161 BEN AHMED Z., Physica 77 (1974)148.

/7/ CHILDS W.J. and GOODMKN L.S., JOSA 6 8 (1978)1348.

/8/ MEGGERS W.F. and TECH J.L., JOU~~.R~S.NBS 83 (1978)13.

/9/ OLSCHEWSKI L. and OTTEN E.W., 2-Physik ~ 7 1 9 6 7 ) 2 2 4 . /10/ OLSCHEWSKI L., 2-Physik 249 (1972)205.

/11/ BROADHURST J.H., C A G E X E . , CLARK D.L., GREENLEES G.W., GRIFFITH J.A.R.

and ISAAK

G.RT,

j.Phys. B 7 ( 1 9 7 4 ) ~ 5 1 3 .

/12/ AHMAD S.A., MACHADO

1.7.

and SAKSENA G.D., Spectroch.Acta 35 B (19791215- 1131 CLARK D.L., CAGE M.E., LEWIS D.A. and GREENLEES G.W., ~h~=v.~2C(1979)239.

1141 MEGGERS W.F., CORLISS C.H. and SCRIBNER B.F.: "Tables of ~ p e c t r a l L i n e Inten- sities" NBS Mono 145 Part I (Washington D.C.: US Govt Printing Office, 1975) /15/ HARRISON G.R.: "MIT

-

Wavelength Tables" (Cambridge, Massachusetts, 1969) 1161 BRIX P., 2-Physik =(1952)579.

/17/ GUTHOHRLEIN G., 2.Physik 214(1968)332.

/18/ ARNESEN A., BENGTSON A.,ALLIN R. e t al, Phys. Scripta

-

24 (1981)747.