RECENT PROGRESS IN THE STUDIES OF ATOMIC IONIZATION PROCESSES INVOLVING SYNCHROTRON AND LASER RADIATIONS

(1)

HAL Id: jpa-00221838

https://hal.archives-ouvertes.fr/jpa-00221838

Submitted on 1 Jan 1982

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

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

RECENT PROGRESS IN THE STUDIES OF ATOMIC IONIZATION PROCESSES INVOLVING

SYNCHROTRON AND LASER RADIATIONS

F. Wuilleumier

To cite this version:

F. Wuilleumier. RECENT PROGRESS IN THE STUDIES OF ATOMIC IONIZATION PROCESSES

INVOLVING SYNCHROTRON AND LASER RADIATIONS. Journal de Physique Colloques, 1982,

43 (C2), pp.C2-347-C2-366. �10.1051/jphyscol:1982227�. �jpa-00221838�

(2)

JOURNAL DE PHYSIQUE

Colloque C2, supplément au n°ll, Tome 43, novembre 1982 page C2-347

RECENT PROGRESS IN THE STUDIES OF ATOMIC IONIZATION PROCESSES INVOLVING SYNCHROTRON AND LASER RADIATIONS

F.J. Wuilleumier

Laboratoire de Spectrosoopie Atomique et Ionique and LURE, Université Paris Sud, 91405 Orsay, France

Résumé.- Cet article passe en revue certains résultats récents obtenus par spectro- mëtrie d'électrons sur des atomes, à l'aide du rayonnement synchrotron émis par l'an-

neau de stockage à électrons ACO, à Orsay, couplé dans certains cas avec l'utilisa- tion du faisceau d'un laser à colorant continu. L'étude du calcium et de l'hélium dans l'état fondamental et d'atomes de sodium préalablement portés dans un état exci- té à l'aide du laser sert à illustrer l'état actuel des recherches en photoionisation atomique.

Abstract.- This paper reviews recent results obtained in photoelectron spectrometry studies carried out on atoms with the synchrotron radiation emitted by the ACO storage ring in Orsay, combined, in some cases, with the use of a cw tunable dye laser.

Photoionization from the ground state of Ca and He and from laser excited sodium a- toms serves to illustrate the present status of the experimental studies in atomic photoionization.

1. Introduction.- Since the first pionnering experiment on autoionizing levels of He revealed with the radiation emitted by the SURF synchrotron at the National Bureau of Standards, in Washington,(1), large progress has been made in the production and in the use of intense flux of synchrotron radiation. Until modern electron storage rings became available, however, experiments with synchrotron radiation were limited mostly

to photoabsorption experiments. During the past few years, the advent of toroidal grating monochromators (2) mounted on electron storage rings extended considerably, at least in the energy region covered by this paper, typically between 5 and 200 eV, the potentialities of synchrotron radiation. With the higher flux of photons now rou- tinely available, selective spectroscopies such as electron spectrometry or fluorescence spectroscopy, could be used in a much more efficient way to analyse, in details the various aspects of the photoionization process in gaseous samples. To illustrate this progress, we show first in Fig.l the photoabsorption spectrum of He in the e- nergy region of the doubly excited states of the n=3 series, measured in 1969 by Dhez and Ederer.O) Only the first member of the series is detectable, with a poor contrast, beacuse of the very low partial cross section associated with this channel, less than 1% of the total photoabsorption cross section.In 1980, Woodruff and Samson (4) used the fact that the final state of the autoionization process following exci- tation of the n=3 series is the n=2 excited state of He

+

. Then, this excited state can only decay via fluorescence emission to the ground state of the ion, in emitting photons of 40.8 eV. The detection of this fluorescence brings direct information on

the cross section for leaving the residual ion in the n=2 excited state within the resonance region, and consequently on the cross section for exciting the resonances of the doubly excited states. These results are shown in Fig.2. They are also a clear illustration of the large progress made possible over a period of 10 years by the improvements in the technology of synchrotron radiation.

Rare gas atoms were the first elements to be extensively studied, because of their easy handling. Considerable information has thus been obtained on these closed shell systems.(5) At the present time, photoionization processes in these atoms are fairly well understood.(6) This is not yet the case for metallic vapors, and, more general- ly, for open-shell systems, because of the difficulties involved in the production of samples of suitable characteristics in the source volume of an electron spectro-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982227

(3)

JOURNAL DE PHYSIQUE

Fig.1- Transmission s c a n of t h e 3s3p 1 p l 0 two-elec- t r o n e x c i t a t i o n resonance i n He (from Ref. 3)

1

I

176.5 177.0 177.5 178.0

Wavelength

(A)

meter. Systematic a n a l y s i s of energy resolved e l e c t r o n s p e c t r a a r e j u s t s t a r t i n g and a n g u l a r d i s t r i b u t i o n measurements of t h e p h o t o e l e c t r o n s a r e s t i l l d i f f i c u l t e x p e r i - ments. The r e a d e r i s r e f e r r e d t o a r e c e n t review ( 7 ) f o r more d e t a i l e d i n f o r m a t i o n on the s t a t e of t h e a r t i n t h i s domain.

Up t o a r e c e n t p a s t , a l l p h o t o i o n i z a t i o n measurements c a r r i e d o u t w i t h synchrotron r a d i a t i o n had been made when t h e i n i t i a l s t a t e of t h e atom under i n v e s t i g a t i o n was t h e ground s t a t e . The coupling of a beam from a cw dye l a s e r with synchrotron r a d i a - t i o n opened r e c e n t l y t h e way t o a whole new c l a s s of experiments on atoms prepared i n e x c i t e d s t a t e s . (8)

I n t h i s paper, a f t e r having b r i e f l y d e s c r i b e d a t y p i c a l experimental s e t up f o r t h e s t u d y of p h o t o i o n i z a t i o n p r o c e s s e s with synchrotron r a d i a t i o n , we w i l l p r e s e n t t h r e e r e c e n t examples of e l e c t r o n spectrometry s t u d i e s t o i l l u s t r a t e t h e types of e x p e r i - ments t h a t a r e p r e s e n t l y a c h i e v a b l e . These a r e energy r e s o l v e d photoemission and Au- g e r emission i n atomic Ca, a n g u l a r d i s t r i b u t i o n of p h o t o e l e c t r o n s l e a v i n g t h e ~ e ~ i o n i n i t s f i r s t e x c i t e d s t a t e , p h o t o i o n i z a t i o n and a u t o i o n i z a t i o n p r o c e s s e s i n l a s e r e x c i t e d sodium atoms.

I I I I I

N=3 THRESHOLD

n=3 4 5 6 78

K = I

1 z E

aio-

5 2

Fig.2- The a u t o i o n i z i n g

I-

B

r e g i o n below t h e n=3

cn i o n i z a t i o n t h r e s h o l d

U) measured i n f l u o r e s c e n -

8

ce (from Ref. 4)

.

The

Q05

-

f i r s t a u t o i o n i z a t i o n

l i n e , c l o s e t o 70 eV, corresponds t o t h e weak s t r u c t u r e observed i n t h e photoabsorpti6n spectrum of Fig.1.

PHOTON ENERGY feV)

(4)

F i g . 3

-

Schematic view of t h e 161' t o r o i d a l g r a t i n g monochromator and t h e cy- l i n d r i c a l m i r r o r e l e c t r o n energy a n a l y z e r used a t t h e ACO s t o r a g e r i n g . M = plane m i r r o r ,

TM

= t o r o i d a l m i r r o r s , G I G2 = i n t e r c h a n g a b l e h o l o g r a p h i c a l l y r u l e d t o r o i d a l g r a t i n g s , S1

*

e n t r a n c e s l i t , S 2 = e x i t s l i t , S = i n t e r a c t i o n zone, C = channel t r o n .

2. Experimental s e t up

.-

A l l experiments d e s c r i b e d h e r e made use of t h e synchrotron r a d i a t i o n e m i t t e d by the ACO s t o r a g e r i n g i n Orsay, i n t h e 20-200 eV photon energy range. F i g . 3 shows a schematic diagram of t h e A61 beam l i n e and t h e v e r t i c a l l y d i s - p e r s i n g 161' t o r o i d a l g r a t i n g monochromator used t o monochromatize t h e synchrotron r a d i a t i o n . ( 9 ) . The l i g h t coming from ACO i s f i r s t r e f l e c t e d i n t h e h o r i z o n t a l p l a n e i n t o t h e A61 beam l i n e by a p l a n e m i r r o r M and f a l l s on a t o r o i d a l m i r r o r PM. This m i r r o r f o c u s e s t h e synchrotron r a d i a t i o n on t h e e n t r a n c e s l i t S1 of t h e monochromator.

A f t e r d i f f r a c t i o n by one of t h e two i n t e r c h a n g a b l e g r a t i n g s G, t h e monochromatic li- g h t passing t h e e x i t s l i t i s d e f l e c t e d back t o t h e h o r i z o n t a l by a second t o r o i d a l m i r r o r RM which focuses t h e monochromatic l i g h t i n t o t h e source volume of an e l e c t r o n

spectrometer. The c h a r a c t e r i s t i c s of t h e photon beam a t t h e i n t e r a c t i o n zone (photon f l u x , h i g h e r o r d e r c o n t r i b u t i o n s , band width and p o l a r i z a t i o n ) have been determined by photoemission experiments on s e l e c t e d atoms.(9)

h

t h e energy range of i n t e r e s t , t y p i c a l photon f l u x of 1012 photons/sec i n a 1 % band width a r e r o u t i n e l y a v a i l a b l e with ACO runing a t 80 mA. Ultimate r e s o l u t i o n of about 0.1% can be o b t a i n e d with t h i s monochromator.

The e l e c t r o n spectrometer i s a c y l i n d r i c a l m i r r o r a n a l y z e r s p e c i a l l y designed f o r experiments with synchrotron r a d i a t i o n . I t has been widely used f o r photoemission expe- r i m e n t s on atoms and molecules.(5) The main a x i s of t h e CMA i s d i r e c t e d p a r a l l e l t o

t h e photon beam. For e l l i p t i c a l l y p o l a r i z e d r a d i a t i o n , t h e d i f f e r e n t i a l photoioniza- t i o n c r o s s s e c t i o n f o r e l e c t r o n s being i o n i z e d i n t o t h e - ith channel i n t o t h e continuum i s :

=

5 {

¹

^- $ pi

[ p 2 ( c 0 8 e z )

-

~ ( C O S 2

-

c 0 s 2 e ) P I

)

2 ^X

d a 4 ~ Y

where (3i i s t h e angular assymetry parameter f o r t h e i t h channel, p i s the magnitude of t h e p o l a r i z a t i o n , P2 i s t h e Legendre polynomial of second o r d e r ,

8 x , 8 y , 8 z

a r e t h e a n g l e s t h e p h o t o e l e c t r o n s make with t h e x , y and z axes, r e s p e c t i v e l y ( s e e

~ i g . 4 ) ~ ~ The photons propagate i n t h e z d i r e c t i o n . I f one c o l l e c t s a l l p h o t o e l e c t r o n s which a r e e m i t t e d i n a cone under the so-called magic a n g l e of 54O44' (P2 = 0 f o r t h i s a n g l e ) , t h e d i f f e r e n t i a l p h o t o i o n i z a t i o n c r o s s s e c t i o n i s simply p r o p o r t i o n a l t o t h e a b s o l u t e c r o s s s e c t i o n and t h e r e l a t i v e i n t e n s i t i e s measured i n an energy r e s o l - ved p h o t o e l e c t r o n spectrum a r e indepent on t h e an u l a r d i s t r i b u t i o n of the photoelec- t r o n s and p o l a r i z a t i o n of t h e synchrotron l i g h t . l b

Fig.5 p r e s e n t s a l a y o u t of t h e e l e c t r o n s p e c t r o m e t e r . When r a r e gases o r molecular g a s e s a r e being s t u d i e d , t h e gaseous samples i s i n t r o d u c e d i n t o t h e i n t e r a c t i o n zone through a m u l t i c a p i l l a r y a r r a y , p e r p e n d i c u l a r l y t o t h e z a x i s and t o the p l a n of t h e f i g u r e . 1 1 For experiments with m e t a l l i c v a p o r s , l 2 , l 3 a s t a i n l e s s s t e e l oven i s placed on t h e a x i s of the CMA. I t i s r e s i s t i v i c a l l y h e a t e d by tantalum w i r e s and a maximum

(5)

JOURNAL DE PHYSIQUE

Y

Fig.4- Experimental ge-

ometry. Photons propaga- t e along t h e z a x i s . The e l e c t r i c v e c t o r of t h e main component of t h e synchrotron r a d i a t i o n i s i n the p l a n of t h e or- b i t and d i r e c t e d along

the x a x i s , t h e small p e r p e n d i c u l a r component has i t s e l e c t r i c v e c t o r d i r e c t e d along t h e y a-

hv

^{x i s .} I n t h i s experiment

-

⁸ h a s always the v a l u e

54'44', and t h e c o r r e s - pondance between t h e va- l u e s of and

8, - 8

i s : f o r IQ = 0 , 8 = 35076' and 8 = 90°; f o r

= 980,

e x

⁼90' and

e Y

= 35'16'.

X

temperature of about 1 0 0 0 " ~ can be reached. Residual magnetic f i e l d i n t h e presence of t h e h e a t i n g c u r r e n t i s l e s s than 2 mOe i n t h e source volume and on the path of t h e e l e c t r o n s i n t h e spectrometer. The photon beam t r a v e r s e s t h e oven and i s monito- r e d by measuring t h e p h o t o e l e c t r i c c u r r e n t e m i t t e d from a gold f o i l . More d e t a i l e d i n f o r m a t i o n 6n t h i s s e t up can be found elsewhere. l l , l 2

For t h e f i r s t experiments combining the use of a cw dye l a s e r t o c r e a t e a s t e a d y po- p u l a t i o n of atoms i n a n e x c i t e d s t a t e and of synchrotron r a d i a t i o n t o photoioniee t h e e x c i t e d atoms, l 4 t h e same CMA was used t o analyze t h e e l e c t r o n s e j e c t e d from t h e i n t e r a c t i o n zone. The l a s e r beam was introduced through a window i n t h e wall of t h e vacuum chamber and i r r a d i a t e d t h e vapor beam a t r i g h t a n g l e t o i t s mean d i r e c - t i o n ( s e e F i g . 5 ) . The l a s e r beam was a d j u s t e d t o f i t t h e shape of t h e source voEume ( l e n g t h along t h e a x i s ~ , 6 m , c e n t e r of t h e zone l o c a t e d a t 8 mm from t h e oven, a c t i - ve volume* 0.05 cm3). The l a s e r was a cw s i n g l e mode r i n g dye l a s e r pumped by an A r i o n l a s e r of 18 w a t t s . I t was a b l e t o d e l i v e r up t o 1.2 w a t t when locked t o t h e 3 F = 2

*

³2 ~ 3 / 2 F = 3 h y p e r f i n e component of t h e D2 resonance l i n e of so-

Fig.5- Layout of t h e e l e c - t r o n spectrometer w i t h t h e oven. The c o o l i n g chamber around t h e oven i s n o t shown. 0 = oven;

GF = gold f o i l with e l e c - trometer a m p l i f i e r moni- t o r i n g t h e photon f l u x ; CH = c h a n n e l t r o n . The photons from t h e synchro- t r o n r a d i a t i o n a r e coming from t h e l e f t , t h e photons from t h e l a s e r a r e coming from t h e top.

(6)

dium a t 5890

i.

For a n g u l a r r e s o l v e d photoemission experiments, t h e CMA can be modified by a p e r t u - r i n g t h e i n n e r - c y l i n d e r t o r e s t r i c t the azimuthal a c c e p t a n c e . ( l 5 , 1 6 ) Only those e- l e c t r o n s a r e d e t e c t e d t h a t a r e e m i t t e d i n t o an a n g u l a r s e c t o r 2' i n t h e 0 , d i r e c - t i o n c e n t e r e d around t h e magic angle of 54'44', and *7' i n t h e azimuthal d i r e c t i o n p e r p e n d i c u l a r t o t h e a x i s of symmetry of t h e spectrometer. P h o t o e l e c t r o n s can be measured a s a f u n c t i o n of a n g l e f o r v a l u e s of ranging from -90' to +90°. The po- l a r i z a t i o n of t h e r a d i a t i o n and the spectrometer f u n c t i o n a r e determined using c a l i - b r a t i o n gases w i t h known asymmetry parameters.

I n t h e following examples, we w i l l d e s c r i b e i n a q u a l i t a t i v e way t h e type of proces- s e s t h a t can be s t u d i e d i n photoemission experiments, r e f e r r i n g t h e r e a d e r t o t h e o- r i g i n a l papers f o r a comprehensive a n a l y s i s and i n t e r p r e t a t i o n of t h e r e s u l t s . 3. Continuous and Resonant Photoemission i n Calcium.

-

From a t h e o r e t i c a l p o i n t of view, atomic calcium i s a v e r y i n t e r e s t i n g system, showing a l a r g e v a r i e t y of many e l e c t r o n e f f e c t s ( 1 7 ) . I n the photon energy range covered by t h e s e experiments, the- r e a r e s e v e r a l s u b s h e l l s r e l a t i v e l y c l o s e i n binding energy, o f f e r i n g an e x c e l l e n t o p p o r t u n i t y t o s t u d y c o r r e l a t i o n e f f e c t s between a r e l a t i v e l y deep i n n e r s h e l l and s e v e r a l o u t e r s h e l l s . Moreover, t h e r e a r e a number of lowlying empty l e v e l s which o v e r l a p s t r o n g l y with t h e occupied l e v e l s . I n a d d i t i o n , t h e 3d wavefunction of t h e

~ a * i o n w i t h a h o l e i n t h e 3p core c o n t r a c t s i n such a way t h a t t h e binding energy i n t h i s o r b i t a l i s h i g h e r than t h e binding energy of t h e 4s e l e c t r o n s , a t v a r i a n c e w i t h t h e ground s t a t e . Thus, shake down a s well a s shake up s a t e l l i t e s may be ob- derved when a Ca atom i s i o n i z e d i n the 3p s u b s h e l l . ( 1 7 ) ( a shake up s a t e l l i t e ap- p e a r s i n t h e p h o t o e l e c t r o n spectrum a t a k i n e t i c energy lower than t h e energy of the maili l i n e : i t corresponds t o a p h o t o i o n i z a t i o n p r o c e s s i n which a second e l e c t r o n i s simultaneously e x c i t e d t o an empty o r b i t a l of lower binding energy; a shake down s a t e l l i t e appears a t h i g h e r k i n e t i c energy than t h e main l i n e and corresponds t o a p h o t o i o n i z a t i o n process i n which a second e l e c t r o n f a l l s simultaneously onto a n o r - b i t a l of h i g h e r binding energy).

The binding energy of t h e 4s and 3p e l e c t r o n s i n n e u t r a l Ca a r e 6.11 eV and 34.31 eV ( f o r t h e 2 ~ 3 1 2 f i n a l i o n i c s t a t e ) and 34.66 eV ( f o r t h e 2 ~ 1 1 2 s t a t e ) , r e s p e c t i v e l y .

Fig.6

-

The Ca I ab- s o r p t i o n spectrum b e t - ween 25 and 40 eV.

a ) Background c o n t i - nuum; b) moderate c a l - cium a b s o r p t i o n ; c ) s t r o n g calcium absorp- t i o n ; d) v e r y s t r o n g calcium a b s o r p t i o n a t high p r e s s u r e (from Ref. 19).

(7)

JOURNAL DE PHYSIQUE

Binding Energy (eV)

<

_I _I _I _I _I

14 12 10

8

6

Fig.7.- P h o t o e l e c t r o n spectrum of Ca o b t a i n e d w i t h He1 r a d i a t i o n (photon energy = 2 1.2 eV)

.

Peaks of i n t e r e s t a r e l a b e l e d by s p e c t r o s c o -

symbols (from Ref.

A wealth of s t r u c t u r e caused by r e s o n a n t t r a n s i t i o n s i n v o l v i n g one o r two 4s e l e c - t r o n s have been observed i n t h e photoabsorption spectrum of Ca, below and above t h e 4s i o n i z a t i o n t h r e s h o l d . ( l 8 ) Photoabsorption i n the energy r e g i o n of t h e 3p i o n i z a - t i o n t h r e s h o l d has been e x t e n s i v e l y measured, r e v e a l i n g t h e e x i s t e n c e of more t h a n 125 l i n e s . ( l 9 ) Fig.6-shows t h i s r i c h spectrum between 25 eV and 40 eV photon energy.

Many of t h e s e resonance l i n e s have been c l a s s i f i e d i n t o s e v e r a l s e r i e s i n v o l v i n g t h e e x c i t a t i o n of one 3p e l e c t r o n , accompanied i n some c a s e s by the simultaneous e x c i t a t i o n of t h e 4s valence s u b s h e l l . ( l 9 )

An e l e c t r o n spectrum of atomic Ca had been p r e v i o u s l y o b t a i n e d , using d i s c r e t e W emission l i n e e x c i t a t i o n (He I , a t 21.2 eV, s e e F i g . 7 ) . ( 2 0 ) I t shows one main peak a t 6.11 eV binding energy, corresponding t o t h e ~ a + ( 4 s 2 ~ ) f i n a l s t a t e and f o u r lower i n t e n s i t y peaks, c a l l e d s a t e l l i t e l i n e s , whose binding e n e r g i e s correspond r e s p e c t i v e l y t o t h e 3d ' ~ ~ / 2 , 5 / 2

,

4p 2 ~ 1 / 2 312

,

5 s 2 ~ 1 / 2 and 4d 2 ~ 3 / 2 , 5 / 2 f i n a l s t a t e s . At 29 eV photon energy, o u t s i d e of m y resonance region, i n a f l a t p a r t of t h e a b s o r p t i o n spectrum

,

i n Fig. 8 , t h e e l e c t r o n spectrum obtained using synchro- t r o n r a d i a t i o n (21) i s b a s i c a l l y t h e same a s a t 21.2 eV. The p r o d u c t i o n of i o n s l e f t i n t h e 3d 2 ~ o r 4p 2~ e x c i t e d s t a t e s can be a t t r i b u t e d mainly t o i n i t i a l s t 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 (ISCI). The ground s t a t e of Ca i s n o t p u r e l y a 4s2 s t a t e , b u t should be d e s c r i b e d a s shown i n Fig.9 ( 2 2 ) , by admixing a d d i t i o n a l configura- t i o n s of t h e same symmetry.(20) The weight of the v a r i o u s c o n f i g u r a t i o n s i s u s u a l l y determined from c a l c u l a t i o n s of t h e t o t a l energy. The N-electron f i n a l s t a t e of t h e photoemission process must have

IP

symmetry. However, i t can be made up of a wide v a r i e t y of s t a t e s of ~ a + p l u s a continuum s t a t e of a p p r o p r i a t e symmetry. Each of t h e one-electron s t a t e i n ~ a + t h a t can be reached by removal of an e l e c t r o n from c o n f i g u r a t i o n s such a s t h e ones shown i n Fig.9 can show up i n t h e e l e c t r o n spectrum.

F i g .8- P h o t o e l e c t r o n spectrum of Ca o b t a i - - ned with synchrotron r a d i a t i o n photons of 29 eV. The e l e c t r o n l i n e s a t about 16 eV k i n e t i c energy a r e due t o t h e Auger decay of a 3p vacancy produced by 2nd o r d e r photons(21-)'

BINDING ENERGY h V 1

(8)

c ~ + ( ~ P ) 4 ~ '

c ~ + ( ~ D ) 3d'

c ~ + ( ~ s ) 4s' A

A t

Fig.9.- I n i t i a l Sta-

t e C o n f i g u r a t i o n In-

Intensity -

t e r a c t i o n i n Ca (from Ref .22).

I n f i r s t approximation, t h e i n t e n s i t y of t h e corresponding l i n e s i n t h e e l e c t r o n spectrum should g i v e a measure of t h e e x t e n t t o which t h e v a r i o u s n e 2 configura- t i o n s a r e admixed i n t o t h e ground s t a t e . A comparison (20) of t h e squares of t h e mixing c o e f f i c i e n t s a 2 , b2 and c 2 o b t a i n e d from a Multi-Configuration H a r t r e e Fock c a l c u l a t i o n s ( 2 3 ) w i t h t h e e x p e r i m e n t a l l y observed s a t e l l i t e i n t e n s i t i e s g i v e a good agreement f o r t h e 4p 2~ s t a t e , b u t n o t f o r t h e 3d 2~ s t a t e : i n t h i s l a t e r c a s e , t h e d i f f e r e n c e s i n p h o t o i o n i z a t i o n c r o s s s e c t i o n s a r e probably too l a r g e t o be n e g l e c t e d . Population of h i g h e r e x c i t e d s t a t e s of the i o n may be accounted f o r by ISCI, i n t e r - channel coupling and, f o r t h e ( n + l ) s 2s s t a t e s by shake up t r a n s i t i o n s ( or,more g e n e r a l l y , by f i n a l i o n i c s t 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 - FISCI), b u t t h e d i f f e r e n - t i a t i o n between t h e i n d i v i d u a l c o n t r i b u t i o n s becomesmore and more d i f f i c u l t .

When one i n c r e a s e s the photon energy by r e g u l a r s t e p of energy i n t e r v a l , t h e shape of t h e e l e c t r o n spectrum changes d r a m a t i c a l l y a t some s p e c i f i c photon e n e r g i e s . For example, a t 29.98 eV, s t r o n g enhancements of t h e 3d 2 ~ and 4p 2~ e l e c t r o n l i n e s a r e observed(24), a s shown i n t h e lower frame of Fig.10. The a b s o l u t e i n t e n s i t y of t h e 4s 2s l i n e does n o t vary a t t h i s energy, b u t the i n t e n s i t i e s of production of t h e

KINETIC ENERGY ( s V ) two f i r s t e x c i t e d s t a t e s a r e i n c r e a s e d

1600 la00 2aW 22.M 2400 2600 by more than one o r d e r of magnitude.

This photon energy corresponds t o t h e e x c i t a t i o n energy of a 3

3

^from

t h e 3p64s2 to the 3p5(3d ~ P ) ~ P i n t e r -

two IW mediate s t a t e . ( l 9 ) Then, t h i s a u t o i o n i -

zing s t a t e decays t o t h e 3p63d ;but t h e

P enhancement of t h e 3p64p f i n a l s t a t e seems

-

^loo0

.

t o i n d i c a t e t h a t a 3p53d24p e x c i t e d s t a t e

of n e u t r a l calcium i s a l s o produced by

z photoabsorption a t t h i s energy.

8

wo An even more s p e c t a c u l a r e l e c t r o n spec-

trum i s o b t a i n e d when t h e energy of the monochromator i s tuned t o 31.62 eV, a s

o

2

e v i d e n t i n Fig. l l . ( 2 1 ) According t o t h e

previous photoabsorption study, ( 19) se-

~ I W 1w u v e r a l f i n a l s t a t e c o n f i g u r a t i o n s c o r r e s -

ponding t o t h e r e s o n a n t e x c i t a t i o n of

8 1 m '

9

.

Fig.10.- E l e c t r o n s p e c t r a following i o -

n i z a t i o n of Ca by photons of 30.57 eV

a

(upper frame, i n a f l a t p a r t of t h e ab-

0 SOD WI s o r p t i o n spectrum, s e e Fig.6) and 29.98

eV(1ower frame, corresponding t o a r e s o - nance i n t h e photoabsorption spectrum

o (from Ref. 24)

.

KINETIC ENERGY (eV)

(9)

JOURNAL DE PHYSIQUE

1200 U.W 18.00 ZOm 2200 24.W 2MO 28.00 30.00

2000 Fig.11.- E l e c t r o n spec-

trum following i o n i z a - t i o n of Ca with 31.62 eV photons. S e v e r a l h i g h l y e x c i t e d s t a t e s

P ",

¹²⁹⁰ of t h e Ca+ i o n a r e r e -

.

s o n a n t l y enhanced a t

I- V) t h i s photon energy.

$

^8C4 (from Ref. 21)

CHANNEL NUMBER

one 3p e l e c t r o n can be reached a t t h i s photon energy w i t h i n t h e band pass of t h e mo-.

nochromator:

5 2 5 2

ca(3p64s2 IS) + h 3

-+

3p 4s 3d, 3p54s24d, 3p53d3, 3p54p23d, 3p 3d 4 s

One observes t h a t a g r e a t number of h i g h l y e x c i t e d s t a t e s of ~ a + a r e s t r o n g l y enhanced, on a r e l a t i v e a s w e l l a s on an a b s o l u t e s c a l e . This g i v e s evidence of t h e s t r o n g rearrangement i n t h e e x c i t a t i o n process and of t h e importance of a u t o i o n i z a t i o n and Auger p r o c e s s e s i n t h e subsequent decay of t h e i n t e r m e d i a t e n e u t r a l e x c i t e d s t a t e . Shake up and c o n j u g a t e shake up t r a n s i t i o n s must a l s o take p l a c e d u r i n g t h e a u t o i o n i - z a t i o n and Auger p r o c e s s e s , s i n c e f i n a l s t a t e s of Ca+ a s high a s 3p65d-6d-4f-5f show l a r g e i n t e n s i t i e s . Since the d i r e c t p h o t o i o n i z a t i o n processes i s very weak f o r most of t h e s e f i n a l s t a t e s , no i n t e r f e r e n c e e f f e c t can occur, a s confirmed by the symme- t r i c shape of most of t h e e l e c t r o n l i n e s . The a p p a r e n t broadening of t h e l i n e around 13.6 eV i s l i k e l y due t o overlapping e f f e c t s r a t h e r than t o p o s t c o l l i s i o n i n t e r a c - t i o n . (26)

I n c r e a s i n g f u r t h e r t h e photon energy, a s soon a s one has c r o s s e d t h e 3p i o n i z a t i o n t h r e s h o l d , t h e spectrum i s dominated by i o n i z a t i o n i n t h e 3p s u b s h e l l . F i g . 12 shows the e l e c t r o n spectrum o b t a i n e d a t 36.5 eV.(25) E l e c t r o n l i n e s due t o i o n i z a t i o n i n t h e o u t e r s h e l l have become very weak. The most i n t e n s e e l e c t r o n l i n e s a t 16.33 and

KINETIC ENERGY ( s V )

Fig.12.- E l e c t r o n spectrum following i o n i z a - t i o n of Ca by photons of 36.54 eV,about 2 eV above t h e 3p i o n i z a t i o n

CO+ 3p5 4s2+ e- t h r e s h o l d . (from Ref.25)

34 32 22 I 8 14 10

BINDING ENERGY (eV)

(10)

BINDING ENERGY (*V)

10000

8000 Y U

--.

⁶⁰⁰⁰

r

^E ^D ^C B A A '

I I 1 I l l F E" D'C" B"A"

a I I I I I I

$ 4 0 ~

2wO

0

KINETIC ENERGY (.V)

Fig.13.- E l e c t r o n spectrum following p h o t o i o n i z a t i o n of atomic calcium by 47.32 eV photons. Peaks l a b e l e d A t o F and A" t o F" a r e p h o t o l i n e s corresponding t o v a r i o u s f i n a l s t a t e s of ~ a + i o n with a 3p h o l e , r e s p e c t i v e l y produced by photons d i f f r a c t e d i n 1 s t o r d e r and i n 2nd o r d e r by the monochromator. Peaks A' t o F' a r e Auger e l e c t r o n s e m i t t e d i n t h e decay of the- s e f i n a l s t a t e s . ( f r o m Ref.24)

16.67 eV a r e due t o t h e Auger decay of a 3p h o l e l e a v i n g t h e r e s i d u a l dcubly charged i o n i n the 3p6 I S s t a t e . The p h o t o e l e c t r o n l i n e s due t o i o n i z a t i o n of a 3p e l e c t r o n , seen below 3 eV k i n e t i c energy, show up w i t h very l i t t l e a p p a r e n t i n t e n s i t y , because t h e e l e c t r o n spectrum h a s n o t y e t been c o r r e c t e d f o r t h e energy d i s p e r s i o n of t h e CMA. Since t h e i o n i c s t a t e s 3p54s2 2 ~ 1 / 2 , 3 / 2 a r e n o t t h e lowest s t a t e s of ~ a + i o n w i t h a h o l e i n t h e 3p c o r e , ( l 7 ) , because of t h e c o n t r a c t i o n of t h e 3d o r b i t a l , one observes, i n t h i s v i c i n i t y of t h e 3p t h r e s h o l d , a l a r g e number o f a d d i t i o n a l Auger l i n e s of lower energy with l a r g e i n t e n s i t i e s . They correspond t o a number of shake down l e v e l s ( a t l e a s t seven a r e e a s i l y d i s t i n g u i s h a b l e ) . For some of t h e s e Auger l i n e s e x c i t e d v e r y c l o s e t o t h r e s h o l d , a l a r g e number of phenomena a s s o c i a t e d w i t h PC1 a r e d e t e c t a b l e . (26)

F i n a l l y we show i n Fig.13 t h e e l e c t r o n spectrum measured a t h i g h e r photon energy (47.32 eV) f a r above t h r e s h o l d . ( 2 4 ) Here, t h e f u l l 3p p h o t o e l e c t r o n s ectrum i s seen.

On both s i d e s of t h e main p h o t o e l e c t r o n l i n e , noted B ( f i n a l s t a t e 3p 4s2 2 ~ ) ,

5

one observes s a t e l l i t e l i n e s : shake up l i n e s , a t lower k i n e t i c energy, noted C t o F ; one shake down l i n e a t h i g h e r k i n e t i c energy, noted A. Each of t h e s e f i n a l s t a t e s decays mostly v i a Auger emission and t h e p h o t o e l e c t r o n spectrum i s m i r r o r e d i n t h e Auger spectrum ( peaks A ' t o F ' ) .

From s p e c t r a such a s t h e ones p r e s e n t e d i n Figs 8 t o 13, t h e energy v a r i a t i o n of t h e p a r t i a l p h o t o i o n i z a t i o n c r o s s s e c t i o n s corresponding t o each f i n a l s t a t e of t h e i o n c a n be e x t r a c t e d and compared t o t h e t h e o r e t i c a l p r e d i c t i o n s . These r e s u l t s w i l l be p r e s e n t e d elsewhere.(25)

4.

P h o t o i o n i z a t i o n of He above the n = 2 i o n i z a t i o n t h r e s h o l d

.-

He i s t h e s i m p l e s t atomic system t h a t e x h i b i t s e l e c t r o n c o r r e l a t i o n e f f e c t s i n t h e p h o t o i o n i z a t i o n pro- c e s s . From a t h e o r e t i c a l p o i n t of view, i t e n a b l e s t h e o r i e s t o be t e s t e d , which can be used l a t e r on f o r more complex atoms. From t h e experimental p o i n t of view, t h e development of i n t e n s e synchrotron r a d i a t i o n sources and of e l e c t r o n spectrometry on gaseous samples o f f e r e d new p o s s i b i l i t i e s t o s t u d y q u a n t i t a t i v e l y t h e d e t a i l s of t h e p h o t o i o n i z a t i o n p r o c e s s , i n p a r t i c u l a r t h e simultaneous p h o t o i o n i z a t i o n and e x c i t a - t i o n of t h e He atom i n t h e f i r s t 50 eV above t h e n=2 i o n i z a t i o n t h r e s h o l d . Thus, i n - t e n s e a c t i v i t y has been r e c e n t l y developed, i n theory a s w e l l i n experiment.

P h o t o i o n i z a t i o n of He c a n l e a v e the r e s i d u a l p o s i t i v e i o n e i t h e r i n i t s ground s t a t e

(11)

JOURNAL DE PHYSIQUE

KINETIC ENERGY ( e V )

80 12.0 16.0 20.0 214 28.0 61.0 660 68.0 He

-

Fig. 14

.-

E l e c t r o n 60000 spectrum f o l l o w i n g

pho t o i o n i z a t i o n of He by 90.6 eV photons.

The n = l , 2 and 3 f i n a l s t a t e s of He+ appear a s i n d i v i d u a l l i n e s .

(from Ref.16) 20000

82.0 78.0 7LO 700 660 280 24.0 20.0 BINDING ENERGY (eV)

(He+, n = l , with t h e t h r e s h o l d a t 24.58 eV) o r i n some e x c i t e d s t a t e s : He+, n=2 (2s o r 2p) above 65.4 eV, He+,n=3 (3s, 3p o r 3d) above 73 eV,.

. .

Fig. 14 shows an energy r e s o l v e d p h o t o e l e c t r o n spectrum o b t a i n e d with 90 eV p h o t o n s . ( l 6 ) Since t o each f i n a l s t a t e of t h e i o n corresponds a s p e c i f i c k i n e t i c energy f o r t h e p h o t o e l e c t r o n , t h e v a r i o u s He+ f i n a l s t a t e s with d i f f e r e n t v a l u e s of t h e p r i n c i p a l quantum number n

show up a s i n d i v i d u a l l i n e s i n t h e e l e c t r o n spectrum. The n = l , nz2 and n=3 He+ s t a - t e s a r e w e l l r e s o l v e d i n Fig.14. For n J 4 , t h e p h o t o l i n e s a r i s i n g from t h e s e h i g h e r e x c i t e d s t a t e s overlap, because of t h e experimental r e s o l u t i o n . I n a d d i t i o n , t h e f i - ne s t r u c t u r e s p l i t t i n g of the e x c i t e d s t a t e s i s s o s m a l l , l e s s t h a n 1 meV f o r n-2, t h a t t h e ns and np f i n a l s t a t e s a r e quasi-degenerate and cannot be d i f f e r e n t i a t e d i n an energy r e s o l v e d p h o t o e l e c t r o n spectrum.

Since FISCI i s s t r i c t l y forbidden i n Hef, t h e o r i g i n of t h e s e e x c i t e d s t a t e s comes from ISCI and from I n t e r c h a n n e l Coupling ( o r continuum s t 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 , CSCI). The energy dependence of the i n t e n s i t y of t h e s e s a t e l l i t e s i s a s t r i n - g e n t t e s t of t h e r e l a t i v e importance of t h e s e two c l a s s e s of c o r r e l a t i o n p r o c e s s e s , s i n c e only CSCI i s expected t o produce l a r g e v a r i a t i c n s of t h e c r o s s s e c t i o n s i n t h e low k i n e t i c energy r e g i o n above t h r e s h o l d .

We comment f i r s t on t h e a b s o l u t e c r o s s s e c t i o n f o r l e a v i n g t h e r e s i d u a l i o n i n an e x c i t e d s t a t e . From s p e c t r a such a s the one p r e s e n t e d i n Fig.14, t h e r e l a t i v e con- t r i b u t i o n of each f i n a l s t a t e t o t h e t o t a l p h o t o a b s o r p t i o n c r o s s s e c t i o n c a n b e determined. Using t h e d a t a o b t a i n e d i n double p h o t o i o n i z a t i o n s t u d i e s (27-29) and normalizing t h e r e l a t i v e c o n t r i b u t i o n s t o t h e t o t a l c r o s s s e c t i o n measured i n photoabsorpti'on experiments,(30) i t was then p o s s i b l e t o determine t h e a b s o l u t e v a l u e s of each p a r t i a l c r o s s s e c t i o n . Such an a n a l y s i s h a s been made f o r the n=2 c r o s s s e c t i o n (31) and f o r t h e very weak n=3 c r o s s s e c t i o n . ( 1 6 , 3 2 ) Fig.15 p r e s e n t s t h e r e s u l t s o b t a i n e d by Wuilleumier e t a1.(31) f o r t h e n=2 c r o s s s e c t i o n . The energy dependence of t h i s c r o s s s e c t i o n was a l s o measured (33) w i t h the f l u o r e s c e n c e technique d e s c r i - bed i n t h e i n t r o d u c t i o n ( 4 ) ; from t h e s e f l u o r e s c e n c e d a t a , t h e v a r i a t i o n of t h i s c r o s s s e c t i o n on a r e l a t i v e s c a l e was obtained (33) and found t o be i n good agreement with t h e e l e c t r o n spectrometry d a t a (31). However, no a b s o l u t e v a l u e s of t h i s n=2 c r o s s s e c t i o n could be e x t r a c t e d from t h e f l u o r e s c e n c e measurements: t h e abso- l u t e s c a l e shown i n t h e ~ u b l i s h e d r e s u l t s (33) could be o b t a i n e d o n l y by normalizing t h e r e l a t i v e v a l u e s t o t h e e l e c t r o n spectrometry d a t a , a t 82.5 eV photon energy.(33) Very r e c e n t l y , a new e l e c t r o n spectroscopy experiment, p r i m a r i l y devoted to t h e s t u - dy of t h i s n=2 c r o s s s e c t i o n a c r o s s t h e a u t o i o n i z i n g doubly e x c i t e d s t a t e s of t h e n=

3 series

provided r e s u l t s i n good agreement (34) with t h e f i r s t e l e c t r o n s p e c t r o -

(12)

h9,PHOTON ENERGY (eV)

Fig. 15.- V a r i a t i o n of the a b s o l u t e v a l u e of t h e p a r t i a l c r o s s s e c t i o n f o r photo- i o n i z a t i o n of H e l e a v i n g t h e r e s i d u a l p o s i t i v e i o n i n the n=2 f i n a l s t a t e . The experimental p o i n t s a r e from e l e c t r o n spectrometry measurements(Ref.31); t h e va- r i o u s curves a r e the r e s u l t s of t h e o r e t i c a l c a l c u l a t i o n s by S a l p e t e r and Zaidy (

- ^,

Ref.35), Jacobs and Burke (----, Ref.36), Chang (-.-, Ref.37) and Berring- t o n e t a l . (.-.-., Ref.39).

scopy measurements. New measurements of Bizau e t a1.(16,32) a r e a l s o i n good agreement.

I n Fig.15, t h e experimental r e s u l t s a r e compared t o f o u r d i f f e r e n t t h e o r e t i c a l calcu- l a t i o n s . S a l p e t e r and Zaidy (Ref.35) took i n t o account only c o r r e l a t i o n s i n t h e i n i - t i a l s t a t e of t h e atom, by u s i n g a h i g h l y c o r r e l a t e d H y l l e r a a s type wave f u n c t i o n f o r the i n i t i a l s t a t e and hydrogenic wave f u n c t i o n s f o r t h e f i n a l s t a t e . Jacobs and Burke (36) included t h e coupling between t h e 2s and 2p s t a t e s of He+ w i t h a 56-term Hylle- r a a s type wavefunction f o r t h e i n i t i a l s t a t e and a Is-2s-2p close-coupling wavefunc- t i o n f o r t h e f i n a l s t a t e . Chang (37) used many-body theory f i r s t developed by Chang and Fano ( 3 8 ) , i n c l u d i n g a l a r g e number of c o n f i g u r a t i e n s t o d e s c r i b e t h e i n i t i a l and f i n a l s t a t e s . Very r e c e n t l y , B e r r i n g t o n e t a l . (39) c a r r i e d o u t c a l c u l a t i o n s u s i n g t h e R-matrix approach: they r e p r e s e n t e d c o n s i s t e n t l y both t h e i n i t i a l s t a t e and f i n a l s t a t e s by-the-same e y a n s i o n b a s i s , i n c l u d i n g I s , 2s and 2p e i g e n s t a t e s of ~ e + a s w e l l a s 3 s , 3p and 3d p s e u d o s t a t e s i n t h e expansion of t h e wavefunctions. The r e s u l t s of t h e s e c a l c u l a t i o n s a r e p l o t t e d i n Fig.15. The s i x - s t a t e l e n g t h c a l c u l a t i o n of Ber-- r i n g t o n e t a l . (39) (which a r e p r e f e r e d t o t h e v e l o c i t y form by t h e a u t h o r s , because they show f a s t e r convergence than t h e v e l o c i t y c a l c u l a t i o n s ) and t h e many-body velo- c i t y c a l c u l a t i o n s of Chang (37) a r e i n very good agreement w i t h t h e experimental measurements (31,16), with maybe a s l i g h t tendancy f o r t h e most r e c e n t c a l c u l a t i o n s (39) t o be t h e c l o s e s t t o t h e experiment.

A more s e n s i t i v e t e s t of t h e v a r i o u s c a l c u l a t i o n s was t o determine t h e r a t i o of t h e c r o s s s e c t i o n f o r l e a v i n g t h e i o n i n t h e 2p s t a t e t o t h e c r o s s s e c t i o n f o r l e a v i n g t h e i o n i n t h e 2s s t a t e . A q u a l i t a t i v e l y d i f f e r e n t behavior was p r e d i c t e d by t h e t h r e e f i r s t c a l c u l a t i o n s b e f o r e experiments could be done. This r a t i o R i s an image of t h e symmetry of t h e f i n a l s t a t e and c o u l d then be determined by a n g u l a r d i s t r i b u -

t i o n measurements. Turning back to t h e g e n e r a l f orm of t h e d i f f e r e n t i a l photoioniza- t i o n c r o s s s e c t i o n ( E q . l ) , c h a s t o be r e p l a c e d by t h e sum of t h e o a r t i a l c r o s s sec-

(13)

JOURNAL DE PHYSIQUE

BINDING ENERGY (eV)

Fig.16.- Angular r e s o l - ved p h o t o e l e c t r o n spec- t r a of He taken a t 90 eV f o r two d i f f e r e n t v a l u e s of the a n g l e : 90' ( l e f t p a r t ) and 0 " ( r i g h t p a r t ) . Both s p e c t r a a r e normalized t o a same i n - t e n s i t y f o r t h e n=l pho- t o l i n e . ( f r o m Ref.l5,16).

t i o n s unZ2 = (uzs

+

mzp) and

13.

by

,

a weighted asymmetry parameter which i s t h e q u a n t i t y measurable e x p e r i m e n t a l l y . Assuming t h a t t h e 2s and 2p f i n a l s t a t e s can be t r e a t e d s e p a r a t e l y , t h e form f o r (3 i s :

I t has been shown t h a t 01 must be e q u a l t o 2 f o r e l e c t r o n s l e a v i n g t h e i o n i n t h e 2s s t a t e . ( 3 6 ) . Thus, from c a l c u l a t e d v a l u e s of (32p and measured v a l u e s of (3

,

one c a n determine t h e r a t i o R from t h e r e l a t i o n :

Using t h e experimental s e t up p r e v i o u s l y d e s c r i b e d , Bizau e t a1.(15) were a b l e t o measure a n g u l a r r e s o l v e d s p e c t r a of He. Fig.16 shows an example o b t a i n e d a t t h e same photon energy a s t h e a n g u l a r i n t e g r a t e d spectrum of F i g . 14. From t h e s e s p e c t r a , t h e v a l u e s o f ( 3 were e x t r a c t e d . The r e s u l t s a r e shown i n Fig.17. For experimental rea- sons, t h e lowest l i m i t of t h e s e experiments was 75 eV, i . e . 10 eV above t h e t h r e s - hold. L a t e r on, a new experiment was c a r r i e d o u t by Schmidt e t a1.(40), using t h e synchrotron r a d i a t i o n a v a i l a b l e a t Hasylab i n Hamburg.-With an improved experimental s e t up s p e c i a l l y designed f o r a n g u l a r d i s t r i b u t i o n measurements, they were a b l e t o measure t h e asymmetry parameter down t o 2 eV k i n e t i c energy f o r t h e n=2 photoelec-

t r o n l i n e . Above 75 eV, t h e new d a t a a r e i n e x c e l l e n t agreement w i t h t h e previous measurements, a s seen i n Fig.17. A t 67.5 eV t h e v a l u e of

(3

was found equal t o ze- r o . I n F i g . 17, t h e i n d i v i d u a l t h e o r e t i c a l v a l u e s c a l c u l a t e d f o r

(3

2p by Jacobs and Burke (36) and by Chang (37) a r e a l s o shown. The d i f f e r e n c e s between t h e two c a l c u - l a t i o n s a r e s m a l l . This i s n o t t h e case a t low photon energy f o r t h e t h e o r e t i c a l va- l u e s of (3 c a l c u l a t e d i n using t h e R v a l u e s determined i n b o t h t h e o r i e s . A t t h r e s h o l d t h e experiment seems t o f a v o r t h e Jacobs and Burke c a l c u l a t i o n s , while above 75 eV, t h e experimental d a t a come c l o s e r t o t h e Chang r e s u l t s . This i s confirmed by two more r e c e n t , s t i l l unpublished measurements of

(3

c a r r i e d o u t over an extended pho-

ton energy range.(34,41). The comparison between theory and experiment i s made ea- s i e r when one p l o t s t h e v a r i a t i o n of R , a s p r e s e n t e d i n Fig.18. I n t h i s f i g u r e a r e shown t h e experimental v a l u e s o b t a i n e d from t h e published a n g u l a r d i s t r i b u t i o n r e - s u l t s (15,40) and

:ram

d a t a o b t a i n e d i n f l u o r e s c e n c e experiments.(4) Using a s t a t i c e l e c t r i c f i e l d t o cause the m e t a s t a b l e l e v e l 2s t o mix with t h e 2p l e v e l and measu- r i n g t h e f l u o r e s c e n c e s i g n a l with and w i t h o u t t h e e l e c t r i c f i e l d a p p l i e d , Woodruff and Samson (4) o b t a i n e d i n f o r m a t i o n on t h e r e l a t i v e p o p u l a t i o n of 2s and 2p l e v e l s . However, t h e i n t e r p r e t a t i o n of such an experiment i s d i f f i c u l t , because of t h e l a r g e number of o t h e r p r o c e s s e s capable of modifying t h e s e p o p u l a t i o n s , i n p a r t i c u l a r t h e

(14)

PHOTON ENERGY (ev)

Fig. 17.- The asymmetry parameter (j vs photon energy. Experimental r e s u l t s a r e from Ref.15 ( a ) and 40 ( O ) . C a l c u l a t i o n s of (3

zp

a r e from Ref.36 ( s o l i d cur- ve) and 15 ( d o t t e d c u r v e ) ; they a r e noted He+ (2p) J B , C . From t h e s e two t h e o r i e s t h e curves f o r

p

were c a l c u l a t e d :JB (dashed-line), and C (dash-dotted l i n e ) . d e s e x c i t a t i o n of the 2s l e v e l through c o l l i s i o n s w i t h He atoms. The f l u o r e s c e n c e d a t a a r e expected t o be more a c c u r a t e i n t h e immediate v i c i n i t y of t h e t h r e s h o l d (4) and t h i s i s indeed t h e c a s e when one examines Fig.18 c a r e f u l l y . A t photon e n e r g i e s l a r - g e r than 85 eV, t h e l a r g e spread of t h e f l u o r e s c e n c e d a t a makes d i f f i c u l t t o draw any d e f i n i t e conclusion on t h e energy dependence of t h i s r a t i o , when one c o n s i d e r s a l s o the s i z e of some of t h e e r r o r b a r s . I n Fig. 18 a r e a l s o shown t h e r e s u l t s of t h e t h r e e most r e c e n t c a l c u l a t i o n s .

We f i r s t d i s c u s s the comparison between t h e v a r i o u s experimental r e s u l t s . A l l angu- l a r d i s t r i b u t i o n measurements (15,40), i n c l u d i n g t h e unpublished d a t a (34,41) a r e i n c l o s e agreement a l l t o g e t h e r n e a r t h r e s h o l d a s w e l l a s above 75 eV. The i n f l u e n c e of t h e a u t o i o n i z i n g s t a t e s belonging t o t h e doubly e x c i t e d s t a t e s of t h e n=3 and n=4 s e r i e s between 69 and 75 eV w i l l n o t be d i s c u s s e d h e r e . Above 75 eV, t h e a n g u l a r d i s - t r i b u t i o n r e s u l t s a r e s i g n i f i c a n t l y lower than suggested by t h e f l u o r e s c e n c e d a t a . For f u r t h e r comparison w i t h theory,we w i l l keep t h e a n g u l a r d i s t r i b u t i o n r e s u l t s . J u s t above t h r e s h o l d , a n g u l a r d i s t r i b u t i o n and f l u o r e s c e n c e r e s u l t s , a r e i n good a- greement. Turning now t o an examination of the t h e o r e t i c a l r e s u l t s , i t was a l r e a d y e v i d e n t , b e f o r e t h e most r e c e n t t h e o r e t i c a l r e s u l t s of Berrington e t a l . became a- v a i l a b l e , t h a t t h e experimental d a t a were favouring t h e c l o s e coupling c a l c u l a t i o n s (36) i n t h e immediate v i c i n i t y of t h e t h r e s h o l d , b u t t h a t t h e d e c r e a s i n g of R with i n c r e a s i n g photon energy was much f a s t e r than p r e d i c t e d by t h i s theory ( 4 2 ) . This was a l r e a d y t h e c a s e f o r the n=2 t o t a l c r o s s s e c t i o n ( 3 1 ) . Above 75 eV, t h e r e s u l t s of Bizau e t a1.(15) were suggesting a v a l u e of R c l o s e t o 1 w i t h a tendency t o de- c r e a s e slowly w i t h i n c r e a s i n g photon energy. Taking i n t o account t h e s i z e of t h e experimental e r r o r b a r s , t h e t h e o r e t i c a l r e s u l t s of Chang (15) were c l o s e r t o t h e experimental r e s u l t s than t h e r e s l l t s of Jacobs and Burke between 75 and 100 eV. This i s f u l l y confirmed by t h e more a c c u r a t e measurements of Schmidt e t a 1 . ( 4 0 ) , b u t t h e t u r n i n g p o i n t and the change i n the v a r i a t i o n of R i n t h e many-body r e s u l t s around 90 eV i s i n c o n t r a d i c t i o n w i t h the experimental d a t a . The c l o s e agreement between t h e experimental d a t a

,

between75 and 80 eV, and t h e many-body r e s u l t s should probably be considered a s a c c i d e n t a l . I t must be mentionned t h a t a p o s s i b l e f a i l u r e of t h e many-body p r e d i c t i o n s below t h e double i o n i z a t i o n t h r e s h o l d a t 79 eV was n o t

(15)

JOURNAL DE PHYSIQUE

PHOTON ENERGY ( e ~ )

Fig.18.- The v a l u e of R v s photon energy f o r t h e 2p-2s f i n a l s t a t e s of ~ e + . Expe- r i m e n t a l r e s u l t s a r e from Bizau e t a l . ( f u l l c i r c l e s ,

i

Ref. 15), Schmidt e t a l . ( s q u a r e s , = Ref.40), Krause and Wuilleumier ( t r i a n g l e s , A Ref.44), Woodruff and Samson(lozenges,

+

R e f . 4 ) . T h e o r e t i c a l c a l c u l a t i o n s a r e from Jacobs and Burke(dashed line,----, Ref.36), Chang ( f u l l l i n e ,

- ,

i n Ref. 15) and Berring ton e t a1

.

(dash-dotted l i n e ,

-.---=- ,

r e f . 3 9 ) .

completely unexpected.(43) One should n o t f o r g e t a l s o than none of t h e c a l c u l a t i o n s i n c l u d e s t h e e f f e c t of t h e resonances due t o t h e doubly e x c i t e d s t a t e s , while i t i s well known t h a t t h e asymmetry parameter and t h e branching r a t i o can be s t r o n g l y mo- d i f i e d w i t h i n an a u t o i o n i z i n g l i n e . The l a t e s t R-matrix c a l c u l a t i o n s o f Berrington e t a l . g i v e e v i d e n t l y t h e b e s t agreement w i t h t h e experimental d a t a i n t h e whole energy range from t h r e s h o l d up t o 130 eV:close t o t h r e s h o l d , they go r i g h t through t h e experimental p o i n t s ; a t h i g h e r energy, t h e f a s t d e c r e a s e they p r e d i c t f o r R i s i n f u l l agreement w i t h t h e angular d i s t r i b u t i o n experiments.Finally, we should men- t i o n t h e e x i s t e n c e of r e c e n t H a r t r e e - Fock c a l c u l a t i o n s , s t i l l unpublished, which seem t o f i t between t h e Jacobs and Burke c a l c u l a t i o n s and t h e B e r r i n g t o n r e s u l t s ( 4 5 ) . To conclude, f u r t h e r c a l c u l a t i o n s i n c l u d i n g t h e e f f e c t of the resonance below 79 eV a r e h i g h l y d e s i r a b l e a s well a s new f l u o r e s c e n c e measurements above 85 eV, c a r r i e d o u t a t lower p r e s s u r e and with improved i n t e n s i t y .

5 . P h o t o i o n i z a t i o n and a u t o i o n i z a t i o n o u t of l a s e r e x c i t e d sodium atoms.

-

The i n f o r - ma t i o n o b t a i n e d from p h o t o i o n i z a t i o n experiments on atoms i n the ground s t a t e , while having a g r e a t v a l u e , i s somewhat r e s t r i c t i v e . B e c a u s e of t h e d i p o l e s e l e c t i o n r u l e s , only a l i m i t e d c l a s s of s t a t e s can be probed. Furthermore, t h e i n i t i a l s t a t e i s o f t e n an ensemble of n e a r l y degenerate l e v e l s , p a r t i c u l a r l y i n open-shell atoms. With t h e r e c e n t advent of high power- frequency t u n a b l e dye l a s e r s , i t has become p o s s i b l e

(16)

t o prepare t h e i n i t i a l s t a t e i n a s p e c i f i c way. I n t e r a c t i o n of photons w i t h such ex- c i t e d s t a t e s i s of fundamental importance i n atomic p h y s i c s . P h o t o i o n i z a t i o n of e x c i - t e d s t a t e s a r e probably among t h e most e a s i l y i n t e r p r e t a b l e experiments t h a t may be performed. I n p a r t i c u l a r , new e f f e c t s have been p r e d i c t e d (46) f o r t h e energy dependence of t h e corresponding p h o t o i o n i z a t i o n c r o s s s e c t i o n s which a r e expected t o pre- s e n t , i n some c a s e s , up t o t h r e e minima i n t h e

e ⁺ ^{( 2 +}

1) channel and one i n t h e

e

^-+

^{( t}

-1) channel. I n a d d i t i o n t o t h e c a p a b i l i t y of p r e p a r i n g a system i n a spe- c i f i c s t a t e , t h e e x c i t a t i o n of an o u t e r e l e c t r o n can modify s t r o n g l y t h e e f f e c t i v e p o t e n t i a l experienced by i n n e r e l e c t r o n s with h i g h o r b i t a l quantum numbers: i n t h i s way, t h e c o l l a p s e (47) o r , a l t e r n a t e l y , t h e c o n t r a c t i o n (48,49) of atomic wavefunc-

t i o n s could be c o n t r o l l e d . Furthermore, when one s t a r t s from an o p t i c a l l y e x c i t e d s t a t e , i t i s a l s o p o s s i b l e t o produce a u t o i o n i z i n g s t a t e s having t h e same p a r i t y a s the ground s t a t e and thus t o o b t a i n experimental i n f o r m a t i o n on t h e geometrical and dynamical p r o p e r t i e s of atoms from s t a t e s h i t h e r t o i n a c c e s s i b l e .

P h o t o i o n i z a t i o n from m e t a s t a b l e e x c i t e d s t a t e s and from l a s e r e x c i t e d s t a t e s h a s been observed.(50) I n most of t h e s e c a s e s , t h e i o n i z i n g r a d i a t i o n was produced by s i n g l e a b s o r p t i o n of a l a s e r beam.With t h i s mode of e x c i t a t i o n , t h e energy range ex- p l o r e d was l i m i t e d t o a few v o l t s above t h r e s h o l d . Pioneering measurements from l a s e r e x c i t e d i n t e r m e d i a t e s t a t e s have been made o v e r a broad photon energy range, using the p u l s e d emission of continuum r a d i a t i o n from a BRV souce between 30 and 100 eV, t o probe t h e photoabsorption s p e c t r a of l a s e r e x c i t e d s t a t e s i n Na (51) and i n L i . ( 5 2 ) . For more d e t a i l e d information about p h o t o i o n i z a t i o n of e x c i t e d s t a t e s u s i n g l a s e r source a s t h e i o n i z i n g a g e n t , t h e r e a d e r i s r e f e r r e d t o a r e c e n t review.(53).

The wide spectrum of e n e r g i e s a v a i l a b l e w i t h synchrotron r a d i a t i o n was a n obvious ex- t e n s i o n of t h e l i m i t e d s p e c t r a l r a n g e t h a t can be reached w i t h p r e s e n t day 1 a s e r s . h p a r t i c u l a r , i n n e r s h e l l p h o t o i o n i z a t i o n of e x c i t e d atoms could be s t u d i e d only with a n i n t e n s e source of continuum r a d i a t i o n i n the VW range. We would l i k e t o g i v e he- r e some i n f o r m a t i o n about t h e f i r s t s u c c e s s f u l use of synchrotron r a d i a t i o n t o s t u d y p h o t o i o n i z a t i o n and a u t o i o n i z a t i o n from l a s e r e x c i t e d s t a t e s i n atomic sodium.(8,54, 5 5 ) . Two s e r i e s of experiments were c a r r i e d o u t i n which e l e c t r o n s p e c t r a e j e c t e d by synchrotron r a d i a t i o n from l a s e r e x c i t e d Ma atoms were energy analyzed w i t h t h e CMA. I n t h e f i r s t s e r i e s of experiments,(8,54,55) t h e maximum power d e l i v e r e d i n t h e i n t e r a c t i o n zone was about 3 watts/cm2. The l a s e r was s t a b i l i z e d u s i n g t h e a b s o r p t i o n s i g n a l produced i n the e f f u s i v e beam of sodium w i t h i n t h e CMA. The d e n s i t y of Na i n t h e ground s t a t e was about 1.5x1013/cm3 i n t h e a c t i v e volume. I n t h e second s e r i e s of experiments, t h e l a s e r i n t e n s i t y could be i n c r e a s e d up t o 10 w/cm2.The l a s e r was s t a b i l i z e d and locked t o t h e F=2 4 F = 3 h y p e r f i n e component of t h e D2 l i n e w i t h a bandwidth of 20 MHz, u s i n g an a u x i l i a r y sodium oven placed o u t s i d e of t h e CMA and producing a sodium beam on t h e path of t h e l a s e r beam. I n a d d i t i o n , a l i q u i d n i t r o g e n t r a p , placed i n f r o n t of the oven, c o n t r i b u t e d t o improve the s i g n a l to n o i s e r a t i o t o a l a r e e x t e n t . The d e n s i t y of atoms i n t h e ground s t a t e was v a r i e d between 10' and lo1? atoms/cm3.

Two main f e a t u r e s have been observed during t h e f i r s t s e t of experiments.(8,54,55).

Fig.19 shows a p h o t o e l e c t r o n spectrum of Na atoms taken a t 75 eV photon energy. I n t h e absence of l a s e r r a d i a t i o n (upper p a r t of the f i g u r e ) , one observes p h o t o l i n e s corresponding t o i o n i z a t i o n of sodium atoms i n t h e 2p s u b s h e l l , w i t h t h e atoms i n i - t i a l l y i n t h e ground s t a t e : the main peak a t 38 eV binding energy corresponds t o a p o s i t i v e i o n being l e f t i n i t s lowest 2p5 1 9 3 ~ s t a t e s , t h e o t h e r peaks of lower i n - t e n s i t y a t h i h e r b i n d i n g e n e r g i e s , a r e s a t e l l i t e peaks corresponding t o i o n s l e f t i n the 2p53p y3S, 3 ~ , e x c i t e d s t a t e s v i a f i n a l s t a t e e l e c t r o n c o r r e l a t i o n s . I n t h e lower p a r t of the f i g u r e ( 1 a s e r o n ) , an a d d i t i o n a l p h o t o e l e c t r o n l i n e a p p e a r s , whose binding energy corresponds t o t h e binding energy of a 2p e l e c t r o n i n an e x c i t e d 2 ~ 6 3 ~ 2 ~atom. This peak, a t about 40 eV binding energy, was a c l e a r m a n i f e s t a t i o n ~ / ~ of t h e presence of e x c i t e d atoms i n t h e vapor. I t has been observed over a n extended photon energy range. Using the f a c t t h a t t h e c r o s s s e c t i o n f o r i n n e r s h e l l i o n i z a t i o n i n sodium depends l i t t l e on t h e o r b i t a l occupied by t h e o u t e r e l e c t r o n (561, a compa- r i s o n of t h e i n t e g r a t e d a r e a of t h i s peak and of t h e main peak a l l o w s t o o b t a i n t h e r e l a t i v e p o p u l a t i o n of atoms i n e x c i t e d s t a t e s , h e r e c l o s e to 10%.

The second f e a t u r e d e t e c t e d d u r i n g t h i s f i r s t phase of t h e experiments was t h e obser- v a t i o n of e l e c t r o n s produced i n the decay of a u t o i o n i z i n g s t a t e s . I n Fig.20, we show

(17)

JOURNAL DE PHYSIQUE

Excited state

+

Ground state . . . . . - . . . . . . . . . . . . . .

Fig.19.- P h o t o e l e c t r o n spectrum of atomic sodium produced by 75 eV pho-

t o n s . Upper frame:the l a s e r i s o f f , the l a r g e peak

6s

due t o photoioni- z a t i o n of a 2p e l e c t r o n , with t h e i o n l e f t i n i t s ground s t a t e ; t h e s m a l l e r peaks a r e due t o i o n i z a t i o n of a 2p e l e c t r o n w i t h simultaneous e x c i t a t i o n of t h e 3s e l e c t r o n onto a 3p o r b i t a l . Lower frame: t h e l a - s e r i s on; i n a d d i t i o n t o t h e nor- mal p h o t o e l e c t r o n spectrum from

t h e ground s t a t e , a new peak appears (hatched a r e a ) due t o t h e i o n i z a - t i o n of a 2p e l e c t r o n i n l a s e r ex- c i t e d sodium atoms (from Ref .54).

O 42 40 38 36

BINDING ENERGY (eV)

a n example of such an a u t o i o n i z a t i o n process i n a doubly e x c i t e d atom, i n which t h e l a s e r e x c i t e d sodium atoms i n t h e 2p63p 2 ~ 3 / 2 d o n f i g u r a t i o n were 3 d d i t i o n a l l y e x c i - t e d by 31.40 eV synchrotron r a d i a t i o n photons t o the 2 p 5 ( 2 ~ ) 3 s 3 p ( P ) 2 ~ ~ / 2 , ~ / ~ s t a t e . The energy of t h i s t r a n s i t i o n was known from t h e photoabsorption measurements on e x c i t e d Na.(51). This s t a t e decays v i a a u t o i o n i z a t i o n t o t h e 2p6 ground s t a - t e of Na+ i o n . I n t h e r i g h t p a r t of t h e f i g u r e an i n t e n s e l i n e (shaded a r e a ) appears, corresponding t o t h e decay of t h e a u t o i o n i z i n g s t a t e . Located a t t h e binding energy of t h e 3p e x c i t e d e l e c t r o n , i t may be viewed a s t h e r e s u l t of r e s o n a n t photoioniza- t i o n of t h i s 3p e x c i t e d e l e c t r o n . The presence of second o r d e r r a d i a t i o n was impor- t a n t h e r e f o r t h e d e t e r m i n a t i o n of t h e d e n s i t y of Na i n t h e ground s t a t e and i n t h e e x c i t e d s t a t e : t h e l e f t p a r t of t h e f i g u r e d i s p l a y s t h e p h o t o e l e c t r o n l i n e s produced by t h e i o n i z a t i o n of sodium atoms i n t h e ground s t a t e w i t h 62.80 eV photons d i f f r a c -

t e d i n second o r d e r by t h e monochromator (The energy of f i r s t o r d e r photons i s too low t o produce i o n i z a t i o n of 2p e l e c t r o n s w i t h 38 eV b i n d i n g energy).

I n t h e second s e r i e s of experiments, with improved l a s e r and sodium beam c o n d i t i o n s , (57). a h i g h e r d e n s i t y o f e x c i t e d atoms was r o u t i n e l y a v a i l a b l e with a s i g n a l t o noi- s e r a t i o q u i t e enhanced. Fig.21 p r e s e n t s t h e p h o t o e l e c t r o n and a u t o i o n i z a t i o n spectrum o b t a i n e d a t t h e same photon energy of 31.40 eV i n f i r s t o r d e r . A l l f e a t u r e s observable i n Fig.19 and Fig.20 a r e seen h e r e on t h e same spectrum, i n much b e t t e r c o n d i t i o n s . One c a n observe s i m u l t a n e o u s l y p h o t o i o n i z a t i o n i n the 2p s u b s h e l l , produced by 62.80 eV second o r d e r photons i n t h e ground s t a t e and i n t h e e x c i t e d s t a t e of Na ( l e f t p a r t of t h e f i g u r e ) and the a u t o i o n i z a t i o n l i n e due t o t h e decay of t h e doubly e x c i t e d s t a t e produced by a b s o r p t i o n of 31.40 eV f i r s t o r d e r photons i n t h e e x c i t e d 2p63p atoms. The p h o t o e l e c t r o n l i n e corresponding t o i o n i z a t i o n of a 2p e- l e c t r o n i n t h e e x c i t e d atoms (marked Na+ 2p53p from E.S.) has now a r e l a t i v e i n t e n - s i t y c l o s e t o 30%. This i s n o t f a r from t h e maximum v a l u e o b t a i n a b l e , t a k i n g i n t o account t h e p o l a r i z a t i o n of t h e l a s e r . ( 5 8 ) Compared t o i t s i n t e n s i t y i n Fig.20, t h e r e l a t i v e i n t e n s i t y of t h e a u t o i o n i z a t i o n l i n e has been i n c r e a s e d by almost a f a c t o r 3, corresponding t o t h e i n c r e a s e i n t h e r e l a t i v e d e n s i t y of e x c i t e d s t a t e s (10% t o 30%).