A THEORETICAL SURVEY OF 4s-4p AND 4p-4d TRANSITIONS IN NICKEL-LIKE IONS

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A THEORETICAL SURVEY OF 4s-4p AND 4p-4d TRANSITIONS IN NICKEL-LIKE IONS

J.-F. Wyart

To cite this version:

J.-F. Wyart. A THEORETICAL SURVEY OF 4s-4p AND 4p-4d TRANSITIONS IN NICKEL-LIKE IONS. Journal de Physique Colloques, 1988, 49 (C1), pp.C1-299-C1-302. �10.1051/jphyscol:1988162�.

�jpa-00227576�

Colloque C1, Suppl6ment au n03, Tome 49, Mars 1988

A THEORETICAL SURVEY OF 48-4p AND 4p-4d TRANSITIONS I N NICKEL-LIKE IONS

J.-F. WYART

L a b o r a t o i r e Aim6 C o t t o n , CNRS XI, Bat. 505, C e n t r e U n i v e r s i t a i r e , F-91405 O r s a y C e d e x , France

En r a i s o n d e s i n v e r s i o n s de p o p u l a t i o n q u i peuvent s e p r o d u i r e e n t r e l e u r s niveaux CxcitCs, l e s i o n s m u l t i c h a r g g s i s o 6 l e c t r o n i q u e s du n i c k e l p r 6 s e n t e n t un i n t 8 r E t a c t u e l . L ' i d e n t i f i c a t i o n d e s t r a n s i t i o n s 4s-4p et 4p-4d a r6cemment pro- g r e s s 6 g r s c e & de n o u v e l l e s e x p e r i e n c e s f a i t e s 1' I.S.A.N., Troitsk(URSS) e t a 1 1 i n t e r p r 6 t a t i o n , & Orsay, d e s p r e m i h r e s c o n f i g u r a t i o n s e x c i t e e s p a r l a methode d e Slater-Condon e t d e s moindres-carres g e n e r a l i s b s & une sequence i s o 6 l e c t r o n i q u e . Pour p r e v o i r l e s t r a n s i t i o n s 4-4 d a n s d e s 6 t a t s de c h a r g e p l u s C l e v 6 s , l e s m6mes c o n f i g u r a t i o n s o n t 6tC 6tudiCes a p r i o r i p a r l a mCthode du p o t e n t i e l p a r a k t r i q u e e t q u e l q u e s r a i e s 4p-4d m e t t a n t e n j e u d e s niveaux i n f 6 r i e u r s d e c o u r t e d u d e de v i e , s o n t donn6s i c i pour 14 616ments d e l a s6quence S r X I

-

Eu XXXVI.

A b s t r a c t

Multicharged i o n s i n t h e i s o e l e c t r o n i c sequence o f n i c k e l have a c u r r e n t i n t e - r e s t , due t o p o s s i b l e p o p u l a t i o n i n v e r s i o n s o c c u r i n g between e x c i t e d l e v e l s . The i d e n t i f i c a t i o n of 4s-4p and 4p-4d t r a n s i t i o n s was r e c e n t l y extended up t o Mo XV, owing t o new e x p e r i m e n t s performed a t I.S.A.N., T r o i t s k (USSR), and t o t h e subse- quent i n t e r p r e t a t i o n o f t h e f i r s t e x c i t e d c o n f i g u r a t i o n s by means o f t h e S l a t e r - Condon method and g e n e r a l i z e d l e a s t s q u a r e s f i t o f energy parameters a l o n g a s e - quence. For p r e d i c t i n g t r a n s i t i o n s i n h i g h e r c h a r g e s t a t e s , t h e same c o n f i g u r a t i o n s have been s t u d i e d a b i n i t i o by u s i n g t h e r e l a t i v i s t i c p a r a m e t r i c p o t e n t i a l method and s e l e c t e d t r a n s i t i o n s i n v o l v i n g s h o r t - l i v e d lower l e v e l s a r e given f o r 14 i o n s i n t h e sequence from S r XI t o Eu XXXVI.

Multicharged i o n s i s o e l e c t r o n i c w i t h n e u t r a l n i c k e l a r e i n t e r e s t i n g w i t h many r e s p e c t s . T h i s sequence i s t r a c e d up t o v e r y h i g h l y charged i o n s t h r o u g h . r e s o n a n c e t r a n s i t i o n s dominated by a 3d-4f s t r o n g e m i s s i o n 111. The 3d94t e x c i t e d s t a t e s a r e m e t a s t a b l e o r c a n decay by means o f 4-4 o r 3-4 t r a n s i t i o n s , whose p r o b a b i l i t i e s have d i f f e r e n t Z,-scalings. S i m i l a r l y t o t r a n s i t i o n s 3s-3p i n n e o n - l i k e i o n s 121,

9

-

^{9 -}

some 3d 4p ( J = l )

-

3d 4d t r a n s i t i o n s i n n i c k e l - l i k e i o n s a r e c a p a b l e o f a m p l i f i e d spontaneous e m i s s i o n due t o p o p u l a t i o n i n v e r s i o n s . S u b s t a n t i a l g a i n s have been p r e d i c t e d i n c o l l i s i o n n a l - r a d i a t i v e models L3,41 and " l a s i n g " l i n e s have been r e c e n t l y observed a t L.L.N.L., Livermore (U.S.A.) i n Eu XXXVI.

B e f o r e 1985, t h e s p e c t r a l a n a l y s i s o f 4-1 t r a n s i t i o n s was l i m i t e d t o e l e m e n t s w i t h atomic number s m a l l e r t h a n 35 151 and a s y s t e m a t i c s e a r c h f o r 4s-4p and 4p- 4d t r a n s i t i o n s s t a r t e d j o i n t l y a t L a b o r a t o i r e Aim6 C o t t o n , Orsay and a t I n s t i t u t e f o r Spectroscopy (I.S.A.N.), T r o i t s k (USSR). The extended a n a l y s i s o f Br V I I I was i n c l u d e d i n a survey o f a l l t h e 3d94t l e v e l s i n t h e framework o f t h e Slater-Condon p a r a m e t r i c t h e o r y L61, and t h e p r e d i c t i o n s of e n e r g i e s and l i n e s t r e n g t h s through Mo XV were s h o r t l y confirmed by experiment [7,81.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988162

C 1-300

JOURNAL DE PHYSIQUE

The d C e x c i t e d c o n f i g u r a t i o n s o f n i c k e l - l i k e i o n s a r e o f 'lone h o l e 9

-

one p a r t i - c l e " type and, inasmuch as second o r d e r e f f e c t i v e operators f o r e l e c t r o s t a t i c i n t e r - a c t i o n are added t o t h e u s u a l f i r s t o r d e r p e r t u r b a t i o n ( e l e c t r o s t a t i c and s p i n - o r b i t h a m i l t o n i a n ) , t h e number o f Russell-Saunders terms equals t h e number o f e l e c t r o s t a - t i c parameters. I n t h e u s u a l a p p l i c a t i o n o f t h e Slater-Condon method, a number p o f energy parameters ( S l a t e r and s p i n - o r b i t ) a r e f i t t e d t o minimize t h e r o o t mean square d e v i a t i o n on t h e energies f o r N l e v e l s i n a g i v e n i o n and c o n f i g u r a t i o n . I n multicharged ions, experimental energies a r e inaccurate;due t o r e l a t i v e l y low i n s t r u m e n t a l r e s o l u t i o n 3 r t o plasma conditions,and t h e r e i s a s t r o n g need f o r i n - c r e a s i n g t h e r a t i o N/p, on which depends t h e r e l i a b i l i t y o f a parametric a n a l y s i s .

By u s i n g hydrogenic wavefunctions, i t i s demonstrated t h a t S l a t e r i n t e g r a l s depend l i n e a r l y on Zc=Z-Ne+l, which had been shown semi-empirically by Edl6n L91, d e v i a t i o n s from l i n e a r i t y a t low-Z,

-

values being accounted f o r by a term C/(Z,+D).

9 9 9

I n our c a l c u l a t i o n s o f 3d 4s, 3d 4p and 3d 4d, t h e S l a t e r i n t e g r a l s have been expressed as : R k = A + B.Z_

+

C/(Z_+l) and t h e s p i n - o r b i t i n t e g r a l s expressed as :

5

=

a

⁺

5.1,

⁺

'r,.~:

^{+'r3.z: +}

T,.z; ,

and t h e c o e f f i c i e n t s A, 8, C, and

ci

have been considered as new a d j u s t a b l e para- meters i n aeneralized l e a s t sguares f i t s (GLS) on a l l known l e v e l s o f a sequence

-

3d944

.

Such a p a r a m e t r i z a t i o n had been used successfull; i n e a r l i e r i n v e s t i g a t i o n s o f ground c o n f i g u r a t i o n s 3dN

[ l o ] .

Due t o t h e f a c t t h a t t h e wavenumbers o f t h e 3-4 resonance l i n e s a r e l e s s accurate than those o f 4-4 t r a n s i t i o n s , t h e average ener- g i e s o f t h e c o n f i g u r a t i o n s r e l a t i v e t o 3d10 have been v a r i e d independently. A t pre- sent, a l l known l e v e l s up t o Mo XV have been used f o r p r e d i c t i n g energies, wave- numbers and l i n e s t r e n g t h s up t o Sn X X I I I C111.

A l l t h e 50 known l e v e l s o f 3d 9 4s from Z n I11 t o Mo XV a r e described by p= 20 f r e e parameters w i t h rms d e v i a t i o n o f 18 cm-1 on t h e energies. F o r 3d94d, a few p e r t u r b e d l e v e l s o f Zn 1 I I . b e i n g discarded, N=154, p=33 and t h e rms d e v i a t i o n i s 54 cm-1. Owing t o t h e 4p-3d decay which i s observed throughout t h e n i c k e l sequence, t h e study o f 3d94p i s n o t l i m i t e d t o Mo XV and 158 l e v e l s o f t h i s c o n f i g u r a t i o n (from Zn I11 t o Ag X X ) were i n t e r p r e t e d w i t h t h e same rms d e v i a t i o n as f o r 3d94d.

A t h i g h Z values, t h e a p p l i c a b i l i t y of t h e Slater-Condon method vanishes: t h e number of welf-resolved observed l i n e s decreases s h a r p l y and energy l e v e l s cannot be d e r i v e d i n a s i n g l e system which i s needed f o r f i t t i n g energy parameters. More- over, t h e i n c r e a s i n g importance o f t h e r e l a t i v i s t i c e f f e c t s makes t h e unique spin- o r b i t parameter unable t o t a k e i n t o account a l l magnetic p a r t o f t h e hamiltonian.

F o r these reasons, r e l a t i v i s t i c ab i n i t i o methods have t o be used i n highly-charged i o n s .

We have a p p l i e d t h e r e l a t i v i s t i c parametric p o t e n t i a l method 112,13,141, t o t h e c a l c u l a t i o n o f a l l c o n f i g u r a t i o n s w i t h one e l e c t r o n e x c i t e d from t h e n=3 t o t h e n=4 s h e l l i n t h e odd p a r i t y and o f the f o u r lowest even c o n f i g u r a t i o n s , namely 3p63d1°,

6 9 6 9 5 10

3p 3d 4s, 3p 3d 4d and 3p 3d 4p. The parameters d e s c r i b i n g t h e c e n t r a l p o t e n t i a l were f i t t e d t o minimize t h e average energy o f e x c i t e d c o n f i g u r a t i o n s . The waveleng- t h s i n

fi

and o s c i l l a t o r s t r e n g t h s ( v e l o c i t y form) o f s e l e c t e d n i c k e l - l i k e t r a n s i - t i o n s are c o l l e c t e d i n Table I. Two s t r o n g l i n e s should t r a c e t h e presence o f 4-4 n i c k e l - l i k e t r a n s i t i o n s i n normal c o n d i t i o n s o f observations; they a r e 4p J=4

-

^4d

J=5 and 4s J=3

-

4p J=4. For t h e o t h e r r e p o r t e d l i n e s , t h e lower L e v e l o f t h e t r a n - s i t i o n are those 3d94p J=1 l e v e l w i t h h i g h e s t t r a n s i t i o n p r o b a b i l i t y t o 3d10.

The d i f f e r e n c e s between experimental and t h e o r e t i c a l wavelengths a r e a v a i l a b l e from Sr X I t o Nb XIV and a r e a l s o r e p o r t e d i n Table I. They show a good i s o e l e c - t r o n i c consistency and t h i s should be h e l p f u l f o r extending t h e experimental analy- s i s o f n i c k e l - l i k e spectra. With r e g a r d t o the r e c e n t r e s u l t s , o n Eu XXXVI, a d i f f e r e n c e o f -68000 cm-l between observed and c a l c u l a t e d wavenumbers makes t h e ab i n i t i o p r e d i c t i o n o f 3d94d

1s

as u n s a t i s f a c t o r y as f o r t h e e q u i v a l e n t term i n t h e neon-like sequence 2p53p

1s.

With v e r y few exceptions, t h e o t h e r p r e d i c t i o n s agree t o b e t t e r than 0.6% w i t h observations.

Now, t h e s p e c t r a o f l a s e r produced plasmas i n t h e p e r i o d from ruthenium t o t i n have been measured by C h u r i l o v and Ryabtsev a t T r o i t s k and new i d e n t i f i c a t i o n s u s i n g t h e t h e o r e t i c a l background described above, should be p u b l i s h e d soon.

ions from Sr XI to Eu XXXVI. Theoretical wavelengths in

b

and oscillator strengths are from the relativistic parametric potential method. Devia- tion between experimental and theoretical wavelength is given when avai- lable 171.

Label for transitions:

A

: (3d )5/2(4s)1/2 J=3 9

-

(3d9)5/2(4p)3/2 J=4

B

: (3d )5/2(4p)3/2 J=4 9

-

(3d9)5/2(4d)5/2 J=5 C : (3d9)3/2(4p)3/2 J=1

-

(3d9)3/2(4d)5/2 J=2 D : (3d9)3/2(4p)1/2 J=l

-

(3d9)3/2(4d)3/2 J=2 E : (3d9)3/2(4p)1/2 J=l

-

(3d9)3/2(4d)3/2 J=l F : (3d9)5/2(4p)3/2 J=l

-

(3d9)5/2(4d)5/2 J=2

G

: (3d9)5/2(4p)3/2 J=1

-

(3d9)5/2(4d)5/2 J=1 H : (~d~)5/2(4~)3/2 J=l

-

3d94d

'so

I

: (3d9)3/2(4p)1/2 J=l

-

3d94d

'so

Nb XIV

X sf

bX 395.225 2.50 -0.61 269.669 5.74 -0.16 269.847 1.53 -0.82 256.769 0.82 -1.18 264.262 0.30

180.173 0.44

Ru XVII Pd XIX

Ag

XX Cd XXI In XXII

A

317.602 2.38 277.937 2.33 260.817 2.28 245.098 2.26 230.648 2.24

B

222.510 5.20 199.332 5.01 189.200 4.76 180.132 4.63 171.844 4.50 C 221.933 1.43 198.449 0.99 188.227 1.18 179.081 1.18 170.733 1.16 F 223.320 0.30 199.915 0.35 189.305 0.37 179.972 0.39 171.470 0.40 G 231.8290.49 207.326 0.53 196.3770.55 186.7800.56 178.0330.58 H 149.1270.41, 134.7520.33 127.0480.38 121.0140.36 115.461 0.35

Sn XXIII A 217.325 2.22 B 164.2334.38 D 142.0820.52 E 147.8770.55 F 163.688 0.42 G 170.019 0.60 H 110.333 0.34

Te

XXV Xe XXVII 193.559 2.19 172.998 2.17 150.733 4.17 139.097 3.98 128.570 0.58 116.783 0.62 133.614 0.60 121.188 0.64 149.958 0.44 138.193 0.45 155.868 0.62 143.726 0.63 101.277 0.31 93.434 0.28

Nd XXXIII 125.380 2.16 111.975 3.53 88.873 0.69 91.843 0.69 111.004 0.55 115.566 0.63 75.000 0.20

Eu XXXVI 107.363 2.18 101.469 3.35 77.968 0.70 80.417 0.70 100.536 0.42 104.679 0.61

67.754 0.18

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