SPECIFIC FEATURES OF STARK BROADENING OF HELIUM-LIKE MULTI-CHARGED ION SPECTRAL LINES

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SPECIFIC FEATURES OF STARK BROADENING OF HELIUM-LIKE MULTI-CHARGED ION

SPECTRAL LINES

V. Gavrilenko, I. Gaisinsky, Y. Ispolatov, E. Oks

To cite this version:

V. Gavrilenko, I. Gaisinsky, Y. Ispolatov, E. Oks. SPECIFIC FEATURES OF STARK BROADEN-

ING OF HELIUM-LIKE MULTI-CHARGED ION SPECTRAL LINES. Journal de Physique Collo-

ques, 1988, 49 (C1), pp.C1-83-C1-86. �10.1051/jphyscol:1988116�. �jpa-00227436�

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JOURNAL DE PHYSIQUE

Colloque Cl, Supplement au n03, Tome 49, Mars 1988

SPECIFIC FEATURES OF STARK BROADENING OF HELIUM-LIKE MULTI-CHARGED ION SPECTRAL LINES

V.P. GAVRILENKO, I.M. GAISINSKY, Y.O. ISPOLATOV and E.A. OKs USSR State Committee for Standards, Leninsky Prospekt 9 , MOSCOW, 11 7049, USSR

Recently a s a r e s u l t of more a c t i v e r e s e a r c h on dense high tem- p e r a t u r e plasmas prominent importance has been acquired by t h e deve- lopment of t h e theory of S t a r k broadening of multi-charged ions' s p e c t r a l l i n e s (SL). This theory must take i n t o account, on t h e one hand, t h e presence of f i n e s t r u c t u r e s i n i o n energy l e v e l s , and on t h e o t h e r hand, t h e e f f e c t s appearing i n t h e dense plasma:(I) d i p o l e a s well as quadrupole i n t e r a c t i o n with plasma i o n microfield; ( 2 ) plasma p o l a r i z a t i o n s h i f t (PPS) of SL due t o t h e mean e l e c t r i c f i e l d where t h e i o n e m i t t e r i s s i t u a t e d . Over t h e recent y e a r s a number of papers has appeared

[i-43

which consider & i f f e r e n t a s p e c t s of t h e theory f o r i o n s with one and with two e l e c t r o n s .

This paper i s concerned with t h e t h e o r e t i c a l i n v e s t i g a t i o n s of SL p r o f i l e s of

el

- l i k e i o n s i n plasmas with t h e e l e c t r o n concent- r a t i o n Ne ( lo2'

-

¹⁰22 ⁾~ m ' ~ , Let us c~ilciider t h a t t h e S t a r k broadening of t h e

[ ~ d

- l i k e i o n (with t h e nucleus charge Z 3 I ) i s due mainly t o a c t i o n by perturbing i o n s with charge Z (while Z .* 2 ) .

P P

A f t e r choosing t h e axe

Ox3

of t h e Decartes system of coordinates

0%

along t h e d i r e c t i o n of t h e t o t a l p e r t u r b i n g i o n s f i e l d F, -v

l e t us represent t h e Hamiltonian of t h e emmitting

I H ~ ^-

- l i k e i o n a s

a

F;

H~H.-,:F-&&Q'.,

^&/ ^- ^" ⁽¹⁾

In ( I ) , Ho i n c l u d e s t h e unperturbed [ ~ e j - l i k e i o n Hamiltonian and t h e i n t e r a c t i o n with t h e e l e c t r i c f i e l d c o n s t i t u e n t inducing PPS;

d l -

d i p o l e moment pro j e c t l o n o p e r a t o r upon t h e a x i s

Ox1

^;

Qix

-quadrupole moment t e n s o r ;

%4/aXk -

i o n f i e l d inhomogeneity tensor. Con- c r e ~ t e c a l c u l a t i o n of t h e SL S t a r k p r o f i l e s were done f o r the!& 2

lh!

t r a n s i t i o n i n t h e Pe XXV ion. I n t h e s e c a l c u l a t i o n s t h e wave f u n c t i -

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988116

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(21-84 JOURNAL DE PHYSIQUE

ons (UP)%

(""L,~)

of t h e Hamiltonian Ho have been r e p r e s e n t e d as expansion on f u n c t i o n s of t h e LS coupling, Hence due t o magnetic in-

3 1

t e r a c t i o n (spin-.orbit, spin-spin), t h e WF of l e v e l s 3 ' ~ ~ . 3 PI , 3 Dl,

where f o r t h e Fe XXV i o n mixing c o e f f i c i e n t s j3

,pS

a r e ( ' ) :

{ZXY

pp*

^0,332,

^fip

0,78. I n (2)

L ~ )

a r e f u n c t i o n s of t h e IS coup- l i n g . The following quantities were used as eigenvalues

ELsf

^{of the}^Hami^{1 tonian}

~ h e r e k ~ ~ $ ~ are eigenvalues of the Fe XXV ion unperturbed Hamiltonian.

I n ( 3 )

,

a f u n c t i o n t a b u l a t e d i n [ 3 ] w a s used a s a f u n ~ t i o n & ~ ( h h , ~ ) The c a l c u l a t i o n of t h e emission spectrum of t h e Fe XXV i o n was based on numerically obtained e i g e n WF and t h e perturbed Hamiltonian H e i - genvalues. I n doing t h i s , not only i n t e r a c t i o n between t h e terms w i t h t h e main quantum number n-3 under t h e i n f l u e n c e of t h e p e r t u r - bing i o n s ' e l e c t r i c f i e l d s , but a l s o t h e i n f l u e n c e of t h e neighbou- r i n g l e v e l s with n=2 and n=4 upon t h e term n=3 were t a k e n i n t o account i n second o r d e r p e r t u r b a t i o n theory. It should be emphasized t h a t an exact c a l c u l a t i o n of t h e emission spectrum of t h e Fe XXV i o n ensemble c a l l s f o r averaging t h e emission spectrum of an i n d i v i d u a l

" aE

^\

i o n over t h e j o i n t p r o b a b i l i t y d e n s i t y f u n c t i o n

W(F, _/a~$)

which i s a hard mathematical t a s k indeed. That i s why accounting f o r t h e quadrupole i n t e r a c t i o n i n ( 1 ) has been performed approximately s i m i l a r l y t o

[q] .

^However^asd i s t i n g u i s h e d from

[&I ^,

t h e i o n micro- f i e l d d i s t r i b u t i o n w a s implied t o be Holtsmarkian which permitted t o use t h e r e s u l t s obtained i n f o r constrained averages.

Fig. 1 shows c a l c u l a t i o n r e s u l t s i n d i p o l e approximation of t h e energy l e v e l s p o s i t i o n dependence of t h e c o n f i g u r a t i o n 1d3e w i t h

Ma

= 0 f o r t h e Fe XXV i o n !& t h e f i e l d s t r e n g t h F. Fig. 2 shows c a l c u l a t i o n r e s u l t s ( i n d i p o l e approximation) f o r t h e c o n f i g u r a t i o n

I1)!Phe a u t h o r s a r e g r a t e f u l t o I.*. Vainshtein f o r providing informa- t i o n on t h e Fe XXV i o n c o e f f i c i e n t

pp , .

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L$ 3e of t h e e v o l u t i o n (dependent on F) of t h e p r o j e c t i o n modules p e r t u r b e d by t h e f i e l d P of t h e

$ y , ( ' + ' ~ ~ )

s t a k e s on t h e s t a t e

\ p ( i ~ < )

dipole-connected w i t h t h e n = l l e v e l state.SL p r o f i l e s fiS'2--4$3-e of t h e Fe XXV i o n s c a l c u l a t e d t a k i n g i n t o account t h e d i p o l e and t h e quadrupole i n t e r a c t i o n with t h e i o n f i e l d as w e l l as PPS

,

a r e shown i n Pig.3 f o r t h r e e plasma i o n c o n c e n t r a t i o n : N =lo1';

P Np=5* lo1'; Np=5*1021 It i s s e e n t h a t t h e most

ram1

changes of p r o f i l e s i n f l u e n c i n g t h e main maximum p o s i t i o n and asymmetry

c h a r a c t e r occur at t r a n s i t i o n from N = 1 0 ~ ~ c r n - ~ t o ~ ~ = 5 ~ 1 0 ~ ~ c r n - ~ P

which c o r r e l a t e w i t h t h e c h a r a c t e r of curve8 i n F i g s . 1,2. The me- t h o d of c a l c u l a t i n g p r o f i l e s of SL

C H ~

- l i k e i o n s g i v e n i n thia pa- p e r could be u s e & i n a n a l y s i s of experimental SL p r o f i l e s of m u l t i - charge i o n s i n ^densehigh-temperature plasmas and t h e i r d i a g n o s t i c s .

~'r j'1

F i 1 P o s i t i o n of energy l e v e l s

f I

&

I

I I

e XXV i o n c o n f i g u r a t i o n ( f o r

M=O) F.

Fig.2. E v o l u t i o n F of t h e abso- l u t e v a l u e s of p r o j e c t i o n s of t h e p e r t u r b e d ( b y f i e l d F)

\YF(

1 D2), q 3 ~ , ) , + ( l p l ) , y F ( 3 ~ o ) , ~ F ( 3 ~ 2 )

s t a t e s onto t h e s t a t e ~ ( ~ ) ( f o r i o n

... ^.

^Pe

^xxv

c o n f i g u r a t i o n If 3 e )

,

Fig.3. S p e c t r a l l i n e p r o f i l e s f o r t h e i o n Fe XXV t r a n s i t i o n f o r

-6)

t h e e v a l u e s of plasma i o n concen-

15g8 ' fzg.3 ^' A 9 2 %5n t r a t i o n , d o t t e d l i n e - ~ ~ = 1 0 ~ ~ c m - ~ , dashed l i n e

-

~ ~ = 5 * 1 0 " , s o l i d l i n e

-

~ ~ = 5 * 1 0 ~ ~ . I o n temperature

Tj= 1 keV.

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C 1-86 JOURNAL DE PHYSIQUE tBFE RENCES

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4.Jauce R,F. ,Waltz L.A., Hooper C.F. Jr. Phys. Rev A ,

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2228.

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