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ON THE APPROXIMATIVE SEMICLASSICAL FORMULA FOR THE ELECTRON-IMPACT WIDTH OF MULTIPLY IONIZED ATOM LINES IN PLASMAS
M. Dimitrijevik, N. Konjevik
To cite this version:
M. Dimitrijevik, N. Konjevik. ON THE APPROXIMATIVE SEMICLASSICAL FORMULA FOR
THE ELECTRON-IMPACT WIDTH OF MULTIPLY IONIZED ATOM LINES IN PLASMAS. Jour-
nal de Physique Colloques, 1979, 40 (C7), pp.C7-815-C7-816. �10.1051/jphyscol:19797393�. �jpa-
00219392�
JOURNAL DE PHYSIQUE CoZZoque C7, suppl6ment
au
n07, Tome 40, JuiZZet 1979, page C7- 815ON THE APPROXIMATIVE SEMICLASSICAL FORMULA FOR THE ELECTRON-IMPACT WIDTH OF MULTIPLY I W Z E D ATOM LINES IN PLASMAS
M. ~irnitrijevi; and N. Konjevig.
I n s t i t u t e o f App t i e d Physics, .11001 Beograd, P. 0. Box 24, Yugos Zavia.
I n t r o d u c t i o n . For e v a l u a t i o n o f S t a r k w i d t h s and Theory: F i r s t , t h e o r e t i c a l l i n e w i d t h s were c a l c u - s h i f t s o f non-hydrogenic s p e c t r a l 1 in e s o f i o n i z e d l a t e d from t h e proposed equat ion1 ) which i n c l u d e s atoms, v a r i o u s t h e o r e t i c a l approaches have been lower l e v e l broadening i n t h e weak c o l l i s i o n terms:
used (see e.g. r e f . 1 ) : s e m i c l a s s i c a l , quantum mechanical, semiempiripal and a p p r o x i m a t i v e semi- c l a s s i c a l . The experimental r e s u l t s f o r s i n c l y i o - n i z e d atom l i n e w i d t h s and s h i f t s a r e g e n e r a l l y i n f a i r l y good aoreement ( w i t h i n 220%) w i t h t h e comp- rehensive s e m i c l a s s i c a l c a l c u l a t i o n s o f Griem and coworkers1). Quantum mechanical c a l c u l a t i o n s o f S t a r k broadening parameters has been performed o n l y f o r s i n g l y i o n i z e d e a r t h a l k a l i n e m e t a l s (see e.g. r e f . 1 ) . Both t h e o r e t i c a l approaches, semi- c l a s s i c a l and quantum mechanical a r e v e r y l a b o r i o u s and t h e r e f o r e n o t v e r y p r a c t i c a l f o r e v a l u a t i o n o f
l a r g e number o f l i n e w i d t h s . Tedious c a l c u l a t i o n s can be avoided i f one uses simple semiemprical f o r - mula') which, f o r s i n g l y i o n i z e d atoms, agrees w i t h t h e experiment i n average w i t h i n 550%. For m u l t i p l y i o n i z e d atoms t h e agreement becomes worse what i n d i c a t e s t h a t f u r t h e r t h e o r e t i c a l e f f o r t has t o be made t o extend t h e a p p l i c a t i o n o f t h i s appro- ach t o h i g h e r i o n i z a t i o n stages. Another a p p r o x i - m a t i v e s e m i c l a s s i c a l approach has been suggested by ~ r i e m ' ) f o r t h e e v a l u a t i o n o f S t a r k 1 in e w i d t h s o f m u l t i p l y i o n i z e d atoms. The t h e o r e t i c a l , r e s u l t s have been compared1) wi t h t h e experimental r e s u l t s f o r C l l l and CIV*) which, a t t h a t time, were o n l y r e l i a b l e data. I n t h e mean t i m e a number o f expe- r i m e n t a l r e s u l t s f o r t h e prominent l i n e s o f A l l l and A I V ~ ) NI 1 14), 01 1 i 5 ) , ~i 1 1 I ~ ' ~ ) and ~i l v 7 ) and C l I 11') become a v a i l a b l e .
were Me, T and
;
a r e e l e c t r o n c o n c e n t r a t i o n , tempe- r a t u r e and average v e l o c i t y r e s p e c t i v e l y , 3 i s t h e e l e c t r o n de B r o g l i e wavelength d i v i d e d by Za, k i s t h e Boltzman c o n s t a n t ,r,,
i s the i o n i z a t i o n0 I
energy o f hydrogen, Z i s t h e charge o f t h e e m i t t e r which t h e o p t i c a l e l e c t r o n "sees" (Z=1 f o r n e u t r a l , 2 f o r s i n g l y i o n i z e d atoms e t c . ) and n" i s t h e e f f e c t i v e p r i n c i p a l quantum number f o r i n i t i a l ( i ) and f i n a l ( f ) l e v e l o f t h e t r a n s i t i o n :
where Eion i s t h e i o n i z a t i o n energy f o r t h e c o n s i - dered s e r i e s o f terms and E i s t h e energy o f t h e l e v e l j.
F i r s t term on t h e r i g h t - h a n d s i d e o f eq. 1 a r e c r o s s s e c t i o n s f o r weak c o l l i s i o n s due t o An = O , R + Q ~ ~ d i p o l e t r a n s i t i o n s , t h e second term g i v e s c o n t r i b u t i o n from t h e i n e l a s t i c c o l l i s i o n s f o r An # 0 p e r t u r b i n g l e v e l s and t h e l a s t two terms a r e t h e s t r o n g c o l l i s i o n and h i g h e r o r d e r i n t e r a c t i o n c o r r e c t i o n s :
&
The aim o f t h i s paper i s t o t e s t a p p r o x i m a t i - m a x ( k , ~ - )
~ 1 2 - m a x ( Q , R - ) ~ p 2
.
ve s e m i c l a s s i c a l t h e o r e t i c a l approach w i t h a v a i - 2 ~ + 1 j l a b l e experimental d a t a . I t w i l l be a l s o proposed
4.5 m o d i f i c a t i o n o f a p p r o ~ ~ i m a t i v e s e m i c l a s s i c a l formu- an(5
- -
l a and t h e o r e t i c a l r e s u l t s o b t a i n e d i n t h i s way
a r e a l s o compared w i t h t h e experiment. ( Z - l ) e 2 uC
k , 2 -
-
mv 3 ( 4 )Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797393
where
P
i s the f a c t o r from Bates and ~ a m ~ a a r d ' ) , w i s t h e plasma frequency, wF t h e f i n e s t r u c t u r e s p l i t t i n g , P a i s f i n e s t r u c t u r e c o n s t a n t , w i s t h e u n s f i i f t e d angular frequency, Aw. i s t h e i o n s p l i t - t i n g and Z and N a r e t h e charge and c o n c e n t r a t -P P
i o n o f p e r t u r b i n g ions, r e s p e c t i v e l y .
For t r a n s i t i o n s An = 0 i n eq. 1 Gaunt f a c t o r s a t a t h r e s h o l d a r e taken v a r i a b l e ( g = C.9-1 .1/Z) and l a r g e r than 0 . 2 ' ) . \!e have m o d i f i e d weak c o l l i - s i o n term o f eq. 1 (eq. 3) f o r An
. .
= 0 t r a n s i t i o n s by r e p l a c i n g ( 5 - 4 . 5 / ~ ) w i t h t h e c o n s t a n t v a l u e o f 1.4 what corresponds t o the c o n s t a n t Gaunt f a c t o r o f 0 . 2 .R e s u l t s and d i s c u s s i o n : The r a t i o o f t h e t h e o r e t i - c a l and experimental r e s u l t s a r e g i v e n i n Table 1.
I n t h i s t a b l e Wu and Wm a r e t h e r e s u l t s o b t a i n e d from unmodified and m o d i f i e d eq. 1 . For t h e sake o f t h e comparison, t h e r e s u l t s from Griem's s e n i - e m p i r i c a l f o r m u l a a r e a l s o g i v e n u n d e r H From
se'
t h e t a b l e i t i s obvious t h a t m o d i f i e d eq. 1 agrees best w i t h t h e experiment
Table 1. Average r a t i o s o f t h e o r e t i c a l
W ,
\4Jm and WSe, and experimental halfwidth!." u "m "se
exp exp
A l l 1 21100 1.48 1 . O O 0.64
AIV 20750 1.87 1.12 0.82
C l l l 60000 0.94 0.90 0.76
CIV 60000 1.20 0.60 0.40
S i l l l 16400 2.22 1.39 0.90
s i
I I I 25600 2.21 1.53 0.94S i lV 25600 2.03 1.20 0.87
01 l l 25900 1.39 0.09 0.53
C11 I 1 24200 2.38 0. a4 0.58
N l l l 24300 1.58 0.10 0.62
averaged values
References:
1. Griem,H.R.: S p e c t r a l L i n e Broadening by Plasmas, Academic Press, London (1974) 2 . Bogen,P., Z.Naturforsch. 27A, 210 (1972) 3. P l a t i S a M., PopoviC,M., D i m i t r i j e v i t , M . ,
K o n j e v i t , t l . , Z.Naturforsch. 30A, 212 (1975) 4. PlatiSa,M., Popovit,M., Konjevit,N., Astron.
Astrophys. 41, 463 (1975).
5 . PlatiSa,M., Popovit,M., KonjeviC,N., A s t r o n . Astrophys. 45, 325 (1975)
6. P u r i t , J . , Djeniie,S., Labat,J., C i r k o v i t , L j . , Z.Phys. 267, 7 1 (1974)
9. Bates,D.R. and Damgaard A., Phil.Trans.Roy Soc., London 242A, 101 (1949).
