CALCULATION OF THE FREE-BOUND CONTINUUM OF RARE GASES

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Submitted on 1 Jan 1979

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CALCULATION OF THE FREE-BOUND CONTINUUM OF RARE GASES

P. Ranson, J. Chapelle

To cite this version:

P. Ranson, J. Chapelle. CALCULATION OF THE FREE-BOUND CONTINUUM OF RARE GASES. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-93-C7-94. �10.1051/jphyscol:1979746�.

�jpa-00219452�

JOURIiAL DE PHYSIQUE CoZZoque C7, suppzdment a u n07, Tome 40, JuiZZet 1979, pageC7- 93

CALCULATION OF THE FREE-BOUND CONTINUUM OF RARE GASES

P. Ranson and

J.

Chapelle.

C.R.P.H.T.

-

C.N.R.S., 45045 OrZ6ans Cddex, France.

The c a l c u l a t i o n o f 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 , w h i c h i s t h e s u b j e c t o f a communication a t t h i s c o n f e r e n c e r e f e r r e d t o a s

1lt&s

u s e d t o de- t e r m i n e t h e f r e e bound continuum. I n t h e c a s e o f r a r e g a s atoms ( e x c e p t He), i f t h e t e m p e r a t u r e i s n o t t o o h i g h , a l l t h e i o n s o f t h e plasma a r e i n t h e ground s t a t e which i s a d o u b l e t term

[

^,p3/,,

2~1!2 s e p a r a t e d by a e n e r g y d i f f e r e n c e

A

E.

So i t 1s n e c e s s a r y t o d i s t i n g u i s h t h e two c h a n n e l s i n t h e r e l a t i o n between p h o t o i o n i z a t i o n and recom- t b i n a t i o n c r o s s s e c t i o n s . The e m i s s i o n c o e f f i c i e n t o f r e c o m b i n a t i o n continuum t o w a r d s a l e v e l i , i s g i v e n by

where n$/, and n112 a r e t h e i o n d e n s i t y f o r t h e two s t a t e s , ne t h e e l e c t r o n d e n s i t y ,

qR

and

C$

a r e t h e r e c o m b i n a t i o n c r o s s s e c t i o n s o f t h e i o n ( I

=

2~311i_, 2

=

on t h e state i, the.uiorikcs v 1 and v2 and t h e f r e q u e n c y

?

a r e c o n n e c t e d by t h e r e l a t i o n h d = El

+ 2.

^mvi

⁼

^E,

⁺ 4

rnv? when El and E2 a r e t h e i o n i s a t i o n e n e r g i e s o f t h e l e v e l i' t o w a r d s t h e two i o n i c s t a t e s . The d i s t r i b u t i o n f u n c t i o n i s assumed t o b e maxwellian.

Biberman and a 1 / 2 / have i n t r d u c p d t h e y f a c - t o r . I t i s d e f i n e d f o r a w a v e l e n ~ h t a s t h e r a t i o o f t h e t r u e e m i s s i o n c o e f f i c i e n t t o t h e c l a s s i c a l

?mission c o e f f i c i e n t o f Kramers.

We have c a l c u l a t e d t h e

9

f a c t o r f o r r a r e ga- s e s ( e x c e p t He) w i t h t h e method g i v e n f n I.

It ^is. a open questi'on how t h e pseudo continuum of l i n e s n e a r t h e p h o t o i o n i z a t i o n t h r e s h o l d c a n b e t a k e n Ento a c c o u n t . The u s e o f t h e I n g l i s s and T e l l e r f o r m u l a e g i v e s t h e p o s i t i o n o f t h e l i n e f o r which t h e w i d t h i s e q u a l t o t h e d i s t a n c e t o t h e a d j a c e n t l i n e . However, t h e s i m p l e a p p l i c a t i o n o f t h i s f o r m u l a e do not remove t h e sudd v a r f a t f o n

t h e

J

f a c t o r

I I which i s n o t o b s e r v e d

I

e x p e r i m e n t a l l y . There- f o r e we p r e f e r t o u s e t h e form d e s c r i b e d b y t h e d a s h c d l i m e on t h e f E g u r e 1. The i n - t r o d u c t i o n o f t h i s phenomenon i m p l i e s t h a t t h e

3

f a c t o r becomes an e l e c t r o - d e n s P t v d e ~ e n d e n t

The r e s u l t s o f t h e c a l c u l a t e d

3

f a c t o r a r e shown on f i s u r e s 2 f o r t h e f o u r r a r e g a s e s Ne, A r , K r , Xe r e s p e c t i v e l y f o r t h e s p e c t r a l r a n g e 2000- 10000

a

(named "visibl;) and f o r t h e s p e c t r a l r a n - se 1 - 5 p m (named " i n f r a r e d " ) and f o r a n e l e c t r o n d e n s i t y o f 1015 ~ m - ~ . It s h o u l d b e n o t e d t h a t t h e i n f l u e n c e o f ne i s n o t t h e same i n t h e v i s i b l e r a n e a s i n t h e i n f r a r e d . I n t h e v i s i b l e r a n g e , t h e s o f f t h r e s h o l d

5

i s s h i f t e d t o w a r d s h i g h e r wave- l e n g t h s , b u t i n t h e i n f r a r e d , t h e f a c t o r i s i n c r e a s e d a l m o s t u n i f o r m l y w i t h i n c r e a s i n g n e .

Comparison w i t h ' 3 c h l u t e r r e s u l t s / 3 / and w i t h H o f s a e s s r e s u l t s / 4 / f o r s u f f i c i e n t l y low ne and T

=

8000 K g i v e s r e l a t i v e l y good agreement i n t h e v i s i b l e r a n g e . I n t h e i n f r a r e d t h e r e s u l t s of Biberman and a 1 /5/ a r e n e a r l y e q u i v a l e n t t o o u r s when t h e e l e c t r o n d e n s i t y i s low (

6

1014 c n - 3 ) .

/1/ F . RANSON, t h e s i s c r l k a n s ( 1 9 7 8 ) .

/2/ L.H. BIBEVIAN, G . E . NORMAN, O p t i c s S p e c t . 8 ,

230 ( 1 9 6 0 ) . -

/ 3 / D . S C H L ~ T E S , Z. A s t r o p h y s .

210,

80 ( 1 9 6 8 ) . / 4 / D . HOFSAESS, J.Q.S.X.T.,

19,

339 ( 1 9 7 8 ) . / 5 / L.M. BIBERMAN. G . E . NORMAN, K . N . ULYANOV,

O p t i c s S p e c t . 1 0 , 297 ( 1 9 6 1 ) , S o v i e t A s t r o n . A J ,

6,

^{77 (196?5.}

F i g . 1 : T h r e s h o l d form of e m i s s i o n c o e f f i c i e n t ; d a s h e d l i n e : s e l e c t e d form.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979746

4 3

NEON

N ~ .

10:n-i-

2 I

^NEON

^N,=10

^{4s cm -3}

I -

^I

4 5 - 3

ARGON N e = 10 cm

I . ^, , A ~ - I (

4s -I

KRYPTON Ne= 10

un

I

F i e . 2 :

9

f a c t o r f o r r a r e gases.

-

T

=

4000 K,

-.,,

^T

⁼

^{6000 K,}

---

T = 8000 K,- - - T =

10 000 K.