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Stark Profile and Widths sf the Hel 5016 A Line in a Plasma

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Stark Profile and Widths sf the Hel 5016 A Line in a Plasma
Revista Brasileira de Física, Vol. 11, NP 4, 5981
Stark Profile and Widths sf the Hel 5016
A Line in a Plasma
J. M. BASSALO
Departamento de Física da Universidade Federal do Par& Belbm, Parh, Brasil
M. CATTANI and V. S. WALDER
Instituto de .Física, Universidade de São Paulo, São Paulo, Brasil
Recebido eni 20 de Agosto de 1981
Using t h e convergent impact t h e o r y , developed
C a t t a n i arid Walder,
by
Bassalo,
t o t r e a t t h e b r o a d e n i n g and s h i f t o f a t o m i c
8
we have arialysed t h e S t a r k p r o f i l e and w i d t h s o f t h e H e l 5016
A v e r y good agreement i s found between o u r p r e d i c t i o n s and t h e
mental r e w l t s o f Chiang e t aZ. The d i s c r e p a n t f a c t o r
1.7
lines,
line.
experibetween
t h e o r y and experiment announced b y Kusch, E i n f e l d and Sauerbrey was n o t
found.
Usando a t e o r i a convergente de impacto d e s e n v o l v i d a p o r Bassalo,
L a t t a n i e Walder para d e s c r e v e r o alargamento e deslocamento
de
l i n h a s e m i t i d a s p o r átomos, nós analisamos o p e r f i l S t a r k e l a r g u r a s da
l inha de 5016
8
do Hél i o n e u t r o . As nossas p r e v i s õ e s t e ó r i c a s e s t ã o
m u i t o bom acordo com os r e s u l t a d o s e x p e r i m e n t a i s de Chiang e t aZ.
em
Um
relatado
f a t o r d i s c r e p a n t e da ordem de 1.7 e n t r e t e o r i a e e x p e r i ê n c i a
p o r Kusch, E i n f e l d e Sauerbrey não f o i e n c o n t r a d o p o r nós.
Griem, Baranger, Kolb and ~ e r t e l " ~(GBKO) have
t h e o r y t o o b t a i n t h e S t a r k broadening and s h i f t o f 1 i n e s
developed a
em i t t e d
by
n e u t r a l atoms and i o n s i n a h o t plasma. T h i s t h e o r y has u s u a l l y been r a t h e r s u c c e s s f u l i n p r e d i c t i n g w i d t h s and s h i f t s o f i s o l a t e d
2
n e u t r a l h e l i u m . However,
He I l i n e s 5016
8
and 3889
Kusch3 c o n c l u d e frommeasurements,
8,
lines
of
of
the
i n a w a l l - s t a b i l i z e d pulsed discharge t h a t
t h e measured w i d t h s r e s u l t s i n e l e c t r o n d e n s i t i e s t o o h i g h by a
%
factor
1.7 i f t h e GBKO t h e o r y was used. E i n f e l d and s a u e r b r e y 4 , w i t h a s i m i -
l a r d i s c h a r g e procedure, confirmed t h i s d i s c r e p a n c y f o r t h e He 15016
8
line.
Since t h i s 1.7
% \.
factor
is
surprisingly
l a r g e compared w i t h
20% agreement t o GBKO t h e o r y observed i n severa1 e x p e r i m e n t s 2
v o l v i n g d i f f e r e n t d e v i c e s , Chiang, Murphy, Chen and
riem^
l y s e d , e x p e r i m e n t a l l y and t h e o r e t i c a l l y , t h e p r o f i l e s o f t h e
8
3889
aZ.
and
have measured t h e w i d t h s o f t h e above m e n t i -
oned l i n e s i n a h i g h p r e s s u r e e l e c t r i c shock t u b e o f e l e c t r o n
2.
5016
t r a n s i t ion.
Chiang e t
i'J
in-
have re-ana-
and tempera u r e T
1 x 10''
sured h a l f - w i d t h s a r e i n
+
?.
1.5 eV. A c c o r d i n g t o them,
densi t y
t h e mea-
0% agreement w i t h t h e c a l c u l a t e d widt'hs ba-
sed on GBKO t h e o r y , so t h a t t h e f a c t o r Q l . 7 d i s c r e p a n c y was n o t c o n f i r med. Chiang e t
aZ.
bel ieve t h a t t h i s very l a r g e discrepancy
found
by
Kusch, and E i n f e l d and Sauerbrey i s due t o a s y s t e m a t i c e r r o r , p o s s i b l y
from o p a c i t y e f f e c t s i n the e l e c t r o d e regions o f the pulse d i s c h a r g e t u bes o r e r r o r s i n t h e e l e c t r o n d e n s i t y d e t e r m i n a t i o n s .
I n a r e c e n t paper, Bassalo, C a t t a n i and w a l d e r 6
have
loped a c o n v e r g e n t t h e o r y t o t r e a t t h e e l e c t r o n impact b r o a d e n i n g
s h i f t o f l i n e s o f n e u t r a l atoms. They have a p p l i e d t h i s
formalism
s t u d y t h e w i d t h s and s h i f t s o f many n e u t r a l h e l i u m l i n e s and
deveand
to
t h e y have
v e r i f i e d t h a t t h e convergent and GBKO t h e o r i e s a r e e q u a l l y s u c c e s s f u l
t o describe t h e experimental r e s u l t s .
I n t h i s paper we a p p l y o u r c o n v e r g e n t approach 6
t h e p r o f i l e and t h e w i d t h s o f t h e He 1 5016
aZ.'.
der
6
to
analyse
a l i n e measured by Chiang e t
Our i n t e n t i o n i s t o t e s t t h e t h e o r y o f Bassalo, C a t t a n i and
Wal-
and a l s o t o v e r i f y i f t h e r e i s a so l a r g e d i s c r e p a n t f a c t o r b e t w e e n
8
~ , E i n f e l d and Sauert h e o r y and exper iment as was announced by ~ u s c h and
b r e y 4.
2. -CALCUiLATION OF THE PROFILE AND WlD.THS
de we
To e v a l u a t e t h e e l e c t r o n i c impact w i d t h s we and s h i f t s
Cattani
use a s e m i - c l a s s i c a l convergent t h e o r y d e v e l o p e d by Bassalo,
and ~ a l d e r " .
To c a l c u l a t e t h e t h e o r e t i c a l p r o f i l e o f t h e H e i 5016
we c o n s i d e r two d i f f e r e n t approachs developed,
and by Barnard,
8
respectivel y by
line
GBKO"*
Cooper and s m i t h 7 .
A c c o r d i n g t o G B K O " ~ t h e t o t a l S t a r k p r o f i l e ~ ~ ( owf an
) isol a t e d n e u t r a 1 atom l i n e i s g i v e n by t h e c o n v o l u t i o n o f e l e c t r o n
impact
p r o f i l e s w i t h a q u a s i - s t a t i c q u a d r a t i c S t a r k e f f e c t f o r t h e i o n broadening:
where
w
if
i s t h e energy d i f f e r e n c e between t h e i n i t i a l
and f i n a l
s t a t e s o f t:he l i n e , F t h e s t a t i c e l e c t r i c f i e l d g e n e r a t e d by t h e
H(F)
f
ions,
t h e Holtsmark d i s t r i b u t i o n f u n c t i o n f o r F and C4 t h e S t a r k parame-
ter.
T h i s IH(w) p r o f i l e w r i t t e n i n d i m e n s i o n l e s s v a r i a b l e s
mes j
A ,R
where
I:
beco-
( x ) g i v e n byl":
= (w
- wif
-
de)/we, A = (2n~,/w~.p;)~'*,
8
= ( n c 4 / p 3 v . ) , vi
m
the
2
mean - i o n v e l o c i t y , R = pm/pD, pm = ( 3 / 4 n ~ ) ' / ~i s t h e mean i o n - i o n separ a t i o n , N t h e i o n d e n s i t y and pD t h e Debye r a d i u s .
A c c o r d i n g t o Barnard, Cooper and s m i t h 7 , t h e t o t a l S t a r k prof i l e j(x,p,A),
i n d i m e n s i o n l e s s v a r i a b l e s , i s g i v e n by
where 0 = w p / V .
em z
J
,
(&
=
the signal
p
+
'
3
,
W =
D1(k)
A 8 / 9 0 - 1 / 3 ~ 1 ( k ) ,k = 1 . 0 3 0
-
4/3x
,
3/I4I3 R ) ,
i s t h e signa! o f d e , and t h e f u n c t i o n s W 1 ( k ) and D b ( k ) a r e
t a b u l a t e d by Barnard
ataL7
Since 4 n o u r case t h e l i n e p r o f i l e i n o n i y s l i g h t l y m o d i f i e d
i f we necjlect t h e Debye s c r e e n i n g e f f e c t s , we p u t , t o s i m p l i f y o u r c a l c u l a t i o n s , R=O.
To compare e x p e r i m e n t a l and t h e o r e t i c a l p r o f i l e s i t
cessary t o r n u l t i p l y j
24
,R
I n , f i g u r e 1 a r e shown t h e e x p e r i m e n t a l p r o f i l e o f
5Gi6
T
8
l i n e , rneasured Ò y Chiang e t
= 1.5 e\],
o r (21, and
is
ne-
( x ) and j ( x , a , ~ ) by a r b i t r a r y c o n s t a n t f a c t o r s .
a ~ . 'for N
= 1.06 x i 0 1 7
the
C B - ~
and t h e t h e o r e t i c a l p r o f i l e s o b t a i n e d w i t h e q u a t i o n s
Hel
and
(1)
(3).
As one can see f r o m f i g u r e I, t h e r e
is a
good
between t h e o r e t i c a l and e x p e r i m e n t a l p r o f í l e s .
Fig.1
5016
- Exparimental and
8 li": for N = 1.05
theoietical
n 10''
r e s n l t s f o r t h e S t a r k p r o f i l e t h e Hel
and 1' = 1 . 5 eV.
agreement
WE: calculate now the total half-halfwidths w of the Hei 5016
8
line and we compare thern with the experimental results of
Chiang
et
a ~5 ..
To obtain the ions contribution to the widths
we use only
the approach developed by riem' that seems to g ve the better descri ption of the experimental widths, as vias verified n our preced ing paper6,
Accord i ng to ~ri em i , the tota 1 ha l f-ha 1 fwidths w is g ~ v e nby
In table I are compare6 the theoretícal widths,obtained with
equation (41, hith thc experimental results of Chiang ~t a2.'
Tab
He
Comparison between t h e masured ind ca lculated widths of
6
8
=
iine for
the
1 .!iev.
Electron density
( 1 0 ' ~ c~n-~)
Heasured
-- -
-
1.41
12. o
1.26
1 O .Z
1 .o8
9.2
1 .oa
9.6
1 .O5
9.6
As cne can see from figure 1 and table 1, the
predictions are in
?
theoretical
10% agreement with the experimental results.
50, we can conclude that: a) the agreement between theoryand
experiment, within the experimental errors, is very good, b)
crepant factor
not conf i rmed .
Q
tne dis-
1.7 focind by ~ u s c h ~and
, Einfeld and 5auerbrey4 was
J.M. Bassalo thanks the "Pró-Rei tor ia de pós-Graduação e Pesquisa" for financia1 support.
REFERENCES
1. H.R.Griem, M.Baranger, A.C.Kolb and G.Oerte1, Phys. Rev.
(1962).
2. H.R.Griem, SpectraZ Line Broadening by Plasma, Academic Press,
York (1974).
3. H.J.Kusch, Z. Naturforsch.
117
125,
New
26a, 1970 (1971).
4. D.Einfeld and G.Sauerbrey, Z.Naturforsch. 32a, 310 (1976).
5. W.T.Chiang, D.P.Murphy, Y.G. Chen and H.R.Griem, Z.Naturforsch. 32a,
818 (1977).
6. J.M.Bassalo, M.Cattani and V.S.Walder, Phys.Rev. 22A, 1194 (1980).
7. A.J.Barnard, J.Cooper and E.W.Smith, J . Q u a n t . S p e c t r o s c . R a d i a t . T r a n s fer 14, 1025 (1974).
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