QUANTUM MECHANICAL CALCULATIONS OF THE STARK BROADENING OF SOME He I LINES FROM PLASMAS

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QUANTUM MECHANICAL CALCULATIONS OF THE STARK BROADENING OF SOME He I LINES

FROM PLASMAS

M. Dimitrijevik, P. Grujik, D. Koledin

To cite this version:

M. Dimitrijevik, P. Grujik, D. Koledin. QUANTUM MECHANICAL CALCULATIONS OF THE

STARK BROADENING OF SOME He I LINES FROM PLASMAS. Journal de Physique Colloques,

1979, 40 (C7), pp.C7-825-C7-826. �10.1051/jphyscol:19797398�. �jpa-00219397�

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JOURNAL DE PHYSIQUE Colloque C7, suppl6ment au n07, Tome 40, JuiZZet 1979, page C7- 825

QUANTUM MECHANICAL CALCULATIONS OF THE S T A W BROADENING OF SOME He I LINES FROM PLASMAS

M.S. ~irnitrijevit', P. ~ r u j i d ' and D.

ole din".

d m t i t u t e of Applied Physics, P. 0. Box 24, 11001 Belgrade, Yugoslavia.

%*Institute of Physics, P. 0. Box 57, 11001 Belgrade, Yugoslavia.

Department of Biophysics, Faculty of Medicine, University of Belgrade, Belgrade, Yugoslav%.

An approximative analytical method rbing levels which belong only to n=3 (n=2) for calculating the scattering

5

^matrix¹ helium states, then the

2

matrix can be has been applied for calculating broaden- calculated by approximate expression1 :

ing of some He1 (n=3+n=2) lines, making _{S = K}* * 1/2 eiK t

t;

^{e i ~}^c+;-1/2 ₍₂

use the quantum the Stark br- where is a diagonal matrix of the pertu- oadening of isolated neutral linese2 We rber momenta, U is a unitary matrix, defi- ^LL start from the standard formula3 for the 6

ned by :

half-halfwidth and shift (atomic units are

6 + [ t ( t

⁺

- ; ]

⁼

^e(p+

^l)

⁺

^{( 3 )}

used, unless otherwise stated):

and :

f

⁼;/r2 is the dipole potential ma- Wid =

y

^(-)

^{e +} ^{e -}

^(2sT+1)^(21;

⁺

^l)

^x

trix. Diagonal matrix

e(e +

1) determines

real numbers:

tr *-si %sT ,

⁽⁴⁾

L ~ S ~ $ L ~ ) S ; ' ( L ~ S ( - ~ $ ~ , L ~ , L ~ S ~ ~ ~ ~ I ] (1) Incase: C j = - 2 1

+

^{i A j ,}( A j - real), we where subscripts refer to the initial (i) have :

8

"

and final (f) levels of the transition, su- tan

rj

⁼^tanh^{( F A}^{./2) cot(}^Ajtn(kj/~o) (5)

3 2

perscript T to the whole perturber-emitter where *o is given by : Ko = 2(E-Er) ' be- system and the capital letter quantum num- ing the energy of the resonance parent sta- hers to the emitter. N is the electron den- te and Er negative sity,

e , -

denote angular momentum quantum ion (in our case

-

^~e-).Further, we have :

-

numbers before and after collision, respec-

zj2

⁼^kj2

+

^CAk:. ^u^:^.^~^, ^j⁼ⁱ ^{f a}⁽⁶⁾

4

-

J

tively and f(v) is the velocity distributi- 2

ET _i= +.ki,+

ei.

⁼Zkf,+ef.+6Jif ¹ ² ( 7 )

on of electrons.

-

2

-

² ² ² ²

The diagonal matrix elements

sirs:

Ki

-

ki. +Aki. I Kf = kf

.

⁺^Akf. ⁽⁸⁾

are usually obtained by solving correspon-

-

where k is the arithmetic mean of two j

-

ding set of coupled integro-differential mutually most separated sublevels,

&

is If One retains terms _the

energy of the substate and

$f

^{is the}

of the direct potential matrix, neglects

angular frequency of the transition.

exchange terms and accounts for the pertu-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797398

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We calculate half-halfwidth and 3 0- 3 shift for the transition : HeI(3 P 2 S), multiplet 2. In this particular case eg.

(1) takes the form :

Quantities needed for evaluating eq. (9) are given in Table 1.

Table 1. Multiplet 2; h = 3888.7

8

Atomic state 3 3 ~ 0

z3s

Energy (eV) 23.006 19.812

~ e - state 3 2 2~

Resonant energy 22.650 19.367

KO (au) 0.1647 0.1809

As shown inL applicability of the

A

present method for evaluating S matrix is restricted to not too small energy region and is determined by the following condi- tions :

v 2 $ max(Aki. ,Akf.), v i e , f' (10) In our case, it means that calculated results are not reliable for plasma tempera- ture below 30000. K.

Computations for the line quoted are in progress. We hope to present nume- rical results, as well as for some other HeI(n=3 ⁴n=2) lines, at the Conference.

The present investigation has been carried out under the financial support from RZN of SR Serbia.

References

1. P.Gruji6 and D. Koledin,to be published 2. M.Baranger, Phys.Rev.,

111,

481, 494,

855 (1958)

3. K.S.Barnes and G.Peach, J.Phys.B: Atom.

Molec.Phys.,

2 ,

350 (1970) 4. P.G.Burke, in Scattering Theory, ed.

A.O.Barut, Gordon and Breach, New York

5. N.Feautrier and Tran Minh, J.Phys.B:

Atom.Molec.Phys.,

2,

3427 (1977) 6. M.J. Seaton,Proc.Phys.,

11,

174 (1961) 7. D.W.O.Heddle, Proc.Roy.Soc.Lond.,A,

352, 441 (1977)

-