Interferometric technique for measuring atomic or molecular oscillator strengths in vacuum U

Day, R. A.

English

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A NEW TECHNIQUE FOR MEASURING OSCILLATOR STRENGTHS I N  THE UV 
R.  A. Day 
Department of Physics, g i v e r s i t y  of Oklahoma, Norman, Oklahoma 73069 
> G &  3 7 - a s 3 - 4 Y 7  
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INTRODUCTION ~ G g - 3 7 - @ 6 3 - 8 r  
Physicis ts  have long been concerned with t h e  measurement and com- 
p i l a t i o n  of atomic and molecular o s c i l l a t o r  strengths") e These mea- 
surements a re  always d i f f i c u l t  but i n  the vacuum UV t h e  ordinary pro- 
blems are enhanced by t h e  lack of adequate comparison sources and by 
t h e  great  o p t i c a l  thickness of the  s p e c t r a l  l i n e s  involved. Ingenious 
techniques have been developed f o r  emission measurements by Lincke and 
Griem"); more standard absorption techniques have been used by a 
number of inves t iga tors (3) .  One technique which is  i d e a l l y  s u i t e d  f o r  
t h e  measurement of o p t i c a l  constants of s t rongly absorbed s p e c t r a l  
l i n e s  is the  "hook" method of Rhozdestenskii which samples the  anoma- 
lous index of r e f r a c t i o n  i n  the  neighborhood of s p e c t r a l  l i n e s  (4,5) 
This technique uses a Mach-Zehnder interferometer  (o r  sometimes a 
Fabry-Perot) t o  c rea te  a s e t  of f r inges which are displaced by t h e  
var ia t ion  of o p t i c a l  path lengths i n  the v i c i n i t y  of a s p e c t r a l  l i n e .  
This technique, however, fa i l s  i n  the  vacuum u l t r a v i o l e t  because of 
t h e  absence of t ransmit t ing materials t o  use as beam s p l i t t e r s .  
Alternat ive devices can be considered; f o r  examplej a Lloyd's 
mirror type interferometer  is i n  pr inc ipa l  possible;  however,:the 
Mach Zehnder derives i t s  s e n s i t i v i t y  from t h e  use of high orders of 
https://ntrs.nasa.gov/search.jsp?R=19700028178 2020-03-11T22:54:04+00:00Z
in te r fe rence ,  a requirement which is  impract ical  f o r  Lloyd’s mirror  
arrangements. 
Another p o s s i b i l i t y  is  given by a new interferometer  which has 
no t ransmit t ing elements(6), but  does have t h e  advantage of mul t ip le  
beams. The present  paper descr ibes  an arrangement of t h i s  i n t e r f e ro -  
meter which has important p o s s i b i l i t i e s  f o r  use i n  the  measurement of 
atomic and molecular energy leve l  populations and o s c i l l a t o r  
s t rengths  i n  t h e  vacuum u l t r a v i o l e t .  
Interferometer Arrangement 
The G I M B I ( 6 )  u t i l i z e s  t h e  in te r fe rence  between a s e t  o f  mul t ip le  
beams t o  produce a s e t  of f r inges  i n  t h e  e x i t  plane of t h e  inter’fero- 
meter. The amplitude i n  t h e  e x i t  plane i s  (6) ~
+N 4 ,  I 
(p = bo l ( - l ) n  r inl  exp{idL2+(nt -a )2  } 
n=-N 
‘ and s ince  grazing incidence r e f l e c t i o n s  a r e  used, r -1 .  Furthermore, 
t h e  expansion 
. *  .) LJl+(-) n t - a  2 rr L ( 1  + +fy 1 nt- - jj-(--+ 1 n t - a  4 + L 
n t  
L can be l imited t o  two terms i f  - <<1. 
axis ,  i . e .  a = 0 ,  then t h e  f r i n g e  maxima occur whenever 
If we u t i l i z e  only modes on 
k t 2  - -  2L - mn (3) 
Consider a d i r ec t ion  perpendicular t o  t h e  ax i s ,  p a r a l l e l  t o  t h e  
interferometer  p l a t e s .  The e f f e c t  of moving t h e  observation poin t  
7 
J 
i n  t h i s  d i r ec t ion  is equivalent t o  t h e  subs t i t u t ion  o f  J- L2+Z2 f o r  L.(Fig. 1) 
Then we can s t a t e  t h e  more general resonance condition 
o r  
(4) 
Now, i f  t h e  interferometer  is posit ioned i n  f ron t  of a s t igmat ic  
spectrograph s o  t h a t  t h e  entrance sl i t  coincides with t h e  plane (a=O,Z) 
of t h e  interferometer ,  then t h e  e x i t  plane of t h e  spectrograph w i l l  
show a s e t  of banded f r inges ,  where t h e  f r i n g e  pos i t ions  a r e  so lu t ions  
t o  t h e  equation 
t 2  m =  
wi thminteger .  
Z=O and Fig.  2 shows a sketch of t h e  f r inges  i n  t h e  region around 
1000 2 f o r  an interferometer  of length 3 cm and p l a t e  separat ion 1 mm. 
The f r inge  sharpness is, of course, increased when t h e  number of beams 
contr ibut ing t o  t h e  in te r fe rence  pa t t e rn  i s  la rge .  However, t h e  f r inge  
pos i t ion  is  independent of t he  number of beams., Thus, i n  t h i s  region 
around 1000 8, t h e  order  number of i n t e r e s t  w i l l  be near 330 depending 
only on t ,  L and Z .  
These so lu t ions  a re  symmetrical with respect  t o  t h e  point  
Interferometer Parameters 
The usual quan t i t i e s  which descr ibe interferometer  performance 
can be ascer ta ined,  e.g.  t he  f r e e  spec t r a l  range ( the change i n  
wavelength equivalent t o  a change i n  order number of 1) is 
Ah t2 l = A m = - ~  
A0 j - F z  
and f o r  Z = 0 
AX; = - -L . 
t 2  
For t h e  spec i f i ca t ions  quoted above t h e  f r i n g e  separat ion is 
approximately 3W 
Another parameter, t h e  separat ion between f r inges  as a 
funct ion of d i s tance  from t h e  point  of symmetry can a l so  be described. 
Using 
L2+Z? = - t 4  
A2m2 
A(Z2) = - t 4  Am 
A 2m2 
Fringes i n  t h e  Neighborhood of a Spec t ra l  Line -- -
The 'above considerat ions have a l l  been f o r  a vacuum; i . e .  n, 
t he  index of r e f r ac t ion ,  is  taken t o  be equal t o  one. However, i n  
t h e  presence of a medium, t h e  index of r e f r a c t i o n  w i l l  not be one, 
* 
but w i l l  r a t h e r  haye contr ibut ions from e lec t rons ,  neut ra l  p a r t i c l e s  
. ,  
and a l s o  resonant f ea tu res  of t h e  spectrum. 
neighborhood of spec t r a l  l ines ,  t he  index of r e f r ac t ion  has t h e  
anomalous behavior , 
In  p a r t i c u l a r ,  i n  t h e  
(5) 
In t h i s  r e l a t i o n ,  e i s  t h e  charge of t he  e lec t ron ,  mec2 is  rest mass 
energy of t h e  e lec t ron ,  X o  is the  wavelength of  t h e  s p e c t r a l  l i n e  re- 
s u l t i n g  from t h e  t r a n s i t i o n  from a lower t o  an upper state,  $, i s  
t h e  o s c i l l a t o r  s t r eng th  of t h e  t r a n s i t i o n ,  N, i s  t h e  number of atoms 
i n  t h e  lower state and W is t h e  width of t he  spec t r a l  l i n e .  
portance of  t h i s  equation t o  us l ies  i n  t h e  dependence of t h e  r i g h t  
hand s i d e  of t h e  equation on t h e  parameters N, and d,. 
u t i l i z e  t h i s  r e l a t i o n  far away from t h e  spec t r a l  l i n e  where 
The i m - %  
We w i l l  
so  t h a t  an appropriate  form here is: 
and A i s  a parameter depending on number diensity a n d : o s c i l l a t o r  
s t rength  lying i n  the  range t o  1 cm. We w i l l  pick A , t o  be .1 l a t e r  
f o r  exhib i t ing  t h e  d i s t o r t i o n  of  f r inges  due t o  t h e  presence of a 
*a 
spec t r a l  l i n e .  This value is a b i t  high and the  f r inges  a r e  conse- 
quently a f fec ted  a t  very la rge  dis tances  !from t h e  spec t r a l  l i n e  but  
t he  in t en t ion  here  is simply t o  exhib i t  t he  p r inc ip l e .  Then using 
t h e  index of r e f r ac t ion  e x p l i c i t l y  one obtains 
6 
t 4  
2 A 2  
L2+Z2 = 
" 7  
o r  
and t h e  important measurable quant i ty ,  t h e  f r e e  s p e c t r a l  range can 
be found using 
1 (1 + - -  2 A-A. 
1 A  t 2  m =  
r n A  
and f o r  Am = 1 
(14) 
a t  wavelengths g r e a t e r  than 100 2 t h e  middle term i n  t h e  braces 
can be ignored. 
And, t h e  f r i n g e  spacing i n  t h e  neighborhood of a s p e c t r a l  l i n e  
is 
Al  = Ahl (1- 1 2 + A o )  2 
i . e .  t h e  e f f e c t  of t h e  index of re f rac t ion  is e s s e n t i a l l y  magnified 
by the  r a t i o  A / ( A - A o ) ,  a number normally on t h e  order of 1000. The 
f r a c t i o n a l  reduction of t h e  f r inge  spacing is  symmetrical on e i t h e r  
s i d e  of t h e  s p e c t r a l  i i n e  and can be expressed as 
Then,ca4measure of t h e  product of o s c i l l a t o r  s t r eng th  and popula- 
t i o n  densi ty  of t he  gas between t h e  interferometer  p l a t e s  is e f f ec t ed  
by measuring the"fract$onal change i n  t h e  f r i n g e  spacing. 
technique is  very a t t r a c t i v e  because A l ,  A x l ,  A and (A-Ao)  a r e  a l l  
quan t i t i e s  whose measurements should be possible  within a few per  
cent a 
This 
1 
% 
Another poss ib le  measurement is  provided by t h e  v e r t i c a l  d i s -  
tance between f r inges ;  then 
( 1 , .  1 , 1 4 1  1 8  ,~ i ,  I .  
with a l l  t h e  q u a n t i t i e s  measureable except f o r  A .  The usefulness of 
t h i s  approach is  l imited by t h e  he ight  o f  t h e  f r inges ,  and w i l l  i n  
general probably be l e s s  than t h e  method u t i l i z i n g  the  change 
i n  the  f r e e  s p e c t r a l  range. 
I . # I  I 
Speci f ic  Case. 
, l  t ,  I 
Figure 2 i l l u s t r a t e s  t h e  f r inges  i n  vacuum (lower p a r t  of t h e  
f igure)  and i n  t h e  presence of a s p e c t r a l  l i n e  (upper p a r t  o f  t h e  
f igu re ) .  Tie parameters used i n  t h i s  sketch are: 
1 1  
1 
L = 3 c m  
t = l m m  
A 0  = 1000 8 
A, = .1 
Then t h e  f igu re  p l o t s  Z vs.  A f o r  constant m where m is on t h e  order 
of 330. 
of t h e  f r i n g e  pos i t ions  and shapes as far away as 20 8 from t h e  
The value of A chosen is la rge  and r e s u l t s  i n  a d i s t o r t i o n  
8 
s p e c t r a l  l i n e .  Actual cases w i l l  reduce t h i s  e f f e c t  considerably. 
The m value of t h e  f r i n g e  is l i s t e d  next t o  the  f r i n g e  a t  the  t o p  
and bottom. 
23 i s  a c t u a l l y  323. 
Note t h a t  300 must be added t o  t h e  number given, . i .e .  
1 ,  
Note t h a t  . , , , I  f o r , c l a r i t y  , , /  only a representat ive sample of f r inges  
a r e  sketched. However, the anomalous behavior of t h e  f r inges  near  
t h e  spect-fal l ine , i ,q  clear1.y c , . .  . evident; a l s o  the,sypmetric,cluqtering 
of t h e  8 f r ingesjaround I /  I ,  , i l l : \  the, s p e c t r a l  l i n e  is  portrayed. 
I " ' , . , ,  
Summary 
I 
We have deicr ibed t h e , u s e  of an interferometer  t o  measure the  
product of o s c i l l a t o r  s t rength  and number densi ty  of absorbers. 
technique should have unique appl icat ions i n  t h e  vacuum UV. 
This 
/ I  I 
< I L  
Acknowledgments 
This work''w& supported i n  par t  by two National Aeronautics 
\ and Space 'A&inistration Grants NGL-37-003-026 and NGR 37-003-047. 
REFERENCES 
1. W. L .  Wiese, M. W. Smith and B .  M .  Glennon i n  NSRDS-NBS4 (1966). 
2 .  R. Lincke and H. R. Griem, Phys, Rev. 143, 66 (1966). 
3. 
-
A review 02 These techniques can be found i n  IISpectroscopy i n  
the Vacum Ultraviolet"  by W.R.S. Garton i n  Advances i n  Atomic 
and Molecular Thysics, Vol. 2 ,  Ed. D .  R .  Bates and I.  Estermann, 
Academic Press I966 e 
4. W .  C .  Marlow, A ~ p 1 .  Optics 6 ,  1715 (1967). 
5. E.  W. Foster,  'la?le Measurement of Osc i l la tor  Strengths i n  Atomic 
Spectra", Pre ts  . Prog. i n  Phys . X X V I I ,  469 (1964) ,, 
6. R. A. Day, Appl. Optics 9 ,  31 (1970). - 
FIGURE CAPTIONS 
Figure 1. This shows t h e  interferometer  i l luminated through a 
pinhole by l i g h t  having a continuous spectrum. The 
f r inges  appear along t h e  Z d i rec t ion  a t  t h e  e x i t  
plane of The interferometer.  
Figure 2 .  Sketch of the  f r inges  as they would appear i n  the  
e x i t  plane of a s t igmat ic  spectrograph. The lower 
p a r t  of  t h e  f igure  shows t h e  f r inges  as they would 
occur i n  t h e  absence of a s p e c t r a l  l i n e .  The f r inges  
i n  t h e  upper p a r t  of t h e  f igure  a re  d i s t o r t e d  by t h e  
presence of  a s p e c t r a l  l ine .  See t e x t .  




A new technique for measuring oscillator strengths in the UV

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