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Submitted on 1 Jan 1979
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DICHROISM OF POLARIZED MÖSSBAUER RAYS
D. Barb, M. Rogalski
To cite this version:
D. Barb, M. Rogalski. DICHROISM OF POLARIZED MÖSSBAUER RAYS. Journal de Physique
Colloques, 1979, 40 (C2), pp.C2-11-C2-13. �10.1051/jphyscol:1979202�. �jpa-00218460�
JOURNAL DE PHYSIQUE
Collogue C2, supplement au n° 3, Tome 40, mars 1979, page C2-11
DICHROISM OF POLARIZED MOSSBAUER RAYS
D. Barb and M. Rogalski
National Center for Physics^ P.O.B. 520?, Bucharest, Romania
Résumé.- On obtient, dans le formalisme de l'opérateur densité, une expression du dichroisme du rayon- nement Mossbauer polarisé dans un absorbeur épais. On met en évidence l'influence réciproque entre le dichroisme et les effets dispersifs, en bon accord avec les résultats expérimentaux existants f\f.
Abstract.- We derive, in the density matrix formalism, an expression of the polarized Mossbauer rays dichroism in a finite thickness absorber. The reciprocal influence between the dichroism and the dis- persive effects is evidenced, in good agreement with the existing experimental results HI.
The present investigation, was prompted by the fact that the dispersive effects of the polarized Mossbauer rays, measured in finite thickness absor- bers l \ l , 111, was theoretically explained /3/ taking into consideration crystals having negligible dich- roism (i.e. absorption is isotropic). Because an unisotropic absorption was found in the studied ab-
sorbers HI, it is desired a closer examination of this effect.
We propose ourself to obtain an expression for the dichroism associated with the dispersive effects, assuming an arbitrary polarization state I , C . <t>
of the incident Mossbauer ray, done by a density matrix p 13/, and an absorber described by the matrix n of his refractive index / 4 / , in a typical polari- metric experiment (Fig. 1) :
f i i
piA
pi i ]
n,, n,. a N. f.
n = = 1 - 777- > . . . . * (1) n,, n,_ 2k L nii nii , . . .
2 1 22 ii 2* 2 2 (x-xij) + x
where x = 2E/T is connected with the ray energy, and x.. and the pj: matrices correspond to the energies and the polarization patterns of the Mossbauer nu- cleus absorption lines. Using the notation :
L exp(iYn) L1 2 exp(iyJ2)
L= exp(inkz) = (2) L2 I exp(iy21) L2 2 exp(iy22)
we obtain the following expression for the dichroism,
*
defined as the difference of the emergent intensities of two orthogonally polarized beams :
D = IoP { s i n 2 ?Q (L2, - L2 2 ) - (3) - 2L1 2 cos 2 CO[ ; LI 1 cos (2a n u " Y1 2) +
+ \ 2 cos (2a + T1 2- Y22)3> exp{-Im(nn+n22)}
Now we proceed to analyse the dichroism varia- tion as a function of the polarization plane direc-
tion a and the wave vector direction 6, making ob- vious the reciprocal influence between the dichroism and the dispersive effects.
Fig. 1 : Schematic representation of the experiment:
S - polarized source, M - transmitter, A - analyser, D - detector.
1.- We first consider the a-dependence of the linear dichroism, which has a simple expression obtained from (3) taking £ = 0 . The connection between the dichroism and the birefringence is illustrated in the case of an iron foil absorber (z = 9.4mg/cm2), 92.8% enriched in 57Fe /l/, in an external magnetic field. In figure 2 is represented the a-dependence of the linear dichroism, for the right half of the Mossbauer spectrum. We have the same dichroism for the 10 MHz and 62 MHz lines, which prove that the absorption is saturated, due to the large thickness of the sample. If the incident ray has an energy corresponding to the absorption lines, a significant a-dependence of the dichroism, which influence the birefringence values is observed in figure 2a. Con- sequently, in the birefringence experiments are used energies corresponding to a negligible dichroism (as an example we considered E = 17.5 MHz III).
The connection between the linear dichroism and the Faraday rotation can be putted in evidence for the experiments using an iron foil absorber (z = 1.94 mg/cm2), 91.2% enriched in 5 7Fe, making an angle 8= 25° with the wave vector k /!/.
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979202
JOURNAL DE PHYSIQUE
LO1 (bl
F i g . 2 : L i n e a r d i c h r o i s m and b i r e f r i n g e n c e (0=90°):
a ) l i n e a r d i c h r o i s m f o r t h e r i g h t h a l f of t h e spec- trum; b ) a-dependence o f t h e l i n e a r d i c h r o i s m f o r d i f f e r e n t e n e r g i e s of t h e i n c i d e n t beam; 0
-
e x p e r i - m e n t a l p o i n t s / I / .Although t h e 10 MHz, 36 MHz and 62 MHz spectrum li- n e s have t h e same i n t e n s i t i e s ( i . e . t h e a b s o r p t i o n i s s a t u r a t e d ) , we o b t a i n a n e g l i g i b l e l i n e a r d i c h - r o i s m f o r t h e 10 MHz and 6 2 MHz l i n e s ( F i g . 3 ) .
Fig. 3 : L i n e a r d i c h r o i s m and F a r a d a y r o t a t i o n (0=25') : a ) l i n e a r d i c h r o i s m f o r t h e r i g h t h a l f o f t h e s p e c t r u m ; b ) t h e Malus c u r v e : 0-experimental p o i n t s .
T h i s c a n b e e x p l a i n e d by t h e a b s o r p t i o n l i n e p o l a r i - z a t i o n p a t t e r n s , which a r e n e a r l y c i r c u l a r , f o r t h e - s e two l i n e s . The d i c h r o i s m o f t h e 36 MHz l i n e d i - s a p p e a r s when a = 31.4', which c o r r e s p o n d s t o a Faraday r o t a t i o n F = 13.6', i n good agreement w i t h / I / .
As i t i s e x p e c t e d , t h e c i r c u l a r d i c h r o i s m , done by ( 3 ) f o r
E0
= w / 4 i s a-independent.2.- The 0-dependence of t h e a b s o r p t i o n was s t u d i e d f o r t h e c i r c u l a r l y and l i n e a r l y p o l a r i z e d beams. Re- p r e s e n t i n g t h i s dependence i n t h e c a s e of a c i r c u - l a r l y p o l a r i z e d r a y a b s o r p t i o n (Fig. 4) a s a t u r a t i o n e f f e c t can b e o b s e r v e d : t h e 10 MHz r i g h t c i r c u l a r l y p o l a r i z e d beam i s s t i l l c o m p l e t e l y a b s o r b e d by a n e l l i p t i c a l y p o l a r i z e d l i n e (9 = 3 0 ° ) , i n t h e i r o n f o i l ( z = 1.94 mg/cm2) p r e v i o u s l y c o n s i d e r e d .
F i g . 4 : The 9-dependence o f t h e 10 MHz r i g h t c i r c u - l a r l y p o l a r i z e d r a y i n t e n s i t y .
The 8-dependence s t u d y o f t h e a b s o r p t i o n e v i - denced t h e i n f l u e n c e of t h e d i s p e r s i o n on t h e l i n e a r d i c h r o i s m . I n f i g u r e 5 a r e r e p r e s e n t e d t h e I,, and IL i n t e n s i t i e s of t h e 36 MHz r a y s , l i n e a r l y p o l a r i z e d p a r a l l e l and p e r p e n d i c u l a r t o t h e m a g n e t i c f i e l d d i - r e c t i o n i n t h e a b s o r b e r .
F i g . 5 : The 9-dependence o f t h e 36 MHz l i n e a r l y p o l a r i z e d r a y i n t e n ~ i t i e s : 1,-
-
p e r p e n d i c u l a r t o the,magnetic f i e l d H i n t h e a b s o r b e r ; I l l-
p a r a l l e l t o H. S o l i d l i n e : t h i c k a b s o r b e r , d o t t e d l i n e : t h i n a b s o r b e r .Because t h e 36 MHz a b s o r p t i o n l i n e i s p e r p e n d i c u l a r l i n e a r l y p o l a r i z e d , f o r any 9 , we e x p e c t a c o n s t a n t I , ,
.
But a s i g n i f i c a n t a b s o r p t i o n , f o r s m a l l 9 , was o b t a i n e d . T h i s c a n b e e x p l a i n e d o b s e r v i n g t h a t t h ep a r a l l e l l i n e a r l y p o l a r i z e d ray a c q u i r e s , f o r t h i s References range of a n g l e s , an e x c e n t r i c i t y
5
f 0 and a Faraday/ I / Imbert, P . , ThSse (19651, Rapport CEA-R 2925 r o t a t i o n o f 30
-
60°, which makes p o s s i b l e t h e ab- ( 1966).s o r p t i o n . For t h i n absorbers, t h i s e f f e c t disappears. / 2 / Housley, R.M., Gonser, U . , Phys. Rev.
fi
(1968) 480./ 3 / Barb, D., Rogalski, M . , 3 . Physique
