THE SPECTRUM OF THE MÖSSBAUER RADIATION PASSED THROUGH A VIBRATING RESONANT MEDIUM

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THE SPECTRUM OF THE MÖSSBAUER

RADIATION PASSED THROUGH A VIBRATING RESONANT MEDIUM

L. Tsankov, Ts. Bonchev

To cite this version:

L. Tsankov, Ts. Bonchev. THE SPECTRUM OF THE MÖSSBAUER RADIATION PASSED THROUGH A VIBRATING RESONANT MEDIUM. Journal de Physique Colloques, 1980, 41 (C1), pp.C1-475-C1-476. �10.1051/jphyscol:19801187�. �jpa-00219676�

JOURNAL DE PHYSIQUE Colloque Cl , supplr'ment au n ^O 1 , Tome 41, janvier 1980, page C1-475

THE SPECTRUM OF M E N~SSBAUEP, RADIATION PASSED TH-ROUGH A VIBRATING RESONANT MEL)IUN

L. Tsankov and Ts. Bonchev

S o f i a U n i v e r s i t y , Department o f Atomic Physics, 1126-Sofia, Bulgaria.

It i s well known t h a t t h e u l t r a s o n i c v i b r a t i o n s applied t o e i t h e r t h e source

o r t h e absorber i n Hijssbauer experiments, influence t h e spectrum of t h e r a d i a t i o n passed, r e s u l t i n g i n a s p l i t t i n g of t h e o r i g i n a l l i a e i n t o an i n f i n i t e s e r i e s of sidebands, spaced e q u i d i s t a n t l y a t multi- p l e s o f 3

,

t h e frequency of t h e e x t e r n a l p e r t u r b a t i o n [I]

.

This phenomenon can b e described adequately e i t h e r from a wave p o i n t of view, i n terms of a frequency modulation of t h e photon wave, o r i n a corpuscular one

-

i n terms of c r e a t i o n and annihilation of phonons, which i n t e r - a c t with t h e gamma-radiation f i e l d .

More complex i s t h e case, when t h e source i s a t r e s t , t h e r a d i a t i o n is pass- ed through a resonant absorber, v i b r a t i n g a t u l t r a s o n i c frequency, and a second ab- sorber s e r v e s f o r analyzing t h e t r a n s m i t t ed r a d i a t i o n . I n t h i s case 'the v i b r a t i n g changes i t s absorption with a period com- parable with t h e l i f e t i m e of t h e excited MSssbauer s t a t e , and it must change app- r e c i a b l y t h e s p e c t r a l d i s t r i b u t i o n of t h e emerging r a d i a t i o n . The experiments of Asher e t a1 [23 shows a similar s p l i t t i n g

of t h e spectrum i n t h i s case. These auth- o r s e q l a i n t h e r e s u l t s using t h e o p t i c a l theorem applied t o t h e forward-scattered

component of t h e r a d i a t i o n . However, t h e i r approach y i e l d s an i n f i n i t e s e t of coupled d i f f e r e n t i a l equations f o r t h e p a r t i a l am- p l i t u d e s , which can be solved i n a few spe- c i a l cases, when t h e modulating absorber i s t h i n , i n p a r t i c u l a r . A t t h e same time, it i s obvious t h a t t h e expected e f f e c t must be i n c r e a s i n g with t h e modulator thickness.

To avoid t h i s d i f f i c u l t y , one may use t h e theory, developed by Hamemesh [3] and H a r r i s [4] f o r t h e transmission of t h e Ni5ss- bauer r a d i a t i o n through a s t a t i o n a r y reso- nant medium. Thus, we aesume a modulator containing resonant n u c l e i , v i b r a t i n g a t t h e same frequency, amplitude and phase.

Then, i n t h e modulator frame, t h e time de- pendence of t h e source r a d i a t i o n is:

Here x = x . ' ~ s the walenumber of t h e photon, A

-

t h e v i b r a t i n g amplitude, and

y

describ- t h e p t a s e of c r y s t a l v i b r a t i o n s a t t-0.

The Fourier tranaform of /I/ is:

Now, t h e spectrum of t h e emerging ra- d i a t i o n i s changed due t o t h e d i s p e r s i v e p r o p e r t i e s of t h e medium 1'31 :

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19801187

C1-476 JOURNAL DE PHYSIQUE

/3/

Here D denotes the effective modulator thickness, and

-

its resonant energy.

The corresponding amplitude in the ti- me domain is:

e

q l l t ) - ~ 74(X9) e . k l ~ i w ' t - ' t 2 ^k

or, alzernatively:

z D f 7 4

oiit)

. ²

^J,[XAI e ' k a ' ? [ e ' ' d ~ t k " ) t - ~ t e ^Q, -";+*n

-

k r - s

The choice between /4/ and /4'/ is de- termined by convergence requirements for the sum over n.

Returning to the lab frame, we have:

multiples of Xi

.

If d,-w,'=ll/i.e. no isomer shift between the source and the absorber/, the spectrum is symmetric with respect to

do

.

If the modulator is at rest /~An0/, /6/ represents the self-absorption of the radiation in a thick stationary absorber, and if ~ 4 % spectrum is reduced to a natu- ral width single Lorentaian, centered at d,.

Therefore, a region in amplitudes of the modulator vibration exsists, wherein the

expected splitting effect is maximal, Nume- rical calculations indicate that this regi- on is at ;xArI.

Figure I represents the calculated spectrum for several amplitudes A /D+, u,-u,' =0, .R -10

r

^/2.

/.

Now, we need the Fourier transform of

/ 5 / . The correspondimg integrals can be ca-

rried out. and the result is:

j ~ ~ . - i * ' ~ ' t k R i # o , Finally, the spectrum of interest is obtained by squaring /6/ and averaging over the initial phase

7 .

The last operation only selects the non-vanishing terns in the sums.

It is seen from /6/ that the spectrum consists a set of equidistant satelites, shifted in energy from the central line by

References:

CI].

Ruby,S.L. ,Bolef ,Do ,Phys.Rev.Lett

2/1960/5.

123. Asher, J. et al, J.Phys.A 2/1974/ 410.

[ 3 ] ,

Lynch,P.et al, Phys.Rev. =/1960/ 513.

I43 .

^{Harris ,S}

. ^,

^{Phys .Rev. E/I960/ 1178.}