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Influence of the hyperfine structure on the time-dependence of Mössbauer transmission

D.L. Balabanski, E.I. Vapirev, P.S. Kamenov

To cite this version:

D.L. Balabanski, E.I. Vapirev, P.S. Kamenov. Influence of the hyperfine structure on the time-dependence of Mössbauer transmission. Journal de Physique, 1985, 46 (8), pp.1387-1393.

�10.1051/jphys:019850046080138700�. �jpa-00210082�

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Influence of the hyperfine structure on the time-dependence

of Mössbauer transmission

D. L. Balabanski, E. I. Vapirev and P. S. Kamenov

Sofia University « Clement Okhridsky », Faculty of Physics, 1126 Sofia, Bulgaria (Reçu le 23 juillet 1984, révisé le 4 février 1985, accepté le 18 avril 1985)

Résumé. 2014 La distribution en temps de la radiation Mössbauer traversant un absorbeur avec une structure

hyperfine est étudiée théoriquement et expérimentalement. Les expérienees sont réalisées avec une source de

(Ba119mSnO3 (raie singulet) et un absorbeur SnO2 (doublet quadrupolaire). Les résultats obtenus sont en assez bon accord quantitatif avec la théorie proposée.

Abstract.

2014

The problem of the influence of the hyperfine structure on the time-dependence of resonant gamma- transmission is investigated both theoretically and experimentally in the present work. The experiments are carried

out with a source Ba119mSnO3 and an absorber SnO2 with a line split by the quadrupole interaction. A theoretical model is derived in the framework of the classical dispersion theory and it appears to be in reasonable agreement with experiment.

Classification Physics Abstracts

76.80

1. Introduction.

Following the classical experiment of Lynch et al. [1],

a series of investigations on the time-dependence of gamma-resonant interactions was carried out by

different groups under different experimental condi-

tions [2-8]. The results were interpreted with the help

of classical dispersion theory [1, 2] or of the quantum

theory of radiation [9] and the calculations are in a

good agreement with the experiment.

All these investigations are related to the simplest possible case

-

source and absorber with single lines

with energies COo and coo’

-

but the first experiment

was carried out with a source and absorber of 57 Fe having a hyperfine structure of six lines. The results

were interpreted with the assumption that each com- ponent of the hyperfine structure is absorbed by the corresponding transition in the absorber, because the distance between the components is great in compa- rison with the natural linewidth-y. Of course, the question exists

-

what is the influence of the hyper-

fine structure on the time-dependence of gamma- resonant transmission ?

In the present work a classical model is applied to

the time-dependence of Mossbauer transmission

through a resonant absorber with a hyperfine structure

and calculations are made for the case of two compo- nents. The results are compared with measurements with Sno2, a compound which is very suitable for this

purpose, because its two lines are near to one another.

This allows the influence of the hyperfine structure on

the time-dependence to be observed. It is also shown that Mitin and Polyakov [10] have used rather crude

approximations to evaluate this influence and their model cannot be applied to all cases. In our calcula- tions, interference terms appear in the formula for the transmission intensity. The conditions are investigated

when those terms vanish, i.e. the approximations of

reference [10] are correct. The results are compared

with a model in which the interference is neglected as

done by Lynch et al. [1]. The discrepancy of those

calculations with the experiment is shown. Thus the influence of the hyperfine structure on the time- dependence of gamma-resonant transmission is demonstrated.

2. Theory.

The resonant properties of the absorbing medium,

which is considered as consisting of random damped

harmonic oscillators with natural frequencies coi, i = 1, 2,... and damping factor y, are described with the

complex index of refraction n(w) [11].

r is a constant depending on the bulk density of

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019850046080138700

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1388

resonant nuclei and p;, i = 1, 2,

...

are the weight

factors corresponding to the resonant frequencies

The incident radiation is represented

as a damped electric wave with frequency coo.

Using the Fourier transform it is decomposed into

monochromatic components with frequency distri-

bution A(co, 0).

Each of the components is altered by a frequency dependent phase change when passing a distance x in

-

the absorber. The frequency distribution of the reso-

nant transmission is :

The amplitude of the transmitted radiation is obtained

by the inverse Fourier transform of this frequency

distribution.

here c is the light velocity in vacuum.

The intensity of Mossbauer transmission is given by the square of the magnitude of this amplitude.

In the case of a double-resonance absorbing medium

with frequencies cvl and W2’ a(t, x) is expressed as

follows :

This integral is solved in the Appendix and the result is :

here (T, fl) is, to within an exponential factor, the amplitude calculated by Lynch et ale [1] for the case of one

resonance with frequency in the absorber.

/,(T, jS) is an interference term in which the influence of the other resonance with frequency coj,, roj’ =F coj, is taken into account.

Jm(x) is the first order Bessel function of rank m and argument x and r (k) is the Gamma-function of argument k.

In these formulae the substitutions

are used, fl is the effective thickness of the absorber,

T is the time in units of mean life time, aj the shifts

of the lines in units of y and Q = ! I A j is the quadrupole splitting of the line.

Mitin and Polyakov [10] propose solving the integral

in equation (1) using the approximation that each of its singularities is infinitely distant from the others, which

leads to the disappearance of the interference terms in

equation (2). Of course, this approximation is correct

under certain conditions, but not for all cases. If we

consider the interference term (Eq. (4)), we see that

it can be neglected when :

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and it appears that the condition of equation (5a) is a

stronger one, i.e. for the case of close frequencies their

mutual influence should be taken into account.

On figure 1 and figure 2 the time-dependence of

ossbauer transmission for thick and thin absorber

with a two line hyperfine structure is shown for different

Doppler shifts of the centre of the two lines Ago and for different splittings of the lines Q, Q = ! I A j 1, Arm and Q

are measured in units y and are expressed as follows :

The time-dependence when the interference terms are neglected is shown by the dotted curve. In the case

when this line is not drawn the time-dependences

calculated in both ways coincide. The results illustrate the correctness of the conditions of equations (5).

Fig. 1.

-

Time-dependence of gamma-resonant trans- mission through a thick absorber with a two-line hyperfine

structure for different splittings Q and different shifts of the centre of the two lines Am.

-

calculations taking account

of the interference terms;

---

calculations in which the inter- ference terms are neglected. The results are multiplied by exp(T).

Fig. 2.

-

Time-dependence for thin absorber for different splittings Q and different shifts Am of the centre of the two lines.

-

calculations taking account of the interference terms;

---

calculations in which the interference terms are

neglected. The results are multiplied by exp(T).

3. Experiment, results and discussion.

The experiments were carried out using the fast

coincidence scheme described in our previous paper [3].

We used a source Ba"’mSno3 and absorber Sno2

with natural abundance of 119Sn. Sno2 has a line with quadrupole splitting accepted to be Q = 1.44. (See

Ref [12] and the papers cited therein).

The start signal of the coincidence scheme is given by

the 25.3 keV X-ray transition feeding the 23.9 keV

metastable level. The 23.9 keV M6ssbauer transition

gives the stop signal. The time resolution for these

energies is not worse than 2.5 ns. Two spectra were recorded with periodic commutation, Isw for the velocity shift Am of the centre of the two lines, and 1

for Doppler velocity v --+ oo. The measurement was

organized in such a way that the measuring times for lAw and I. were equal. A blocking signal was applied

to the multichannel analyser during the back run of the

constant velocity drive, so only events with the neces-

sary velocity shift were registered.

The ratio of the two spectra was calculated after

subtraction of the prompt peak and the random

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1390

Fig. 3.

2013

Experimental results for a thick absorber of Sn02 compared with different theoretical models : calcula- tions with the model developed in this paper;

---

model in which the interference terms are neglected;

- - -

model in

which the influence of the hyperfine structure is neglected totally.

coincidences. This procedure allows any possible non-

linearities of the instrument to be avoided.

On figure 3 and figure 4 the experimental results for

thick and thin absorbers for different shifts Aco are

shown. The results are in agreement with the model from the previous section. The calculations done with this model are shown by solid lines. Dotted lines show the calculations when the interference terms are

neglected. In these calculations the non-resonant part of the radiation is also taken into account. The experi-

mental results for the thick absorber are compared also

with a model assuming the independence of the

resonances

-

i.e. the transmission intensities due to

different frequencies are summed, as done by Lynch

et al. [1].

Fig. 4.

-

Experimental results for a thin absorber of Sn02 compared with the theory developed in this paper.

here f is the Debye-Waller factor. This interpretation corresponds to a model in which the influence of the

hyperfine structure is totally neglected. The experi-

mental results differ from the theoretical calculations in this case, especially for the shorter times where the statistics are better.

Finally, it can be said that the simple classical model

developed in the previous section reasonably describes

the experimental results.

Acknowledgments.

We wish to thank Mrs. Ekaterina Borisova for technical assistance.

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Appendix.

The integral of equation (1)

is solved by contour integration in the upper part of the complex plane. After the expansion of n(ro) up to the first term and using the standard approximation w + (oi = 2 co, as is usually done, for this integral we write :

It has three singularities in the points and z the last two being of

infinite rank. The first integral is solved with the substitution z = OJ - z, :

The integration of the remaining two integrals is carried out by extension of the integrand in powers of z after

making the substitution z = OJ - z, or z = OJ - z2 and evaluating the coefficients of the z- I power. The extension is done using the formulas [13, 14] :

For the integrand then we can write :

The first term in the expansion of the exponent in equation (A. 6) leads to an expression for the coefficient in front of the z-’ power analogous to that calculated by Lynch et al. [1]

and the other terms :

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1392

So for the integral we find :

Using the substitutions and T = yt we write :

With the help of equation (A. 5) we find a better convergency of the series in equation (A .11) in the case when

and finally we write

where gj(T, fl) is :

and /,(T, P) is :

Combining equation (A. 3) with equation (A 12) for the integral of equation (A .1) we find :

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References

[1] LYNCH, F. J., HOLLAND, R. E., HAMMERMESH, M., Phys. Rev. 120 (1960) 513.

[2] THIEBERGER, P., MORAGUES, J. A., SUNYAR, A. W., Phys. Rev. 171 (1968) 425.

[3] VAPIREV, E. I., KAMENOV, P. S., BALABANSKI, D. L., ORMANDJIEV, S. I., YANAKIEV, K., J. Physique 44 (1983) 675.

[4] HAYASHI, N., KINOSHITA, T., SAKAMOTO, I., FURU- BAYASHI, Nucl. Instrum. Methods 134 (1976) 317.

[5] DROST, H., PALOV, K., WAYER, G., J. Physique Colloq.

35 (1974) C6-679.

[6] VAPIREV, E. I., KAMENOV, P. S., DIMITROV, V., BALA- BANSKI, D. L., Nucl. Instrum. Methods 219 (1984)

376.

[7] WU, C. S., LEE, Y. K., BENCZER-KOLLER, N., SIMMS, P., Phys. Rev. Lett. 5 (1960) 432.

[8] KAMENOV, P. S., VAPIREV, E. I., BABALIEVSKI, F., Bulg.

J. Phys. 7 (1980) 251.

[9] HARRIS, S. M., Phys. Rev. 124 (1961) 1179.

[10] MITIN, A. V., POLYAKOV, N. V., Fiz. Tverd. Tela

(USSR) 25 (1983) 2180; Frause. sov. Phys. Solid

State 25 (1984) 1254.

[11] LONDON, R., The Quantum Theory of Light (Clarendon Press, Oxford) 1973.

[12] HEMBREE, G., PRICE, D. C., Nucl. Instrum. Methods 108 (1973) 99.

[13] ABRAMOWITZ, M., STEGUN, I. A., Handbook of Mathe-

matical Functions (NBS, Washington DC) 1964.

[14] PRUDNIKOV, A. P., BR’ICHKOV, Yu. Ya., MARICHEV,

O. I., Integrali i ryadi, elementarnie functsii

(Moskva, Nauka) 1981.

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