Time dependence of filtered resonance radiation of57Fe

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INSTRUMENTS

AND

METHODS

I34

(I976) 317-318;

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NORTH-HOLLAND

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CO.

T I M E D E P E N D E N C E OF FILTERED RESONANCE RADIATION OF STFe NOBUYUKI

HAYASHI*, TAMIYOSHI

K I N O S H I T A , ISAO S A K A M O T O

and BUNJI FURUBAYASHI

Electrotechnical Laboratory, Tanashi, Tokyo, Japan Received 7 J a n u a r y 1976 T h e time dependence o f resonantly filtered 14.4 keV S7Fe ),-rays was m e a s u r e d by m e a n s o f delayed-coincidence techniques• Excellent a g r e e m e n t between theoretical a n d experimental decay curves has been obtained• T h e agreement indicates a possibility o f m e a s u r i n g the recoilless fraction o f 14.4 keV 7-rays emitted f r o m the source•

The technique of coincidence M6ssbauer spectroscopy (CMS) has recently been applied to the studies of solid-state physics1'2). The fundamental work was done by Lynch et al. in 19603), where the line shapes of y-rays transmitted through a M6ssbauer absorber were measured, using y-ray coincidence techniques• In the case of 57Fe, the second excited state which is formed by electron capture decay of 57Co emits 122 keV y-rays to the 14.4 keV M6ssbauer level. Thus, the detection of the 122 keV radiation serves as the signal of the formation of the 14.4 keV excited states• Since some 14.4 keV y-rays are not recorded, "time filtering" effects result in line shapes that are nonLorentzian and non-exponential decay curves• Although a fit of theory and experiment in time filtering effects is very important for the application of

CMS to solid-state problems, the quantitative agreement has not fully been accomplished• Hamill et al. +) have noted that in the CMS velocity spectrum a good fit of the data was obtained by a numerical integration of the exact expression over the experimental time window. However, it is extremely useful if the transmitted y-ray intensity be measured explicitly as a function of time. The results of such a measurement are described in this communication• The equations for the transmitted intensity l(v, T, fl) through a resonant filter, or absorber, can be written in two forms depending on the time region of interest3). The form

* Present address: D e p a r t m e n t o f Physics, T h e J o h n s H o p k i n s University, Baltimore, M a r y l a n d 21218, U.S.A.

gives rapid convergence for

I ( v ' T' fl) = e - r , =~o( 4 i v ~" ( fl T ~+" J" (x/ fl T ) 2

(1)

fl] \ 4 ]

2 v (fl T)+/fl < 1 ; while

l(v,T, f l ) = e - r I - e x p { i ( v T + B c ) } +

,°+I

v=o 0.43 mg/cm 2

,'.~

+f+! o

[ 1

l

l

+ 2

I

i 3

I 4

Fig. 1. T i m e spectra obtained with energy shifts o f v = 0. T h e absorber was a stainless steel foil (0.43 m g / c m 2 o f 57Fe, natural isotopic abundance)• t is the time a n d r is the m e a n life o f the excited state•

is appropriate for 2 v (fl T)½/fl > 1. Here T is time in nuclear meanlife (z) units, v is the frequency difference between the emission and absorption lines in units of natural linewidth, J.'s are integral Bessel functions, and fl=naofis the absorber thickness ( n = n u m b e r of 57Fe atoms/cm 2, a t = c r o s s section at resonance, f = the recoilless fraction of absorption)• Previous efforts to fit experimental data have led the authors to a certain difficulty; Lynch et al. 3) had to assume that fl is twice the value as that actually used in the experiments• Neuwirth 5) postulated an inhomogeneous absorber and hence a special distribution of

318

NOBUYUKI

v=O 1,0 mg/cm z 10: t~ Is k) 10 ~

10 0

2

3

t/'r

4

Fig. 2. Time spectra obtained with energy shifts of v = 0. The absorber was a stainless steel foil (1.0 mg/cm 2 o f S7Fe in an enriched foil), t is the time and r is the mean life of the excited state.

103

•

v=2r

~\~

1,0 mg/cm 2

tO

0 U

102

":': .e.. L

10 i

I

I

,

I

I

1

2 t/'r

3

4

Fig. 3. Time spectra obtained with energy shifts of v = 2F, where v is given in terms of the natural linewidth. The absorber was a stainless steel foil (1.0 mg/cm 2 of STFe). t is the time and r is the mean life of the excited state.

57Fe in the absorber. However, the results were not fully satisfactory. The experimental system was a standard slow-fast arrangement with a M6ssbauer instrument in addition. To detect 14.4 keV 7-rays RCA 8850 was used as a photomultiplier and the detector consisted of a I, 2lrr diam. and 0.08" thick NaI(T1) crystal. The measurements were made with a source of 57Co imbedded in a cupreous foil (,~ 1/~Ci). The source was mounted on a velocity drive which could be used to shift the resonant frequency of the source by the Doppler effect. The source was moved at constant velocity. Thin foils of 310 stainless steel were used as absorbers, the isomer shift of which was - 0 . 3 9 mm/s. The instrumental time resolution was obtained by a direct measurement of the

H A Y A S H I et al.

14-122 keV X-ray-7-ray prompt coincidence from SSy source. The observed full width at half-maximum was 5.5 ns. Some examples of the results are shown in figs. 1-3. In these figures the decay curves of 14.4 keV states were measured with the change of some experimental parameters (v and fl). For comparison, broken lines are shown in these figures, which represent exponential decay curves obtained by the measurements without absorbers. The solid curves were calculated from eq. (1) and (2). In the calculations a value of 0.68 was used as the recoilless fraction of the source6). In these figures of the time spectra the data are shown after random coincidences were subtracted. The ratio of random to real coincidences at the maximum of the time spectra was about 2%. The quantitative agreement between theory and experiments is satisfactory as shown in these figures. It is supposed that this agreement has been achieved because of the improvement of the instrumental time resolution in the present work. The value of fl was calculated from the known thickness of the absorber. The dotted curve shown in fig. 1 was calculated with a value of 0.75 as the recoilless fraction that was adopted by Lynch et al.3). The comparison of the solid curve with the dotted one indicates that the calculated curve is sensitive to the value of the recoilless fraction in the source and that the value could be measured by fitting the calculated curve to experimental data. The published value of the recoilless fraction of 57Fe in Cu ranges from 0.684 6) to 0.727 7). Our results indicate that the lower value of the recoilless fraction is pertinent to the case of 5VCo in Cu source. This method is rather simple in principle and, moreover, there is a possibility that the time-dependent recoilles fraction 2m) could be measured. With experimental systems of improved time resolution, it is expected that a more exact value of the recoilless fraction can be obtained when more data are accumulated and the statistical errors are reduced.

References 1) W. Triftsh~iuser and P. P. Craig, Phys. Rev. 162 (1967) 274. 2) A. Szczepanski, Sol. Stat. C o m m . 10 (1972) 447• 3) F . J . Lynch, R. E. Holland and M. Hamermesh, Phys. Rev. 120 (1960) 513. ~) D. W. Hamill and G. R. Hoy, Phys. Rev. Lett. 21 (1968) 724. s) W. Neuwirth, Z. Physik 197 (1966) 473. 6) j. A. Moyzis Jr., G. DePasquall and H. G. Drikamer, Phys. Rev. 172 (1968) 665. v) W. A. Stuyert and R. D. Taylor, Phys. Rev. 134 (1964) A716. s) G. R. Hoy and P. P. Wintersteiner, Phys. Rev. Lett. 28 (1972) 877.