QUANTUM BEATS OF RECOIL-FREE γ-RADIATION

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QUANTUM BEATS OF RECOIL-FREE γ -RADIATION

G. Perlow, J. Monahan, W. Potzel

To cite this version:

G. Perlow, J. Monahan, W. Potzel. QUANTUM BEATS OF RECOIL-FREE γ-RADIATION. Journal

de Physique Colloques, 1980, 41 (C1), pp.C1-85-C1-93. �10.1051/jphyscol:1980115�. �jpa-00219635�

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JOURNAL DE PHYSIQUE

Colloque C l , supplkment au n

^O1 ,

Tome

41,

janvier 1980, page

C1-85

QUANTUM

BEATS OF

RECO

I

L-FREE Y-RAD

IATION

G.J. Perlow, J.E. Monahan and W. ~ o t z e l ~

Physics Division, Argonne NationaZ Laboratory, Argonne, I L 60439 USA.

Teehnische Universit8t Wnchen, 8046 Garching b e i Wnchen, W . Gemany.

ABSTRACT.- The radiation from a Mdssbauer source of 5 7 ~ o in a copper matrix is frequency-modulated by vi- brating the source with a quartz piezo-crystal driven by an oscillator. If the radiation passes through a resonant absorber (a"filter"), a time structure containing the oscillator frequency and its harmonics appears in the resulting counting rate

.

It may be seen by sorting the time of each count with respect to the cross-over time of a subharmonic of the oscillator. These quantum beats are caused by interferences between the frequency components of the photon amplitude, and vanish unless there is some alteration of relative phase or amplitude of the original radiation by the filter. The harmonic constitution of the beats is

a

sensitive function of the relative shift of source and filter and may be used as a sensitive probe of small shifts. This is demonstrated by measuring the temperature shift in 5 7 ~ e - ~ e . If a velocity spectrum is made with counts collected during on1y.a part

of

the vibration cycle, prominent dispersion effects are seen, with counting rates higher than background in some portions of the spectrum. A classical optical theory of the phenomenon is presented in summary. It explains the beats, the dispersion effects, and the sensitivity of the harmonic ratios to relative shifts

.

-+

+

1. INTRODUCTION where a = k. ro, the modulation index, is the

The term quantum beats is generally maximum phase shift of the radiation due to motion applied to describe the time-dependent intensity of the source with amplitude ro, and -+

$

^{is the}

of the radiation, from the de-excitation of a set wave-vector of the y-ray that is being observed.

of coherently excited upper states to a common

lower state. For states separated by AE in energy, The radiation field is thus in a coher- the intensity contains the interference frequency ent superposition of states characterized by w

n Q=AE/%.

A

familiar example is perturbed angular and each of these in turn is a superposition of correlation, where the coherence is between Zeeman the sharp frequencies that make up the line shape.

levels in a magnetic field. There are, of course One notes parenthetically the resemblance to other ways to describe this particular phenomenon. "time-filtering'' [2,3] which may be considered an

example of quantum beats among the frequency com- The situation we wish to discuss

[I]

is ponents of a single line. If the frequency-modu- somewhat different as only one excited nuclear lated radiation is detected, there is no time state is involved. The interference is between structure (other than statistical) in the counting states of the radiation field itself. These are rate, but if a resonant absorber is interposed produced by frequency modulation.

A

source of 5 7 ~ o between source and counter so that the transmitted in Cu is vibrated piezoelectrically at (angular) radiation is altered in amplitude or phase, the frequency Q, chosen so that az>X where

A

-1 is the counting rate will indeed be time-dependent. Such mean lifetime of the

14.4

kev nuclear state. Under an absorber will henceforth be called a "filter"

such conditions the radiation consists of lines to distinguish it from the absorber used to obtain centered at the frequencies w = w f nS1, n = 0, 1, a velocity spectrum.

n o

2, 3..

. ,

where %wo is the central energy of the

source, when it is at rest, and n numbers the side- The time-dependence can be seen easily band. If the source is thin and all atoms move in for a special case,[l] namely, complete absorption unison, the intensities of the lines are propor- of the central line. Before reaching the filter, tional to the familiar Bessel quantitites J L(a), the radiation amplitude corresponding to a single

photon may be described by:

*

This research was performed under the auspices of

the Division of Basic Energy Sciences of the United f -h(t-to)/Z .i(w0t f a sinat)

~ ( t , t ~ ) =

A

e @(to, t). States Department of Energy.

(1) Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1980115

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C1-86 ^JOURNAL^DE^PHYSIQUE

Here to is the (unmeasured) time of formation of the nuclear state, and 8(to,t) is zero for t<to and unity afterward. In traversing the filter the amplitude of the central line is subtracted, and the emerging amplitude E1(t,to) is given by:

The probability of detecting the photon at labora- tory time

t

is obtained by squaring E1(t,to) and integrating over to. The latter introduces no sur- prises, but the cross product in the curly brackets yields a term:

which contains only even harmonics of Q. Here we have used the identity:

m

ia sin&

=

C ^Jn(a)e ^inQt

³

nr-m (4)

and the relations ~,(a)

=

(-)"~-,(a) .

Note that in this case, as in all interference phenomena, one treats amplitudes according to the rule, "Add now, square later." As

to

is an obser- vable quantity, integration is done after squaring.

It is important to note, however, that in the ex- periments to be described bnlike the experiments on "time filteringl')we do not employ a previous nuclear event to determine the origin of time. Our counting rates are typically 500-1000 / sec. This is two orders of magnitude higher than is practical in a coincidence experiment.

2.

APPARATUS AND EXPERIMENTS

Fig. 1 shows schematically how the quan- tum beat apparatus was arranged. The Fe-Be filter

PULSE-HEIGHT

UNGATED ,

TIME

SPECTRUhl G4TED

Fig. 1. Apparatus for detecting quantum beats.

was made by chemically depositing 5 7 ~ e on beryllium and diffusing it in. It is an unresolved doublet with nearly zero shift vs. Fe-Cu. The source foil was cemented to an x-cut quartz crystal. The detector was a 0.5

mm

NaI scintillation crystal.

By means of the time-to-amplitude converter (TAC) the arrival time of an event in the counter was measured with respect to a synchronizing pulse derived from the oscillator. The TAC output was recorded in a PDP-11 computer after conversion by the analog-to-digital converter

(ADC).

As is common in timing circuits, there was a "slow"

channel for identification of the radiation and a

"fast" channel for timing. The slow channel could be used to obtain normal Missbauer velocLty spectra if an absorber were moved in the beam. In addition, mixed spectra could be obtained by selecting a time interval with a single channel analyzer set on the output of the TAC and accumulating only the selected pulses into a velocity spectrum.

Fig. 2 shows a 9.95 MHz frequency modula-

ted velocity spectrum as scanned by an enriched

sodium ferrocyanide (NFC) absorber both without

and with the Fe-Be filter. With the NFC removed,

and the filter in place one obtains a time spec-

trum as in Fig. 3 showing primarily the second

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VELOCITY SPECTRA WITH COPPER SOURCE AND SODIUM FERROCYANIDE ABSORBER

I t I " " " ' I

SOURCE VIBRATED at 9.95 MHz and

t

CENTER LINE REMOVED FROM a)

I I I I I I I I I

-5 - 4 -3 -2 - 1 0 1 2 3 4 5 VELOCITY (mm/sec)

Fig. 2. V e l o c i t y s p e c t r a of frequency-modu- l a t e d 5 7 ~ o - ~ u s o u r c e scanned w i t h NFC absorber: a ) w i t h o u t , and b) w i t h s t a t i o n a r y Fe-Be f i l t e r .

I I I I I I I I

CRYSTAL FREQUENCY: 9.95 MHz a t I0 V

I I I I I I I

I

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 T l M E ( p s e c )

Fig. 3. Typical time-spectrum showing quantum b e a t s . The r a d i a t i o n i n c i d e n t on t h e d e t e c t o r i s t h a t scanned i n Fig. 2b.

harmonic frequency, 2 ( 0 / 2 ~ ) = 19.90

mz.

The experimental time spectrum may b e f i t t e d w i t h a Fourier s e r i e s , u s u a l l y truncated a t t h e s i x t h harmonic,

I f t h e f i l t e r has some r e l a t i v e isomer s h i f t w i t h r e s p e c t t o t h e s o u r c e , t h e odd harmonic amplitudes appear prominently. T h i s i s seen i n Fig. 4 where t h e f i l t e r was a composite of e n r i c h e d 310 s t a i n - l e s s s t e e l and NPC. The isomer s h i f t of t h e com- b i n a t i o n w i t h r e s p e c t t o t h e Cu s o u r c e is about -0.3 m / s e c . The second harmonic c o e f f i c i e n t i n Fig. 4 i s seen t o be much smaller than t h e fundamental.

I n o r d e r t o determine i n d e t a i l t h e v a r i - a t i o n of t h e time spectrum w i t h s h i f t , t h e ( h i t h e r - t o s t a t i o n a r y ) Fe-Be f i l t e r was mounted i n our n e a r l y l i n e a r v e l o c i t y d r i v e . This i s a mechanical system which could b e a d j u s t e d t o t r a v e r s e from +0.3 t o -0.3 mm/sec i n about 30 s e c . The address-advance s i g n a l s d e r i v e from l i g h t p u l s e s from a s l o t t e d o p t i c a l s h u t t e r . A m u l t i p l e x i n g scheme, devised by Richard Kash, o p e r a t e d s o t h a t d u r i n g t h e time t h a t t h e a d d r e s s advanced from nl t o n we o b t a i n e d one time spectrum, and t h e n

2

another from n2 t o n3 e t c . f o r a maximum of 1 3 s p e c t r a , s t o r e d i n s u c c e s s i v e blocks of memory i n t h e computer. I n t h e c o u r s e of a day o r two o f d a t a t a k i n g a t t y p i c a l counting r a t e s of

t

COMPOSITE ABSORBER OF ENR. S.S. AND

SODIUM FERROCYAN IDE

1

0.81 I I I I

0 0.1 0.2 0.3 0.4

TlME ( r s e ~ )

Fig. 4. Quantum b e a t s when t h e f i l t e r resonance h a s an isomer s h i f t

(-0.3 mm/sec) w i t h r e s p e c t t o t h e source.

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CI-88

JOURNAL DE PHYSIQUE

500 to 1000/sec, we could simultaneously accumu- late 13 time-spectra of adequate quality, and could assign each to the mean velocity associated with its range of address-advance signals. Each such time-spectrum would then be fitted with Eq.

5,

using modifications of familiar least-squares codes. Fig. 5 shows a sample set of spectra (at 5.71MH.z) and Fig. 6 shows a plot of the ratio D ~ / D ~ of the fundamental to second harmonic Fourier coefficient obtained from the fits to a rather more carefully obtained set of spectra, to which we shall have later reference. The plot is remarkably linear. The phases of the odd harmonics shift by

5.71 MHz at 0.84~

f I I I I I I 1

0.1 a2 0.3 0.4 0.5 0.6 0.7 T I M E ( p s e c )

Fig. 5. Spectra with different values of the relative shift. Note phase change of fundamental frequency upon crossing resonance.

I

1 . 2 ~ 5.71 MHz

Fig. 6. Variation of the Fourier components D1/D2 with relative shift. These data were used as calibration in the measurement of temperature shift.

n

on going through v=O, as one may see by examining the spectra of Fig. 5. Thus Dl/D2 not only

measures the shift between source and filter, but its sign as well. It is in fact a very sensitive measure of small shifts. If it does not exactly vanish at "zero" shift, it is because the latter is not so easily determined by conventional means.

An interesting dispersion phenomenon occurs in the mixed or time-gated velocity spectra mentioned earlier. Here one accepts only Y-rays emitted during a selected interval of the oscillator cycle. A filter is used only as an aid in setting the boundaries of the time interval and is then replaced by a Msssbauer absorber which scans the spectrum in the normal way. Fig.'7 shows two such velocity spectra. The time gates are set as in the insert, covering successive intervals of

n

in the double-frequency beat spectrum or n/2 in the oscillation cycle. The spectra are fit with Lorentzian absorption and dispersion lines. Note

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( a ) = c e x b- 2 (7)

GATING DIAGRAM

E E I

Fig. 7. Mixed s p e c t r a , showing d i s p e r s i o n .

t h a t a t some v e l o c i t i e s t h e counting r a t e i s h i g h e r t h a n background. However, i f one s t r e t c h e s t h e counting i n t e r v a l t o cover t h e e n t i r e c y c l e , one of c o u r s e s e e s t h e normal frequency modulation spectrum a s i n F i g . 2a.

N e i t h e r t h e d i s p e r s i o n nor t h e v a r i a t i o n of t h e harmonic c o n t e n t of t h e b e a t s w i t h s h i f t can be o b t a i n e d from t h e simple c o n s i d e r a t i o n s t h a t l e d t o Eq. 3 . However an o p t i c a l t h e o r y , which s t a r t s from t h e i d e a s expressed i n Ref. 3 e x p l a i n s both phenomena i n a n a t u r a l way. [ 4 ]

3 . THEORY

Equation 1 may be r e - w r i t t e n :

Upon t r a n s m i s s i o n through t h e r e s o n a n t f i l t e r whose a b s o r p t i o n i s c e n t e r e d a t w o T , each monochromatic component cn(u) i s a l t e r e d t o cnT(w),where t o a good approximation

A t w = w

',

t h e exponent becomes -2b/X. Thus t h e t h i c k n e s s parameter b i n more f a m i l i a r terms i s given by

The t r a n s m i t t e d amplitude is:

The time and frequency dependence of t h e i n t e n s i t y of t h e t r a n s m i t t e d r a d i a t i o n i s o b t a i n e d by i n t e - g r a t i o n of l ~ ' ( t , t , )

I *

over t h e unobserved t i m e to, v i s .

l i m

T ( ~ , A U I /t d t O l ~ * ( t . t O )

I

²

-T

where Aw = w -w

' .

0 0

The e v a l u a t i o n of I(t,Aw) i s a non- t r i v i a l e x e r c i s e i n i n t e g r a t i o n i n t h e complex plane. D e t a i l s a r e found i n Ref. 4. The r e s u l t i s :

The c o e f f i c i e n t s Gd(Aw) a r e given i n Ref. 4 a s a s e r i e s i n ascending powers of t h e t h i c k n e s s parameter b/A

The l e a d i n g term, a p p r o p r i a t e t o a t h i n f i l t e r , is given below. It i s adequate t o show a l l t h e new phenomena. The t h i c k n e s s broadening comes from

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c1-90

t h e remaining terms. b e a t s may be seen a s c o n t o u r s f o r f i x e d Aw and t h e v e l o c i t y s p e c t r a a s c o n t o u r s f o r f i x e d t . I f one G

: :

) (Aw) = i b I _ 1 T

(Aw+nQ-il A w + L - i l

)

^{( I 2 )} forms t h e i n t e g r a l ,

6

dtI(t,Aw) where T i s t h e fundamental p e r i o d , t h e d i s p e r s i o n d i s a p p e a r s and Eq. 1 0 with GnL given by

c:: )

of Eq. 1 2 may be one is l e f t only with t h e customary frequency-modu-

c a s t i n t o r e a l form: l a t i o n a b s o r p t i o n spectrum.

An = J o ( a ) c o s n n t

+

^{cos BnL}

+

^(-)a ^{c o s}^sL), 11=1

B n = J o ( a ) s i n n Q t

+

^{s i n}

Brie+

^(-)L s i n

x

4. OTHER THEORETICAL RESULTS

I f t h e l i n e s a r e w e l l s e p a r a t e d , t h e t h i n f i l t e r approximation g i v e s t h e following f o r t h e F o u r i e r c o e f f i c i e n t s D and t h e phases Bk of

k Eq. 5: For k even

s i n kBk==O

2 2

Dk(Aw) = -4bX Jo ( a ) J k ( a )

/

[(Aw)

+

^A

1,

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each v a l u e of n i n Eq. 13 d e f i n e s a given l i n e . Each l i n e c o n t a i n s t h e Lorentz denominator w i t h t h e time dependent a b s o r p t i o n -2bXJn(a)An(t) and t h e time dependent d i s p e r s i o n 2bJn(a) (Aw

+

nn)B,(t).

A t a f i x e d v a l u e of t , t h e a b s o r p t i o n i s an even f u n c t i o n of t h e s h i f t Aw+nn about t h e l i n e c e n t e r and t h e d i s p e r s i o n is an odd function. Thus t h e i n t e n s i t y i s i n c r e a s e d on one s i d e of t h e l i n e and decreased on t h e o t h e r . Which s i d e is i n c r e a s e d and which decreased depends on t h e time. A t a f i x e d v a l u e of Aw, I(t,Aw) d i s p l a y s t h e quantum b e a t s v i a t h e time dependence i n t h e t r i g o n o m e t r i c terms, a l t h o u g h t h i s p a r t i c u l a r way of grouping terms i s n o t t h e most s u i t a b l e f o r showing them.

I n F i g . 8 we s e e t h e whole shape of t h e I(t,Aw) s u r f a c e a s a p e r s p e c t i v e p l o t . The c a l - c u l a t i o n i s t o second order i n b/X with a s 1 . 5 , Q / 2 r = 9.95 MHz, f i l t e r t h i c k n e s s n a o f a = l , and A = 7.09 x 10 G r a d / s e c , e q u i v a l e n t t o 0.0970 m / s e c . The t - a x i s r u n s from Q t = 0 t o D t = n . The second h a l f - c y c l e of Q t m i r r o r s t h e f i r s t . The quantum

and

I

D ~ ( A ~ )

I

h a s a maximum a t &w= 0. For k odd

c o s kgk;' 0

which h a s extrema a t Aw=fh. From t h e s e we g e t t h e l i n e a r r e l a t i o n :

The a n g u l a r b r a c k e t s imply an average o v e r a i f t h e s o u r c e does not have a unique modulation index.

I n t h e i d e a l c a s e , t h e b r a c k e t s may be removed and t h e J (a) f a c t o r s c a n c e l l e d i n numerator and denominator. While a unique modulation index i n t h e c a s e of 57Fe h a s n o t been t h e observed i n t h e p a s t , t h e r e a r e i n d i c a t i o n s both elsewhere [ 5 ] and i n our l a b o r a t o r y t h a t w i t h good u l t r a s o n i c t e c h n i q u e t h i s i d e a l c a s e can b e c l o s e l y approached.

A s t a t i s t i c a l argument, given i n d e t a i l i n Ref. 4 compares t h e s t a n d a r d e r r o r a' of a n

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F i g . 8 . The s u r f a c e I(t,Aw) p l o t t e d i n d i m e n s i o n l e s s t i m e and f r e q u e n c y u n i t s .

unknown s m a l l s h i f t measured by u s e of t h e r a t i o D1/D2 t o t h e c o r r e s p o n d i n g q u a n t i t y o f o r t h e method i n which t h e c o u n t i n g r a t e i s compared a t two p o i n t s , one on e a c h s i d e of t h e a b s o r p t i o n l i n e . The l a t t e r scheme was employed i n measure- ments of t h e g r a v i t a t i o n a l r e d s h i f t [ 6 ] . I f t h e p a r a m e t e r s i n b o t h methods have t h e i r optimum v a l u e s , one f i n d s :

The i n e q u a l i t y i s t o b e used i f a l l p a r t s of t h e s o u r c e do n o t v i b r a t e w i t h t h e same a m p l i t u d e and phase. D e s p i t e t h e somewhat g r e a t e r t h e o r e t i c a l

4 . MEASUREMENT OF THE SECOND ORDER DOPPLER SHIFT OF Fe-Be

A s a n o p e r a t i n g t e s t of t h e D / D method

1 2

we measured t h e second o r d e r Doppler s h i f t i n Fe-Be produced by changing i t s t e m p e r a t u r e . We d i d n o t e x p e c t new i n s i g h t s i n t o t h e m a t e r i a l p r o p e r t i e s of t h e sample a s t h e measurement had been c a r e f u l l y performed by t r a d i t i o n a l v e l o c i t y s p e c t r o s c o p y i n t h e p a s t 171, t y p i c a l l y w i t h t e m p e r a t u r e i n t e r v a l s between d a t a p o i n t s of a b o u t 50°C. Our measurement however covered a t o t a l r a n g e of 80°C and c o n t a i n e d 9 d a t a p o i n t s . The s o u r c e was a t room t e m p e r a t u r e and was c o n t r o l l e d i n t e m p e r a t u r e ( w i t h i n about 2°C) by t h e room e r r o r of t h e new method, we b e l i e v e t h a t when a i r - c o n d i t i o n i n g . The t e m p e r a t u r e was c o n t i n u o u s l y o t h e r s o u r c e s of e x p e r i m e n t a l e r r o r a r e c o n s i d e r e d , monitored by a s i l i c o n thermometer and s t r i p c h a r t i t i s a t l e a s t a s u s e f u l a t e c h n i q u e a s c o u n t i n g r e c o r d e r . The a v e r a g e , t y p i c a l l y 21°C, was used

a t two p o i n t s . a s t h e s o u r c e t e m p e r a t u r e . The f i l t e r was

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C1-92

c o n t a i n e d i n a c o n s t a n t t e m p e r a t u r e e n c l o s u r e and c o n t r o l l e d t o 0.l0C. The t e m p e r a t u r e was v a r i e d between a b o u t -20 t o +60°C. The o v e r a l l a c c u r a c y i n t h e t e m p e r a t u r e d i f f e r e n c e was a b o u t O.Z°C.

Other t h a n t h e v i b r a t i o n a l motion of t h e s o u r c e a t 5.71 MHz, t h e r e was n o r e l a t i v e motion of s o u r c e and f i l t e r e x c e p t when t h e c a l i b r a t i o n was made.

The c a l i b r a t i o n c u r v e i s t h a t of F i g . 6, mentioned e a r l i e r .

The t e m p e r a t u r e d a t a a r e shown i n F i g . 9.

Over t h e r e g i o n shown t h e v a r i a t i o n of D1/D2 i s l i n e a r .

From t h e c a l i b r a t i o n we o b t a i n e d t h e s l o p e of t h e l i n e a r p l o t of D /D v s v a s

1 2

SECOND ORDER DOPPLER SHIFT ABSORBER FeBe

SOURCE' 5 7 ~ ~ u

-20 0 20 40 60 AT (K)

hT= (TEMP.), -(TEMP.)S

F i g . 9. V a r i a t i o n of D / D w i t h r e l a t i v e

1 2

t e m p e r a t u r e of Fe-Be and 5 7 ~ o - ~ u . The s o u r c e t e m p e r a t u r e was 2 1 1 1 ° d u r i n g t h e s e r u n s .

m v = 2.17 2 .04 (-/see)-l. From t h e t e m p e r a t u r e r u n s we o b t a i n e d t h e s l o p e mT of D /D v s T a s

1 2

m T = (1.36 ? .04) x l f 3 ( ' K ) - ~ . From t h e r a t i o of s l o p e s we g e t f o r t h e s h i f t p e r d e g r e e d s / d ~ = (-6.2

+

^0.2) ^x rnm/sec-OK f o r t h e sample temp- e r a t u r e r a n g e l l ° C t o 84-C. I f we u s e t h e v a l u e 9 = 4 5 Z 0 f o r t h e Fe-impurity i n b e r y l l i u m deduced

D

f o r low sample t e m p e r a t u r e by J a n o t and c o l l a b o r a - t o r s , we e x p e c t -6.5 x 1 0 -4 m / s e c - O ~ f o r t h e same q u a n t i t y , i n r e a s o n a b l e agreement.

One may a s k how s m a l l a t e m p e r a t u r e i n - t e r v a l c a n b e r e s o l v e d by t h e quantum b e a t method.

As t h e experiment was performed, a 1 2 hour r u n a t a b o u t 1000 c o u n t s / s e c a l l o w s o n e t o s e p a r a t e two p o i n t s a b o u t 3OC a p a r t . The m o d u l a t i o n i n d e x f o r t h e s e r u n s was chosen t o maximize D2 (which i s r e l a t i v e l y i n s e n s i t i v e t o s h i f t )

.

T h i s is n o t optimum. Subsequent t e s t s show t h a t a n i n c r e a s e i n m v by a f a c t o r somewhat g r e a t e r t h a n 5 i s ob- t a i n e d by d e c r e a s i n g t h e i n d e x . On t h i s b a s i s t h e same c o n d i d t i o n s y i e l d a r e s o l u t i o n of a b o u t 0.6OC o r a b o u t 1 x mm/sec. Longer t i m e s , h i g h e r r a t e s , o r improved a c o u s t i c c o u p l i n g of t r a n s d u c e r t o s o u r c e s e r v e t o d i m i n i s h t h e s e numbers.

The q u e s t i o n a r i s e s c o n c e r n i n g p o s s i b l e a p p l i c a t i o n s o f t h e new t e c h n i q u e s . A few t h i n g s c a n be s a i d , a l t h o u g h we hope t h a t t h e i n g e n u i t y of o u r c o l l e a g u e s w i l l l e a d t o many new i d e a s s t a r t i n g from what we have done. P h a s e t r a n s i - t i o n s t h a t l e a d t o s m a l l isomer s h i f t s a r e a n a t u r a l u s e of t h e D / D method. S i m i l a r l y o n e

1 2

c a n l o o k a t t h e isomer s h i f t s i n a c e n t r a l atom a s s o c i a t e d w i t h s u b s t i t u t i o n s of a remote member of t h e molecule. We o u r s e l v e s a r e l o o k i n g f o r p o s s i b l e s h i f t s upon a p p l i c a t i o n of a m a g n e t i c f i e l d . Some c a u t i o n must b e observed when s o u r c e

(10)

o r f i l t e r i s s p l i t , b u t i t seems p o s s i b l e t o t a k e 5. ACKNOWLEDGMENTS

t h i s i n t o a c c o u n t . One n o t e s t h a t i f t h e f i l t e r The w r i t e r s would l i k e t o acknowledge l i n e i s e i t h e r s p l i t o r asymmetric, t h e r e is s t i l l h e l p and comments from t h e i r c o l l e a g u e s . a unique v a l u e of t h e r e l a t i v e s h i f t a t which t h e Gerald Kara a s s i s t e d i n many of t h e measure- r a t i o D1/DZ v a n i s h e s and i t i s l a r g e l y independent ments and i n t h e computer work, Richard Kash of m o d u l a t i o n i n d e x . It may however depend some- d e s i g n e d much o f t h e e l e c t r o n i c c i r c u i t r y . what on t h e f i l t e r t h i c k n e s s . Henry S t a n t o n programmed t h e f i t t i n g r o u t i n e

f o r t h e F o u r i e r c o e f f i c i e n t s . H. J . L i p k i n and M. P e s h k i n a i d e d w i t h u s e f u l p h y s i c a l i n s i g h t s .

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