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VOLUME

APRIL 1, 1960

NUMBER 7

APPARENT WEIGHT OF PHOTONS
R. V. Pound and G. A. Rebka, Jr.
Lyman Laboratory of Physics, Harvard University, Cambridge, (Received March 9, 1960)

Massachusetts

As we proposed a few months ago, ' we have now

' measured the effect, originally hypothesized by
Einstein, of gravitational potential on the ap-

parent frequency of electromagnetic radiation by

using the sharply defined energy of recoil-free

ycorvaeyrsedembyitteMdosasnbdauaebr.so'rbeWde

in solids, as have already

dis-
re-

ported' a detailed study of the shape and width of

the line obtained at room temperature for the
14.4-kev, O. 1 -microsecond level in Fe". Partic-

ular attention was paid to finding the conditions

required to obtain a narrow line. We found that
" the line had a Lorentzian shape with a fractional
full-width at half-height of 1.13 x10 when the

source was carefully prepared according to a

prescription developed from experience. We have
also investigated the 93-kev, 9.4-microsecond level of Zn" at liquid helium and liquid nitrogen

temperatures using several combinations of

source and absorber environment, -but have not

observed a usable resonant absorption. That work will be reported later. The fractional width and
intensity of the absorption in Fe" seemed suffi-

cient to measure the gravitational effect in the

laboratory. As a preliminary, we sought possible sources

of systematic error that would interfere with

measurements of small changes in frequency using this medium. Early in our development of the in-

strumentation necessary for this experiment, we

concluded that there were asymmetries in, or frequency differences between, the lines of given

combinations of source and absorber which vary from one combination to another. Thus it is ab-

solutely necessary to measure a change in the

relative frequency that is produced by the perturbation being studied. Observation of a fre-

quency difference between a given source and

absorber cannot be uniquely attributed to this

perturbation. More recently, we have discovered

and explained a variation of frequency with perature of either the source or absorber.

'

tem-
We

conclude that the temperature difference between

the source and absorber must be accurately

known and its effect considered before any mean-

ing can be extracted from even a change observed

when the perturbation is altered.

The basic elements of the apparatus finally

developed to measure the gravitational shift in

frequency were a carefully prepared source

containing 0.4 curie of 270-day Co", and a care-

fully prepared, rigidly supported, iron film ab-

sorber. Using the results of our initial experi-

ment, we requested the Nuclear Science and

Engineering Corporation to repurify their nickel

cyclotron target by ion exchange to reduce cobalt
carrier. Following the bombardment, in a special

run in the high-energy proton beam of the high-

current cyclotron at the Oak Ridge National

Laboratory, they electroplated the separated Co'7 onto one side of a 2-in. diameter, 0.005-in.

thick disk of Armco iron according to our pre-

scription. After this disk was received, it was

heated to 900 -1000 C for one hour in a hydrogen

' atmosphere' to diffuse the cobalt into the iron
foil about 3x10 cm.

The absorber made by Nuclear Metals Inc. , was composed of seven separate units. Each

VOI.UMS 4, NUMSaR 7

PHYSICAL RKVI EW LETTERS

A@Rid. 1, 1960

unit consisted of about 80 mg of iron, enriched
in Fe" to 31.9%, electroplated onto a polished

side of a 3-in. diameter, 0.040-in. thick disk of

beryllium. The electroplating technique required

considerable development to produce films with

absorption lines of width and strength that satis-

fied our tests. The films finally accepted, reso-

nantly absorbed about 1/3 the recoil-free y rays from our source. Each unit of the absorber was

mounted over the 0.001-in. Al window of a

3 in. x1/4 in. NaI(T1) scintillation crystal in-

tegrally mounted on a Dumont 6363 multiplier

phototube. The multiplier supply voltages were

separately adjusted to equalize their conversion

gains, and their outputs were mixed.

The required stable vertical baseline was con-

veniently obtained in the
of the Jefferson Physical

eLncalboosreadt,oryi.so'latAedstatotwise-r

tical argument suggests that the precision of a

measurement of the gravitational frequency shift

should be independent of the height. Instrumental

instability but more significantly the sources of

systematic error mentioned above are less criti-

cal compared to the larger fractional shifts ob-

tained with an increased height. Our net operating

baseline of 74 feet required only conveniently

realizable control over these sources of error.

The absorption of the 14.4-kev y ray by air in the path was reduced by running a 16-in. diameter, cylindrical, Mylar bag with thin end win-
dows and filled with helium through most of the distance between source and absorber. To
sweep out small amounts of air diffusing into the
bag, the helium was kept flowing through it at a rate of about 30 liters/hr.
The over-all experiment is described by the
block diagram of Fig. 1. The source was moved sinusoidally by either a ferroelectric or a moving-
coil magnetic transducer. During the quarter of
the modulation cycle centered about the time of maximum velocity the pulses from the scintilla-
tion spectrometer, adjusted to select the j.4.4kev y-ray line, were fed into one sealer while,
during the opposite quarter cycle, they were fed into another. The difference in counts recorded was a measure of the asymmetry in, or frequencyshift between, the emission and absorption lines. As a precaution the relative phase of the gating pulses and the sinusoidal modulation were dis-
played continuously. The data were found to be
insensitive to phase changes much larger than the drifts of phase observed.
- A completely duplicate system of electronics, controlled by the same gating pulses, recorded

v~v
SOURCE

HYDRAULIC MASTER

~HYDRAULIC
SLAVE TRANSDUCER

"" HERMO-
OUPLE
Yq

— HP OSCILLATOR

8 RACK

PI NION

CLOCK DR I VE

V IV "V

FLOWING HE LIUM
NTP

PHASE SHIFT
8 SQUARE
WAVE
GATE GENERATOR
i

TRIGGER p PFR CYCLE

MONITOR CHANNEL

Na I
8
P. M.

CHART

Fe

RECORDER

THERMOCOUPLE

SIGNAL

l
CHART RECORDER
CHANNEL

AMPLIFIER AND
PULSE HEIGHT SELECTOR
AMPLIFIER AND
PULSE HEIGHT SELECTOR

COINC I DENCE CIRCUIT
8
PISCRIMINATOR
COINCIDENCE C I R CUIT
8
P I SCR IMINATOR

GATE PHASE DISPLAY

— L I COUNTER
MERCURY

RELAYS

] COUNTER I

MERCURY REL AYS

~COUNTERI

l. FIG. A block diagram of the over-all experimental arrangement. The source and ab-
sorber-detector units were frequently interchanged. Sometimes a ferroelectric and some-
times a moving-coil magnetic transducer was used with frequencies ranging from 10 to 50 cps.

VOLUME 4, NUMBER 7

PHYSICAL REVI EW LETTERS

APRIL I, 1960

data from a counter having a 1-in. diameter, 0.015-in. thick NaI(T1) scintillation crystal covered by an absorber similar to the main absorber. This absorber and crystal unit was mounted to see the source from only three feet away.
This monitor channel measured the stability of the over-all modulation system, and, because of its higher counting rate, had a smaller statistical uncertainty.
The relation between the counting rate difference and relative frequency shifts between the
emission and absorption lines was measured directly by adding a Doppler shift several times the size of the gravitational shift to the emission line. The necessary constant velocity was introduced by coupling a hydraulic cylinder of large bore carrying the transducer and source to a master cylinder of small bore connected to a rack-and-pinion driven by a clock.
Combining data from two periods having Dop-
pler shifts of equal magnitude, but opposite sign, allowed measurement of both sensitivity and relative frequency shift. Because no sacrifice
of valuable data resulted, the sensitivity was calibrated about 1/3 of the operating time which was as often as convenient without recording the data automatically. In this way we were able to
eliminate errors due to drifts in sensitivity such as would be anticipated from gain or discriminator drift, changes in background, or changes in
modulation swing.
The second order Doppler shift resulting from lattice vibrations required that the temperature difference between the source and absorber be controlled or monitored. A difference of 1 C would produce a shift as large as that sought, so the potential difference of a thermocouple with one junction at the source and the other at the main absorber was recorded. An identical system was provided for the monitor channel. The recorded temperature data were integrated over a counting period, and the average determined
to 0.03 C. The temperature coefficient of frequency which we have used to correct the data,
was calculated from the specific heat of a lattice having a Debye temperature of 420 K. Although at room temperature this coefficient is but weakly dependent on the Debye temperature, residual error in the correction for, or control of, the temperature difference limits the ability to measure frequency shifts and favors the use of a large height difference for the gravitational experiment.
Data typical of those collected are shown in
Table I. The right-hand column is the data after

correction for temperature difference. All data
are expressed as fractional frequency shift &10".
The difference of the shift seen with y rays rising and that with y rays falling should be the result of gravity. The average for the two directions of travel should measure an effective shift of other origin, and this is about four times the difference between the shifts. We confirmed that
this shift was an inherent property of the particular combination of source and absorber by measuring the shift for each absorber unit in turn, with temperature correction, when it was six inches from the source. Although this test was not exact because only about half the area of each absorber was involved, the weighted mean shift from this test for the combination of all absorber
units agreed wel. l with that observed in the main
experiment. The individual fractional frequency shifts found for these, for the monitor absorber,
as well as for a 11.7-mg/cm' Armco iron foil, are displayed in Table G. The considerable var-
iation among them is as striking as the size of
the weighted mean shift. Such shifts could result
from differences in a range of about 11% in ef-
fective Debye temperature through producing differences in net second order Doppler effect.
Other explanations based on hyperfine structure including electric quadrupole interactions are also plausible. Although heat treatment might be expected to change these shifts for the iron-plated beryllium absorbers, experience showed that the line width was materially increased by such treatment, probably owing to interdiffusion. The presence of a significant shift for even the Armco
foil relative to the source, both of which had re-
ceived heat treatments, suggests that it is unlikely one would have, without test, a shift of this sort smaller than the gravitational effect expected in even our "two-way" baseline of 148 feet. The
apparently fortuitous smallness of the shift of
the monitor absorber relative to our source cor-
responds to the shift expected for about 30 feet of height difference.
Recently Cranshaw, Schiffer, and Whitehead
claimed to have measured the gravitational shift
using the y ray of Fe". They state that they be-
lieve their 43% statistical uncertainty represents the major error. Two much larger sources of error apparently have not been considered: (1) the temperature difference between the source
and absorber, and (2) the frequency difference inherent in a given combination of source and absorber. From the above discussion, only 0.6'C of temperature difference would produce a shift

339

VOLUME 4, NUMBER 7

P HY SIC%I. REVI EW LETTERS

APRIL 1, 1960

Table I. Data from the first four days of counting. The data are expressed as fractional frequency differences
between source and absorber multiplied by 10 ~, as derived from the appropriate sensitivity calibration. The negative signs mean that the y ray has a frequency lower than the frequency of maximum absorption at the absorber.

Period

Shift

Temperature

Net

observed

correction

shift

Feb. 22, 5 p. m. Feb. 23, 10 p. m. Feb. 24, 0 a. m.
Feb. 25, 6 p. m.

Source at bottom
-11.5+ 3.0 -16.4+ 2.2 -13.8+ 1.3 -11.9 +2.1 -8.7+ 2. Oa -10.5 + 2. 0
Source at top
-12.0 +4. 1
-5.7 +].4
-7.4 6 2. 1a -6.5 + 2. 1a -13.9 3 ]a -6.6 +3.0 -6.5 +2.0a -10.0 + 2.6

-9.2

-20. 7+ 3.0

-5.9

-22. 3 + 2. 2

-5.3

-19.1 + 1.3

-8. 0

-19.9 +2.1

-10.5

-19.2 +2.0

-10.6

-21.0 +2.0

Weighted average = -19.7 + 0. 8

-8. 6

-20. 6 + 4. 1

-9.6

-15.3 + 1.4

-7.4

-14.8+ 2. 1

-5. 8

-12.3 + 2. 1

-7.5

-21.4+ 3.1

-5. 7

-12.3 +3.0

-8.9

-15.4 + 2. 0

-7.9

-17.9+ 2. 6

Weighted average = -15.5 ~ 0. 8

Mean shift = -17.6 + 0. 6

Difference of averages = -4. 2 + 1.1

aThese data were taken simultaneously with a sensitivity calibration.

Table II. Data on asymmetries of various absorbers in apparent fractional frequency shift multiplied
by 10~5. In the third column we tabulate the Debye temperature increase of the absorber above that of the
source which could account for the shift.

Absorber
No. 1 No. 2 No. 3 No. 4 No. 5 No. 6 No. 7 Weighted mean of No. 1-No. 7 Monitor absorber Armco foil

(b, p/p)xlo
-8.4 + 2.5 -24 + 3.5 -28 + 3.5 -19 + 3.5 -24 + 3.5 -17 + 2. 5 -19+ 3.5
-19 + 3.0 +0.55+ 0.15
+10+ 3.5

&0~ in K
+15 +4 +41~ 6 +48 +6 +33+ 6 +41+ 6 +29+ 4 +33 +6
+33+5
-0.95 + 0.26
-17 +6

as large as the whole effect observed. Their additional experiment at the shortened height difference of three meters does not, without concomitant temperature data, resolve the question
340

of inherent frequency difference. Their stated disappointment with the over-all line width ob-
served would seem to add to the probability of
existence of such a shift. They mention this broadening in connection with its possible influence on the sensitivity, derived rather than measured, owing to a departure from Lorentzian shape. Clearly such a departure is even more
important in allowing asymmetry. Our experience shows that no conclusion can
be drawn from the experiment of Cranshaw et al. If the frequency-shift inherent in our source-
absorber combination is not affected by inversion of the relative positions, the difference between
shifts observed with rising and falling y rays measures the effect of gravity. All data collected
since recognizing the need for temperature cor-
". rection, yield a net fractional shift, -(5.13 + 0.51)
&&10 The error assigned is the rms statistical
deviation including that of independent sensitivity
calibrations taken as representative of their re-
", spective periods of operation. The shift observed
agrees with -4.92 x10 the predicted gravita-
tional shift for this "two-way" height difference.

VOLUME 4, NUMBER 7

PHYSICAL REVI EW LETTERS

APRIL 1, 1960

Expressed in this unit, the result is
(hv) exp /(b, v)theor =+ 1.05+ 0.10,
where the plus sign indicates that the frequency increases in falling, as expected.
These data were collected in about 10 days of operation. We expect to continue counting with some improvements in sensitivity, and to reduce the statistical uncertainty about fourfold. With our present experimental arrangement this should result in a comparable reduction in error in the measurement since we believe we can take ade-
quate steps to avoid systematic errors on the re-
sulting scale. A higher baseline or possibly a narrower y ray would seem to be required to extend the precision by a factor much larger than this.
We wish to express deep appreciation for the generosity, encouragement, and assistance with details of the experiment accorded us by our colleagues and the entire technical staff of these laboratories during the three months we have

been pr'eoccupied with it.
Supported in part by the joint program of the office of Naval Research and the U. S. Atomic Energy Commission and by a grant from the Higgins Scientific Trust.
~R. V. Pound and G. A. Bebka, Jr. , Phys. Rev.
Letters 3, 439 (1959). 2A. Einstein, Ann. Physik 35, 898 (1911). 3R. L. Mossbauer, Z. Physik 151, 124 (1958);
Naturwissenschaften 45, 538 (1958); Z. Naturforsch. 14a, 211 (1959).
4B. V. Pound and G. A. Rebka, Jr. , Phys. Rev.
Letters 3, 554 (1959).
SR. V. Pound and G. A. Bebka, Jr. , Phys. Rev.
Letters 4, 274 (1960).
6We wish to thank Mr. F. Bosebury of the Research
Laboratory of Electronics, Massachusetts Institute of Technology, for providing his facilities for this treatment.
See E. H. Hall, Phys. Rev. 17, 245 (1903), first
paragraph.
ST. E. Cranshaw, J. P. Schiffer, and A. B. White-
head, Phys. Rev. Letters 4, 163 (1960).

TEMPERATURE-DEPENDENT SHIFT OF y RAYS EMITTED BY A SOLID
B. D. Josephson
Trinity College, Cambridge, England
(Received March 11, 1960)

Recent experiments by Mossbauer' have shown

I, The change in energy,

of the solid is given

that when low-energy y rays are emitted from nuclei in a solid a certain proportion of them are
unaffected by the Doppler effect. It is the purpose of this Letter to show that they are never-

by

0E

= (aH)

= 0(P.'/2m.

)

=

-5m.i

(P.'/2m. Z

i')

theless subject to a temperature-dependent shift

to lower energy which can be attributed to the

relativistic time dilatation caused by the motion

of the nuclei.

Let us regard the solid as a system of inter-

acting atoms with the Hamiltonian

r, H =Qp.'/2m. + V(r, ). ~ ~ ~

2

g

The Mossbauer effect is due to those processes

where Tz is the expectation value of the kinetic
energy of the ith atom. The energy of the y ray must accordingly be reduced by 5Z so there is a shift of relative magnitude 0E/E =Tg/mtc'. The
same formula can be deduced by regarding the shift as due to a relativistic time dilatation.
To estimate Ti we make the following assumptions: (i) The atoms all have the same mass,

in which the phonon occupation numbers do not
change. It might appear that in such cases the energy of the solid is unaltered, but this is not so, as the nucleus which emits the y ray changes

and the kinetic energy is equally distributed
among them. (ii) The kinetic energy is half the
total lattice energy, i.e., we assume that the
forces coupling the atoms are harmonic. Under

E/c'- its mass, and this affects the lattice vibrations.
Suppose the nucleus of the ith atom emits a y ray
of energy E, its mass changing by Dmin =

these assumptions Tf/m; = -',U, where U is the lattice energy per unit mass. The relative shift is thus given by 0E/E = U/2c'. For Fe at 300'K

341