zotero/storage/ZPNH2QZ2/.zotero-ft-cache

LETTE RS TO THE EDITOR

tracks in the 6000 pictures was 1.8X10'. Comparison of this
number with the 69 higher energy tracks gives a branching ratio
of one to an upper limit of 26,000. It was only possible to give an
upper limit to this phenomenon; the total number of positron tracks belonging to the higher energy spectrum would be higher than the number counted for two reasons. First, tracks emerging at certain angles are obscured by the dense cloud of low energy tracks. Secondly, only those of su%ciently high energy to reach the glass baffle were included. Those tracks of energy less than
0.95 Mev could not be identi6ed positively as tracks due to
posi trons.
Figure 2 exhibits a t.ypical case of a high energy positron originating at the source and stopping in the glass ba6ie.

"' Assisted bv the Joint Program of the ONR and AEC.

'~ ' '

FGGPr.o.ivoOTdapt,.peSePneehacabeosiolmmergsem,ruananniadcdnadtIiDo.nEePue.trsPlcm.whaT,intho,mPhlRiGyness..vo.nOR,MweveoPn.dh.6y9sPa.,nh3dyR1se.3vJ.2(.015,96T45,o86w85)Sn.8s&en(11d99483)9o. )f.

this

lab'oEra.toFreye.nberg and K. C. Hammacl. , Phys. Rev. 75, 1877 (1949).

Positive Particles Associated with

Beta-Ray Emitters

K. L. ERDMAN,

T. G»

KQKoTAELo, + AND

D. B. ScoTT

Department of Physics, University of Alberta, Edmonton, Alberta, Canada

August 29, 1949

" t N a nine-inch cloud chamber using air at atmospheric pressure,
~ ~ a search has been made for the positive particles reported to accompany the decay of certain beta-ray sources. Stereoscopic
photographs of sources S'~, UX, Ra(D+E) and P3' were taken,
the chamber being illuminated by a beam of light approximately one inch in height. A lead foil„34 mg/cm~ was stretched across the
chamber ten cm from the source. Collimated and uncollimated
sources were used.
An initial count with an uncollimated UX source giving approximately 50 tracks per picture produced 0.1 positive tracks per electron. Count of apparent pairs produced by electrons in the lead
foil gave a cross section of the order of 10~ cm~. Both 6gures
disagree with theory. &4 The confusion resulting from large number of tracks and reQec-
tions from every surface in the chamber made these results untrustworthy. Accordingly, a source of reduced strength was collimated so that emergent particles were limited to the illuminated part of the chamber. With these modi6cations many of the "positive" tracks were seen to be reQections back to the source. Only positive tracks which showed no indication of being reQections were counted.
In Table I appear the counts made on this basis with collimated
sources of UX, Ra(D+E), and P~, with the recent results of other
workers where available.
It is possible that even these so-called positive particles were
reQections back to the source, of electrons for which part of the track was outside the illumination. A count was therefore taken of the number of de6nite reflections from all surfaces. Considering the relative source and chamber diameters, the ratio of the number of tracks which could be reQected back to the source, to the number of electron tracks, has the following values for UX,
TABLE I. Maximum possible positive particle count with UX. Ra(V+8), and W~.

UX
Ra(D+E)
P41

Total

Approximate Total number of

number of number of positive

tracks per electrons particles

picture

(N )

(X+)

31

5340

8

17

3490

6

13

6100

6

0.0013 0.0017 0.0010

& C. B. A. McCusker, Nature 161, 564 (1948). b T. H, Pi and C. V. Chao, Phys. Rev, 72, 638 (1947).

N+/N observed by others recently
0.001~ 0.0011~

Ra(D+E), and P~, respectively: 0.01, 0.003, and 0.003. These

figures are greater than the corresponding values of E+/N in
Table I.

The majority of the positive tracks included in the counts were
of the order of 0.1 Mev, judging by their curvature. Bethe's scat-

tering formula~ shows that for electron energies less than about 0.1 Mev, the scattering radius of curvature is of the same order

as that due confirmation

to the magnetic 6eld (250 of this, photographs of

gSau"ss(m) auxsiemdumin

this work. In energy 0.12

Mev) showed tracks which were completely disordered. It was

quite impossible to determine the direction of the magnetic 6eld

from the photographs.

Frpm these results, one may conclude that the positive particles

which have been reported are one of the (a} electrons which have

been reQected back to the source, (b) electrons whose tracks are

nearly closed circles, part of the track being out of the illumination

or obscured by other tracks, or (c) electrons of low energy with "positive" curvature due to scattering.
It is worth noting that the theoretical work of Arley and Mgller4 gives E+/E a value of zero for internal pair conversion by elec-

trons from sources whose end-point energy is less than 4 Mev.

Numerous apparent pairs produced in the lead foil by incident

electrons were found. Upon examination however, these were seen

to be one of the (a) electrons which penetrated the foil and curved

back to strike the foil again in the same vertical line as another

electron which had penetrated the foil, or (b) electrons which

penetrated the foil and curved back to the foil, being reQected at

a point in the same vertical line as another electron whose track

could be distinguished only up to the foil. From the results of these experiments it seems unnecessary to

propose either the existence of positive particles of lighter mass

than the electron' or positive particles of greater mass than the
' electron. ' Groetzinger eI, ul. have reported four cases of positive particles

branching from tracks of electrons with a P~ source. In two cases,

a change of curvature of the electron track appeared at the branch

point, but in no case was there a change in direction. The experi-

ments here reported included a careful search for such events.

None were found.

This work was supported by grants from the National Research

Council of Canada.

4' Now with Socony-Vacuum, Paulsboro, New Jersey.

' Bradt, Heine, and Scherrer, Helv. Phys. Acta 16, 491 (1943).

"-
'

JL..

Smith and G. Groetzinger, Phys. R. Oppenheimer, Phys. Rev. 4/,

Rev. 70, 96 146 (1935).

{1946).

4 N. Arley and C. Mufller, Kg). Danske Vid. Sels. Math. -fys. Medd. XV,

9

(''1HG9r.3o8Ae)t.z. iBngeethr,e,

Phys. Rev. 70, 821 (1946). Ribe, and Smith, Phys. Rev.

75,

342

(1949).

A Precise Determination of the Proton Magnetic
Moment in Bohr Magnetons*
J. H. GARDNER AND E. M, PlrRCELL
Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts
August 26, 1949
w E have completed an experimental determination of the ratio of the precession frequency of the proton, au~= y„Hp, to the cyclotron frequency cu, =eHp/mc of a free electron in the same magnetic 6eld. The result, ou„/cu„ is the magnitude of the
proton magnetic moment ps~, in Bohr magnetons, since y„=2p, „/A.
The proton resonance absorption in mineral oil was observed by the bridge technique' at a frequency of 14,24 Mc/sec. The electron resonance, at approximately 9360 Mc/sec. , was obtained as follows. An evacuated rectangular wave guide, its broad dimension parallel to Ho, is traversed by a beam of slow electrons which originate outside the wave guide, enter the guide through a 2.0XO.i-mm slit in the narrow wall, and drift across the guide in the direction of the magnetic Geld. The 6eld prevents the ribbonshaped beam from spreading, so the electrons can pass through a
similar slit in the opposite wall of the guide, to be collected. If

LETTE RS To THE E B I TOR

1263

now the guide is excited by a source of frequency cu„ the oscillating electric 6eld expands the helical trajectories of the electrons. We had intended originally to recognize this condition by the decrease in collector current resulting from the failure of the expanded beam to get through the second slit. The effect was indeed observed and it behaved as predicted by an analysis of the electron trajectories.
It was found, however, that when the beam current was limited
by a space-charge potential minimum within the wave guide and when a very weak microwave 6eld was applied, a peak in the collected current appeared at resonance, owing to the expansion of the electron cloud at the minimum with a consequent reduction in the depth of the minimum. Because the depth of the minimum is very sensitive to the presence of those electrons that nearly stop there and are exposed for an unusually long time to the oscillating
6eld, this resonance e6ect is very sharp. It was used for the deter-
mination of au, /cos, . The full width of the current peak, at halfmaximum, was about 1 in 10'.
The electron beam and the proton sample were about 1.5 cm apart; their positions could be interchanged to eliminate the effect of 6eld inhomogeneity. The two resonances were displayed simul-
taneously on an oscilloscope while the magnetic field was modu-
lated at 60 c.p.s. After adjustment for symmetry and coincidence, the ratio of the frequencies was determined by comparing the
657th harmonic of the proton frequency with the electron fre-
quency ~,. As the difference was only a few megacycles, the error
introduced in this step was negligible. Nine complete experiments were carried out, over a period of a
month. The mean value of the ratio au, /cu„, uncorrected for diamagnetism, was 657.4752 with a mean deviation of 0.0037 and a
maximum deviation of 0.0056. The accuracy of the result depends,
however, on the extent to which systematic errors can be excluded. We have carefully investigated possible sources of systematic error (magnetic 6eld of 6lament, magnetic contamination of parts, e8ect
of space charge on au„etc.} and we believe that the true ratio,
uncorrected for diamagnetism, lies within the range:
ca,/co„= 657.4?5~0.008.
' The diamagnetic correction to the field at the proton is 1.8 X 10 ~
in the case of atomic hydrogen. If we apply the same correction
here, the proton moment, on Bohr magnetons, becomes:
' p = (1.52100&0.00002}X 10 '(eh/2':).
This is to be compared with the result (1.52106&0.00007) X10
obtained by Taub and Kusch. s The agreement may be regarded as further con6rmation of the correction&' to the spin-moment of the electron, for our experiment amounts to a comparison of the
orbital g-factor (e very large)) of the electron with the proton
g-factor, whereas Taub and Kusch compared the proton g-factor
and the g-factor of a ~5~ state, applying the factor 2(1+a/2~) to
obtain the number just quoted.
' Our result, like that of Taub and Kusch 3 can be combined with
the absolute ys, measured by Thomas, Driscoll, and Hippie, to yield e/mc, and with cE and the hydrogen h.f.s. splitting' to
yield a. The accuracy of e/mc is still limited by the uncertainty in y~. The value of a is improved to the point where the present
uncertainties in c and in the theoretical formula become important.
~ Assisted by the Joint Program of the ONR and the AEC. I Bloembergen, Purcell, and Pound, Phys. Rev. 73, 679 f1948).
'k W. E. Lamb, Jr., Phys. Rev. 60, 817 (1941). ~ H. Taub and P. Kusch, Phys. Rev. VS, 1481 (1949). 4 P. Kusch and H. M. Foley, Phys. Rev. 74, 250 (1948). k J. Schwinger, Phys. Rev. 73, 416 (1948).
4 Thomas, Driscoll, and Hippie, Phys. Rev. 75. 992 (1949).
7 J. F.. Nafe and E. B. Nelson, Phys. Rev. 73, 718 (1948).
Gamma-Radiation from Br82
KAI SIEGBAHN, ARNE HEDGRAN, AND MARTIN DEUTSCH+
.Vobel Institute for Physics, Stockholm, 5u,'eden
July 13, 1949
'HE y-radiation from Br~ has been re-examined in this
laboratory using higher resolution than in the previously pubhshed investigation. ~ The radiation was studied in a double-

I

C

FIG. 1. Internal conversion spectrum of Br".

focusing spectrometer (p=50 cm} with the resolution of the instrument set to ~one percent. The radiation was earlier thought
to consist of three p-rays of equal intensity emitted in cascade after a simple P-spectrum. The result of the present investigation show that the disintegration is more complicated. The spectrum is complex and there are seven &-rays of different intensities. We have found the photoelectron lines from a lead converter corresponding to these p-rays and also the internal conversion lines
E in the P-spectrum. The internal conversion spectrum (all lines)
is shown in Fig. 1.
The energies of the y-lines as obtained from the photo and
internal conversion line spectrum are given in Table I together
TABLE I. Energies of the y-lines as obtained from the photo
and internal conversion line spectrum of Br».

No. of y-ray

Hr. from secondary electron spectrum (Mev)
Hr. from internal conversion spectrum (Mev)
Relative intensities of the conversion lines

0.553
0.547 0.68

0.613
0.608 0.78

0.685
0.692 0.42

0.772
0.766 1.00

0.826
0.823 0.13

1.045
1.031 0.18

1.317
1.312 0.14

with the relative intensities of the corresponding internal conversion lines.
A complete description of the experiments is planned together with a discussion of the disintegration scheme.
+ On leave from Massachusetts Institute of Terhnology, Cambridge, Massachusetts.
I Roberts, Downing, and Deutsch, Phys. Rev. 60, 544 {1941).

The Transformation between One- and ThreeDimensional Power Spectra for an Isotropic Scalar Fluctuation Field

LFSLIE S. G. KOVASZNAY, MAHINDER S. UBEROI,
AND STANLEY CORRSIN
Department of Aeronautics, The Johns Hopkins University, Balti more, Maryland
September 2, 1949

W K should like to call attention to a mathematically simple result that may have some signi6cance in the (still unfor-
mulated) theory of the relative behaviors of vector and scalar quantities in the incompressible turbulent Bow of a continuum.
%. Heisenberg& has shown that in isotropic turbulence the one-
dimensional velocity po~er spectrum can be expressed in terms
of the three-dimensional power spectrum as follows:

f„(F( F (k ) =,

k)/ k)[1 —(k '/k')Qk,

(1)

j where
space

k is and

the magnitude of kI is a coordinate.

thTeheradpi1us—v(kepc/tkosr)

in the wave number factor arises from

the fact that the velocity spectral vector is always perpendicular

to the wave number vector (due to continuity), whereas FI(kI) is

proportional to the energy in a differential slab perpendicular to

the k» axis.