zotero/storage/7U8LTT3B/.zotero-ft-cache

LETTERS TO THE EDITOR

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FRACTION OF RANGE

Fia. 2. Feather plot for Ca&,

12,000 counts per minute, and the contribution due to

gamma-rays and other unabsorbed contaminants was less
than one part in 3000 with the strongest source, thus
indicating the absence of any appreciable amount of gamma-radiation. The absorption curve obtained with the
strongest source is shown in Fig. 1. The Feather plot, shown in Fig. 2, gives a range of 64+1 mg/cm'.
Glendenin' has shown that a reliable range-energy curve
for the low energy region can be derived from the data of Marshall and %'ard' for monoenergetic electrons and beta-

ray spectrograph data on low energy beta-emitters. Glen-

denin's curve is identical with that of Marshall and Nard

below 0.5 Mev. Using this range-energy curve, we have

found that the Ca~ beta-radiation has a maximum energy of 260+5 kev. %'e have found no evidence of any harder

— beta-radiation,
course of this

or of any investigation.

g'amma-radiation

at all in the

Ackeomledgesents. This work has been supported with

funds from the Office of Naval Research. The authors wish

to express their appreciation to Miss Jacqueline Becker for

her assistance in making the counts.

~%'alke, Thompson, and Holt, Phys. Rev. 5V, 171 (1940).

~ Solomon. Gould, and Anlnsen, Phys. Rev. 2'2, 1097 (1947).

~ Feather, Proc. Camb. PhiL Soc. 35, 599 (1938).
' Glendenin, Nucleonics, in press for January, 1948. J. ~ Marshall and Ward, Can. Research 15, 29 (i939).

~ This result Redioiwtopes,

CisekianbggooaIdsdagIr'rekeemeJnitsfwNitoh.

a value of
Z, revised

250 kev. given in September, 1947,

distributed, by Isotopes Branch, United States Atomic Energy Commis-

sion. Uafoftunately, the Atomic Energy Commission's result is not

supported by any published experimental evidence.

On Quan&~m-Electredyne~Ics and the
Mgnetlc Moment of the Electron
Jm.net ScawtNGER
Heroerd Ueisersigy, Cnmbridgc, Massachusetts December 30, 1947
TTEMPTS to evaluate radiative corrections to elec-
tron phenomena have heretofore been beset by divergence difficulties, attributable to self-energy and vacuum polarization effects. Electrodynamics unquestion-
ably requires revision at ultra-relativistic energies, but is presumably accurate at moderate relativistic energies. It would be desirable, therefore, to isolate those aspects of the
current theory that essentially involve high energies, and are subject to modification by a more satisfactory theory, from aspects that involve only moderate energies and are thus relatively trustworthy. This goal has been achieved by transforming the Hamiltonian of current hole theory electr&ynamics to exhibit explicitly the logarithmically divergent self-energy oF a free electron, which arises from

the virtual emission and absorption of light quanta. fhe

electromagnetic self-energy of a free electron can be

ascribed to an electromagnetic mass, which must be added

to the mechanical mass of the electron. Indeed, the only

meaningful statements of the theory involve this combina-

tion of masses, which is the experimental mass of a free
electron. It might appear, from this point of view, that

the divergence of the electromagnetic mass is unobjection-

able, since the individual contributions to the experimental

mass are unobservable. However, the transformation of the

Hamiltonian is based on the assumption of a weak inter-

action between matter and radiation, which requires that

the electromagnetic mass be a small correction ( (8/Ac)mo) to the mechanical mass mo.

The new Hamiltonian is superior to the original one in

essentially three ways: it involves the experimental elec-

tron mass, rather than the unobservable mechanical mass;

an electron now interacts with the radiation 6eld only in

the presence of an external field, that is, only an accelerated

electron can emit or absorb a light quantum;~ the inter-

action energy of an electron with ah external field is now

subject to a fixate radiative correction. In connection with

the last point, it is important to note that the inclusion of

the electromagnetic mass with the mechanical mass does

not avoid all divergences; the polarization of' the vacuum

produces a logarithmically divergent term proportiona1 to

the interaction energy of the electron in an external field.

However, it has long been recognized that such a term is

equivalent to altering the value of the electron charge by a

constant factor, only the final value being properly identi-

fied with the experimental charge. Thus the interaction

between matter and radiation produces a renormalization

of the electron charge and mass, all divergences being

contained in the renormalization factors.

The simplest example of a radiative correction is that

for the energy of an electron in an external magnetic field.

The detailed application of the theory shows that the

radiative correction to the magnetic interaction energy

corresponds to an additional magnetic moment associated

with the electron spin, of magnitude bp/p, =($x)H/hc
=0.001162, It is indeed gratifying that recently acquired

expen'mental data con6rm this prediction. Measurements

on the hyperfine splitting of the ground states of atomic

hydrogen and deuterium' have yielded values that are

definitely larger than those to be expected from the directly

measured nuclear moments and an electron moment of one

Bohr magneton. These
by a smaB additional

discrepancies electron spin

camnagbneetaicccoumnotemdentf.or'

Recalling that the nuclear moments have been calibrated

in terms of the electron moment, we find the additional

moment necessary to account for the measured hydrogen
and deuterium hyper6ne structures to be bp/p, =0.00126 %0.00019and Spa/p, ~ 0.00131&00. 0025, respectively. These

values are not in disagreement with the theoretical predic-

tion. More precise conformation is provided by measure-

' ment of the g values for the sSy, sP~, and sPIg~ states of'
sodium and gallium. To account for these results, it is

necessary to ascribe the following additional spin magnetic
moment to the electron, 8g/p, =0.00118~0.00003.

LETTERS TO THE EDITOR

The radiative correction to the energy of an electron in a Coulomb 6eld wiB produce a shift in the energy levels of hydrogen-like atoms, and modify the scattering of elec-
trons in a Coulomb field. Such energy level displacements
' have recently been observed in the 6ne structures of hydro-
gen, deuterium, and ionized helium. s The values yielded by our theory differ only slightly from those conjectured by Bethe' on the basis of a non-relativistic calculation, and are, thus, in good accord with experiment. Finally, the 6nite radiative correction to the elastic s'cattering of electrons by a Coulomb 6eld provides a satisfactory termination to a subject that has been beset with much confusion.
A paper dealing with the details of this theory and its applications is in course of preparation.

+A classical non-relativistic theory of this type was discussed by

H. A. Kramers at the Shelter Island Conference, held in June 1947

J. under the auspices

t
D.

E. Nafe, E. Nagel,

E. R.

SBo..fJNutehlilesaonnN,,ataainondndalJI..AIR.ca.RdZaebamic,yhaPrhoiayfss,S, cRiPeehnvyc.es.s7.1R, e9v1.4

(1947); VZ, 971

(1947).

s G. Breit, Phys. Rev. 71, 984 (1947).However, Sreit has not correctly

drawn the consequences of his empiriml hypothesis. The e8ects of a

nuclear magnetic field and a constant magnetic 6eld do not involve

different combinations of p, and bla.

~ P. Kusch and H. M. Foley, Phys. Rev. 'N, 1256 (1947), and further

unpublished work.

4
s

JW..EE. .MLaacmkb,anJdr.Na.ndAuRst.erCn,.

Retherford, Phys. Rev.

Phys. Rev. V2, 241 VZ, 972 (1947).

(1947).

& H. A. Bethe, Phys, Rev. 72, 339 (1947).

Excitation Curves of (e, n); (I, 2n); (e, 3n)
Reactions on Silver
8. N. Gmosm. r.
Dcpertnccnt of Physks, Veiscrsity of California, Bcrkcky, California January 5, 1948
ILVER bombarded with e-particles from the 60-in.
cyclotron produces radioactive substances with the following three half-lifes: 65 min. , 5.2 hr. , and 2.7 d. All of these activities have been chemically attributed to indium
and have been assigned by mass-spectrograph separation
to In"' In'o', and In», respectively. Tendam and Bradt'
recently announced similar activities. Their assignment of 65-min. and 2./-d activities agrees with ours. The 23-min. activity found by them was not looked for in the present experiment.
The excitation curves for the isotopes reported above have been determined for a-energies up to 37 Mev and are
reproduced in Fig. 1. The abscissae give the energy in Mev, the ordinates the cross sections in arbitrary units. The
ordinate units are, ho~ever, the same for reactions leading to the formation of the same isotope. Evaluation of absolute cross sections has not yet been possible due to lack of knowledge regarding the efficiencies of the diferent radiations for the ionization chamber used.
From the 6gure it is seen that the 65-min. activity belonging to In»s (emitting positrons of 1.7 Mev), a product
of Ag'"{ot, e} reaction, has a threshold of 11 Mev. ~ The
yield after attaining a peak at 17.5 Mev drops rapidly to low values when the (a, 2n) process appears as a competing process. After attaining a minimum, the 65-min. activity again increases and does not reach saturation even at 37 Mev. Apparently this part of the curve is due to Ag"'(a, 3e}In»s. The sharpness of the peak at 1i'.5 Mev

is also interesting. The di8erence of 4 Mev between (e, n) and (a, 2e) thresholds is much smaller than that between
(a, 2e) and {a,3e) thresholds (~8 Mev}. This difference
seems to be due to the Coulomb barrier which cuts off the
production of any alpha-reaction below 11 Mev.
The 2.7-d activity belonging to In"' has a threshoM of
about 15 Mev, which is in agreement with that found by
Tendam and Bradt. ' This activity is produced by the Agi (a, 2n) process, and emits a p-ray of about 0.2 Mev (no positrons). After attaining a peak around 27 Mev, the
yield begins to drop and reaches about 16 percent of maximum at 37 Mev.
The 5.2-hr. period is produced by Ag"'{a, 2e)In'0' reac-
tion. The excitation cur ve is similar to the excitation curve
of In"', as is expected, since both are products of (n, 2n) reactions. The threshold of In'so is about 13.5 Mev, slightly lower than that of In'". At higher energies, how-
ever, the two curves dier widely. Instead of decreasing,
the 5.2-hr. curve goes on increasing even beyond 30 Mev, after which it drops slightly, the yield at 37 Mev being 80
percent of the maximum.
This suggests the production of a different isotope at
higher e-energies having a very similar half-life. A comparison with the Ag'os{a, 3n)In»s curve and with the Agis {a,2g}In'» curve suggests that this new activity is probably due to Ag's7{a, 3n}In«'. The possibility of its
being due to Ag'oo(a, 3n}In»o (an isomer of 65-min. period}
is ruled out by the fact that the threshold and low energy part of the curve is similar to the other (a, 2n} curve and
not to the (a, e) curve.
To verify this conclusion, two foils were bombarded, one
with 37-Mev alphas (foil 1) and the other with 20-Mev alphas (foil 2). The latter is not likely to have any In'Os in
it, while the former should mostly contain In'" with little In' '. The absorption curves for the radiations from the
two foils, corrected for In»', showed marked differences. Foil 1 showed a p-ray of about 0.65 Mev, whi1e foil 2 showed a y-ray of about 0.5 Mev. No positrons were
detected. These conclusions were also corroborated by

0 ln so tn (+In ?)

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30 Mcv 10

PEG. 1. The abscissa represents energy of the bombarding a-particles in Mev. The ordinate represents cross section in arbitrary units. The
curve with open circles represents the cross section for the formation of In~+. The one with crosses represents the cross section for the formation of In»o, while the curve with solid circles represents the cross section for the formation of In~os. and at the higher energies probably of Intos also.