An Experiment on the Limits of Quantum Electro-Dynamics Page: 8 of 70
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where m0 is the rest mass of the electron; so qc.m.< E02 , with q and
E0 in Mev. A 10% experiment at 8-Bev laboratory energy could just detect
a cutoff length 1/A = 0.5 X 10-13 cm. In order to probe to a distance
(defined as A 1) small compared with a nucleon radius--say, 1/6 of
0.7 X 10-13 cm--we would require a 10% experiment at 1000 Bev.
(b) Electron-proton scattering. In this experiment, carried out
by Hofstadter and collaborators, the first-order diagram is similar to
that of M/ller scattering (Fig. I-2).
However, the mass of the proton lowers
q
the c.m. velocity, and allows q to
protonelectron
be much higher for a given E0. If we proton
make the same modification to the
virtual photon propagator as before,
Hofstadter's results can be written Feynma d.iar for e trn-
proton scattering.
measured =(r2)proton + (6/A ) = (0.8 X 10-13 cm).
Even if we assume the "true" charge radius of the proton to be zero, this
experiment limits A-1 to [(r2)measured /6] < 0.33 X 1013 cm. If we
guess [(r )proton ] - 0.4 x 10-13 cm, A~1 would be 0.29 x 10-13 cm.
As a measure of an upper limit on a cutoff for electrodynamics, Hof-
stadter's experiment is therefore equivalent to e-e scattering at about
20 Bev.
(C) Lamb shift. The agreement of existing theory with experiment
on the 1057-Mc splitting between the 2S1 and 2P1 levels in hydrogen is
2 2 -13
now within 0.2 Mc. An apparent proton size of 0.8 X 10 cm would cause
an 0.12-Mc shift in the 2S level, so the Lamb-Retherford experiment
limits A~1 to 0.5 x 10-13 cm or less.
(D) Ground state energy level in hydrogen. The diagram for this
is the same as for e-p scattering, and the same questions of interpreta-
tion arise in both experiments.
(E) Anomalous magnetic moment of the muon. Berestetskii, Krokhin,
and Khlebnilov3 have worked out an order-of-magnitude result. The factor
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Barber, W. C.; Richter, B.; Panofsky, W. K. H.; O'Neill, G. K. & Gittelman, B. An Experiment on the Limits of Quantum Electro-Dynamics, report, June 1, 1959; Stanford, California. (https://digital.library.unt.edu/ark:/67531/metadc865960/m1/8/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.