Subatomic Physics

150 Structure of Subatomic Particles
Figure 6.8: (a) Penning trap—a combination of a magnetic field B and a cylindrical electric
quadrupole field. (b) Motion of an electron in the combined fields of the Penning trap. (c)
Magnetic energy levels of the electron in the trap.
spin and momentum pointing in the same or opposite direction, are injected into
a solenoidal magnetic field. In this field, the electrons move in circular orbits, and
their spins and momenta are observed after a large number of revolutions. If the g
factor were exactly 2, spin and magnetic moment of the outcoming electrons would
still be parallel, regardless of the time spent in the field B. The small anomalous
part a, however, causes a slightly different rotation for spin and magnetic moment.
After a time t in the field B, the angle α between p and J becomes
where
α = aωct, (6.33)
ωc = eB
mc
(6.34)
is the cyclotron frequency. If the product Bt is very large, α also becomes very large
and a can be measured very accurately. This method has been applied to electrons
and muons of both signs.
The linear field arrangement shown in Fig. 6.7 works well for electrons because
they are stable and reach the end of the coil after many turns even if they have a
small velocity. Muons, however, decay and it is desirable to use muons with large
velocity in order to gain flight time and distance [Eq. (1.9)]. The number of turns
of high-energy muons in a linear field is too small to achieve the desired accuracy.
The problem was overcome at CERN by replacing the linear by a circular field.
Pions of 3.1 GeV/c momentum were injected into a storage ring of 14 m diameter;
their decay in flight into muons produced polarized muons in the storage ring. With
such an arrangement, |g|−2 could be determined with great accuracy for muons of
both signs. (23) A more recent experiment at the Brookhaven National Laboraory
AGS uses the same energy pions, but the muons from their decays are injected
23 F.J.M. Farley and E. Picasso, Annu. Rev. Nucl. Part. Sci. 29, 243 (1979).