Subatomic Physics

6.5. Leptons Are Point Particles 151
directly into the ring. This method provides a gain in the number of stored muons
by a factor of about 10. The magnetic field in the storage ring is optimized for
uniformity. The results are sumarized in Table 6.2.
The second approach to the measurement of |g| −2, pioneered by Dehmelt
and his collaborators, (24) is based on a sophisticated form of a Zeeman experiment
and constitutes a triumph of experimental ingenuity. A single electron is
confined for weeks in a “trap” formed by a combination of a magnetic and an electric
quadrupole field (Penning trap). Electron and apparatus constitute an atom
with macroscopic dimensions that is called geonium, the earth atom. In the trap,
sketched in Fig. 6.8(a), the electron performs a motion that consists of three components
illustrated in Fig. 6.8(b): a cyclotron motion in the uniform magnetic field,
an axial motion in the electric field, and a magnetron motion in the combined
fields. Consider first an electron with spin down. The motion of this electron in
the magnetic field is quantized. The orbits shown in Fig. 6.8(a) and (b) can have
only energies allowed by quantization; the higher the energy the larger the radius.
The energy difference between any two Zeeman levels [Fig. 6.8(c)] is given by the
cyclotron frequency ωc, Eq. (6.34), as
�ωc =2µBB. (6.35)
The energy can, however, also be changed by flipping the spin. If the spin is
reversed from down to up, the corresponding energy change, indicated in Fig. 6.8(c)
is
�ωs = gµBB. (6.36)
By applying the proper rf field, transitions can be induced in which only the orbit is
changed, or in which spin and orbit both change. The resonance frequency is given
by ωc in the first case and by
ωa = ωs − ωc = (|g|−2)µBB
�
in the second case. The ratio of the two frequencies yields
ωa
=
ωc
(|g|−2)
. (6.37)
2
By measuring these frequencies accurately, the values of |g| −2 for the electron
and the positron were measured with extreme accuracy. (25,26) In Table 6.2, we list
24R.S. VanDyck, Jr., P.B. Schwinberg and H.G. Dehmelt in New Frontiers in High Energy
Physics, (B. Kursunoglu, A. Perlmutter, and L. Scott, eds) Plenum, New York, 1978, p. 159; P.
Ekstrom and D. Wineland, Sci. Amer. 243, 105 (August 1980); H. Dehmelt, in Atomic Physics,
Vol 7. (D. Kleppner and F. Pipkin, eds) Plenum, New York, 1981.
25R.S. VanDyck, Jr., P.B. Schwinberg, and H.G. Dehmelt, Phys. Rev. Lett. 38, 310 (1977); P.
B.Schwinberg,R.S.VanDyck,Jr.,andH.G.Dehmelt,Phys. Rev. Lett. 47, 1679 (1981); R.S.
VanDyck Jr., P.B. Schwinberg and H.G. Dehmelt, Phys. Rev. Lett. 59, 26 (1987); B. Odom et
al., Phys. Rev. Lett. 97, 030801 (2006).
26G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, and B. Odom, Phys. Rev. Lett. 97, 030802
(2006).