Subatomic Physics

158 Structure of Subatomic Particles
p
G /µp
M
1
10 -1
10 -2
10 -3
10
0 10 20 30 40
-4
Q 2 [(GeV/c) 2 ]
1.2
p p
µ pG / G
E M
1
0.8
0.6
0.4
0.2
0
0 2
4
6
Q 2 [(GeV/c) 2 ]
Figure 6.13: Left: Magnetic form factor for the proton plotted against the squared momentum
transfer |q| 2 . The different symbols correspond to different experiments. The ‘dipole’ function
–described in the text and shown as a continuous line– describes the GM data quite accurately
below |q| 2 ≈ 10 (GeV/c) 2 . Right: GE/GM . The distributions of charge and magnetism in the
proton are quite different. [See C.Hyde-Wright and K. de Jager, Annu. Rev. Nucl. Part. Sci.
54, 217 (2004).]
been significant progress using polarized electron scattering on polarized targets to
extract directly the ratio of the electric and magnetic form factors. The conclusions
are summarized in Fig. 6.13.
Some features of the nucleon structure emerge from these relations:
1. Nucleons are not point particles. For point particles, the form factors are
constant.
2. The proton charge distribution, although not acurately described by the dipole
formula, shows that nucleons are extended systems but do not have welldefined
surfaces.
3. The charge distribution is small within the neutron:
G n E ≈ 0. (6.43)
4. The proton and neutron magnetic form factors are roughly described by the
dipole formula, Eq. (6.42), so the radial distribution follows from Table 6.1 as
�
ρ(r) =ρ(0) exp − r
�
a
a = �
q0
=0.23 fm. (6.44)
One remark must be added: The Fourier transform used here is valid only for
small values of |q| 2 . For large values of |q| 2 , the proton that was initially at
rest recoils with a velocity approaching that of light, and GE (GM ) no longer