Subatomic Physics

6.6. Nucleon Elastic Form Factors 159
n
G
M
µ n G D
1
0.8
0.6
0.4
0 4 8
Q
12
2 [(GeV/c) 2 ]
n
G
E
0.1
0.08
0.06
0.04
0.02
0
0 0.5 1 1.5
Q 2 [(GeV/c) 2 ]
Figure 6.14: Magnetic (left) and electric (right) form factors for the neutron. Here we show
the magnetic form factor divided by the dipole formula. The magnetic form factor shows rough
agreement with the dipole formula for |q| 2 < 5(GeV/c) 2 . [See C.Hyde-Wright and K. de Jager,
Annu. Rev. Nucl. Part. Sci. 54, 217 (2004).]
represents the charge (magnetic) distribution. The contributions of charge
and magnetism are mixed in both GE and GM .
5. The distribution of electric and magnetic charges within the proton are significantly
different. Since GE falls faster with q 2 than GM theelectriccharge
is spread out more than the magnetic one.
6. If a certain property, for instance the charge, is described by a form factor G,
with G(0) = 1, then Eq. (6.20) shows that the mean-square radius for this
property can be found from the slope of G(q2 )attheorigin:
〈r 2 〉 = −6� 2
� 2 dG(q )
dq2 �
q2 . (6.45)
=0
From the dipole fit, Eq. (6.42), one obtains 〈r 2 E (proton)〉 ≈0.7 fm2 . However,
a more accurate estimation (38) yields 〈r 2 E (proton)〉 ≈0.8 fm2 . Nevertheless,
the mean-square radii are in the range
〈r 2 E (proton)〉 ≈〈r2 M (proton)〉
≈〈r 2 M (neutron)〉 ≈0.7 − 0.8 fm 2 . (6.46)
The estimate for the proton radius, given earlier in this section, by considering
virtual pions, qualitatively agrees with this value. The assumption that the
38 I. Sick, Phys. Lett. 576, 62 (2003).