Subatomic Physics

146 Structure of Subatomic Particles
Figure 6.4: Fermi distribution for the nuclear charge density. c is the approximate half-density
radius and t the surface thickness.
4. The actual charge distribution is more complex than the two-parameter Fermi
distribution. In particular the density in the interior of nuclei is not constant
as assumed in Eq. (6.24); it can decrease or increase toward the center, as
shown in Fig. 6.5 for 40 Ca and 208 Pb. (9) These variations arise, primarily,
from shell structure effects; see Chapter 17. It is possible to extract the
charge distribution from the measured electron scattering cross section in an
almost model-independent manner (10) by writing the charge distribution as a
superposition of Gaussians,
ρ ∝
N�
i=1
�
2 (r − Ri)
Ai exp −
δ2 �
.
The charge distributions shown in Fig. 6.5 were obtained in this manner. (9)
5. Nuclei that have nonzero spins also possess magnetic moments; the distribution
of the magnetization can also be described by a form factor. Experimental
information about the magnetization density is obtained from large angle
(backward) (11,12) electron scattering.
The information given so far in this section provides a glimpse into the structure
of nuclei. Considerably more is known—finer details have been investigated, (9,13)
still higher momentum transfers have been studied with 4 and 10–20 GeV electrons,
particularly in the lightest nuclei, 2H, 3 He, 3 H. (12) In addition, inelastic scattering
10I. Sick, Nucl. Phys. A218, 509 (1974).
11S.K. Platchkov et al., Phys. Rev. C25, 2318 (1982); S. Auffret, Phys. Rev. Lett. 54, 649
(1985); T.W. Donnelly and I. Sick, Rev. Mod. Phys. 56, 461 (1984).
12R.G. Arnold et al., Phys. Rev. Lett. 35, 776 (1975); B.T. Chertok, Prog. Part. Nucl. Phys.,
(D.H. Wilkinson, ed.), 8, 367 (1982); P.S. Justen, Phys. Rev. Lett. 55, 2261 (1985); R.G. Arnold
et al., Phys. Rev. Lett. 58, 1723 (1987).
13J.M. Cavedon et al., Phys. Rev. Lett. 58, 1723 (1987).