Subatomic Physics

172 Structure of Subatomic Particles
x f(x)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
x
Figure 6.22: Plot of parton distribution functions, f(x), times x, as a function of x for the proton.
From PDG.
we will discuss in more detail in Chapter 10. The decrease in the ratio of F2 for
0.2 � x � 0.7 is now known to be, at least in part, due to the binding of the nucleon
in the nucleus and the increase beyond x ≈ 0.7 is caused by the motion of these
bound nucleons (see Chapter 16). (58) Is this the complete explanation, or are there
subtle differences between a bound and free nucleon? Is a nucleon somewhat larger
(say ∼ 5%) in a nucleus than when free? Such questions have been raised and the
so-called EMC effect remains of keen interest, because it has not yet been fully
explained.
6.11 More Details on Scattering and Structure
The material in Sections 6.3–6.10 demonstrates that much information concerning
subatomic structure can be obtained from scattering experiments. Even a glance at
a differential cross section, without detailed computation, can reveal gross features.
As an example, the information contained in Figs. 6.3, 6.5, 6.11, and 6.13 is reproduced
schematically in Fig. 6.24. It highlights one difference between heavy nuclei
and nucleons: Typical heavy nuclei have well-defined surfaces; as in optics, interference
effects then produce diffraction minima and maxima in the differential cross
section. Nucleons, in contrast, do not have such surfaces; their density decreases
smoothly, and they do not show prominent diffraction effects.
The Scattering Amplitude In the present section, we shall treat scattering in
somewhat more detail than we have done before. A glance at any current book on
scattering (59) will show that the material presented here constitutes only a minute
58 D.F. Geesaman, K. Saito, and A.W. Thomas, Annu. Rev. Nucl. Part. Sci. 45, 337 (1995).
59 M. L. Goldberger and K. M. Watson, Collision Theory, Wiley, New York, 1964; R. G. Newton,
Scattering Theory of Waves and Particles, McGraw-Hill, New York, 1966; L. S. Rodberg and R. M.