Subatomic Physics

10.10. The Photon–Hadron Interaction: Real and Spacelike Photons 321
Figure 10.27: Energy dependence of σeff /σ for copper and dependence of σeff /σ on atomic number
at 60 GeV photon energy. [After D. O. Caldwell et al., Phys. Rev. Lett. 42, 553 (1979).]
Above a few GeV, however, the total cross section is no longer proportional to
A. (21) This shadowing effect is displayed in Fig. 10.27 as a plot of σeff/σ against
E. (22) σeff/σ is the ratio of the photo-production cross section of a nucleus of Z
protons and N neutrons to the sum of the individual cross sections of the constituent
nucleons. If the high-energy photons were to see all nucleons in a nucleus equally
well, σeff/σ would be unity. Fig. 10.27 shows that the ratio σeff/σ at 60 GeV
decreases markedly with increasing A; for a fixed A (Cu, A = 64), it decreases
steadily with increasing energy. To show that this experimental result provides
more evidence for the existence of a hadronic contribution to the photon, we shall
discuss the behavior of the two components, |γ0〉 and |h〉, separately. Consider first
the bare photon, |γ0〉. The mean free path of photons of about 15 GeV energy in
nuclear matter (an infinitely large nucleus) is about 600 fm. This number follows
with Eq. (2.17) from the values of the photon–nucleon cross section of Fig. 10.26,
σ ≈ 10 −2 fm 2 , and the nuclear density given in Eq. (6.28), ρn ≈ 0.17 nucleon/fm 3 .
Since the nuclear diameter of even the heaviest nucleus is less than 20 fm, bare
photons “illuminate” nuclei uniformly, and the contribution of the term c0|γ0〉 to
the cross section is proportional to A. The hadronic term, ch|h〉, produces two
contributions to the total cross section. As will be shown in Chapter 14, the cross
section for hadrons is of the order of 3 fm 2 ,andthemeanfreepathisabout2fm.
21 E. M. Henley, Comm. Nucl. Part. Phys. 4, 107 (1970); F. V. Murphy and D. E. Yount, Sci.
Amer. 224, 94 (July 1971); D. Schildknecht, hep-ph/0511090, published in Acta Phys. Polon.
B37, 595 (2006).
22 D. O. Caldwell, V. B. Elings, W. P. Hesse, G. E. Jahn, R. J. Morrison, F. V. Murphy, D. E.
Yount, Phys. Rev. Lett. 23, 1256 (1969); D. O. Caldwell et al., Phys. Rev. Lett. 42, 553 (1979);
N. Bianchi et al., Phys. Rev. C 60, 064617 (1999).