Subatomic Physics

6.12. References 189
Some characteristic features stand out: an initial rapid drop, a shallow minimum,
and then a slower decrease in dσ/dt. These features can be understood with
Eq. (6.110). The first two terms, corresponding to single scattering, possess diffraction
peaks of widths ∝ 1/k, as expected from diffraction from a dark disk (see
Eq. 6.91.) In double scattering, each nucleon absorbs half the momentum transfer;
the corresponding diffraction width is larger. The first rapid drop-off is due
to single scattering; the double scattering dominates at larger values of t. The explicit
calculation of dσ/dt shows that scattering indeed explores the structure of a
nucleus. (76) As we shall discuss in more detail in Section 14.5, the two nucleons
in the deuteron are predominantly in a state with relative orbital angular momentum
L =0(s state), but there is a small admixture of angular momentum L =2
(d state) (Fig. 14.8). To obtain the good agreement exhibited by the solid lines,
this small d-state admixture (4–6%) is required; it washes out the deep interference
minimum between single and double scattering.
The technique described here for the deuteron has been used to explore the
structure of other nuclides. (69,77) It can also be applied if particles other than the
proton, for instance, pion or antiproton, are employed as probes. •
6.12 References
Results on elastic and inelastic electron scattering from nucleons and nuclei can
be found in a number of references: Electromagnetic Form Factors of the Nucleon
and Compton Scattering C.E. Hyde-Wright and K. de Jager, Annu. Rev. Nucl.
Part. Sci. 54, 217 (2005); Nuclear charge-density-distribution parameters from
elastic electron scattering, H.DeVries,C.W.DeJagerandC.DeVries,Atom.
Data Nucl. Data Tabl. 36, 495 (1987); B. Frois in Nuclear Structure 1985, (R.
Broglia, G. Hageman, and B. Herskind, eds) North-Holland, Amsterdam, 1985, p.
25; J. Heisenberg and H. P. Blok, Annu. Rev. Nucl. Part. Sci. 33, 569 (1983); D.
Drechsel and M. M. Giannini, Rep. Prog. Phys. 52, 1089 (1989).
The theory behind nuclear structure studies by electron scattering can be found
in T.W. Donnelly and J.D. Walecka, Annu. Rev. Nucl. Sci. 25, 329 (1975); and in
J.D. Walecka, Theoretical Nuclear and Subnuclear Physics, World Scientific, 2004.
In the present chapter, only one technique for determining the nuclear charge
distribution has been treated, namely elastic electron scattering. However, many
other approaches exist. Of particular importance is the observation of muonic X
rays. This topic is reviewed in the following publications: F. Scheck, Leptons,
Hadrons and Nuclei, North-Holland, Amsterdam, 1983; J. Hufner and C.S. Wu, in
Muonic Physics, (V.W. Hughes and C.S. Wu, eds) Vol. I, Academic Press, N.Y.,
1975, Ch. 3; also R.C. Barrett in the Appendix; Exotic Atoms. (K. Crowe, G.
Fiorentini, and G. Torelli, eds.), Plenum, New York, 1980.
76 M. Bleszynski et al., Phys. Lett. 87B, 198 (1979).
77 W. Czyz, Adv. Nucl. Phys. 4, 61 (1971).