Subatomic Physics

6.8. Inelastic Electron and Muon Scattering 161
6.8 Inelastic Electron and Muon Scattering
In inelastic scattering, the differential cross section is measured for electrons that
have lost a certain amount of energy to the target. The diagrams for elastic and
inelastic electron scattering from a proton are shown in Fig. 6.15. The interaction
between the electron and proton, or nucleus, is mediated by a photon, as in
Fig. 5.18. In elastic scattering, the final state is the same as the initial one and no
new particles are created. In inelastic scattering, excited nuclear states are reached
or additional particles are produced. For a nuclear target, a typical scattering spectrum
is sketched in Fig. 6.16. Several features stand out, an elastic peak, relatively
narrow resonances, a broad shoulder or resonance, and a continuum. The narrow
resonances correspond to excited states of the nucleus, which can be studied in
detail; (14,44) for example transition form factors can be obtained. The shoulder or
broad resonance is called a quasi-elastic peak; the name stems from its explanation
as elastic scattering from a single nucleon rather than the whole nucleus. In the
laboratory system, the recoil energy of the nucleus in elastic scattering is also the
energy loss, ν, of the electron
It is given by
Figure 6.15: Elastic and inelastic electron scattering.
ν = E − E ′ . (6.49)
ν = |q2 |
, (6.50)
2mA
where mA is the mass of the nucleus and q2 is the square of the four-momentum
transferred from the electron to the nucleus, (35)
q 2 = ν2
c2 − (p − p′ ) 2 = ν2
c2 − p′2 h , (6.51)
where p and p ′ are the electron momenta before and after the collision, respectively,
and p ′ h the momentum of the hadron after the collision, as shown in Fig. 6.15(a),
44 B. Frois, Annu. Rev. Nucl. Part. Sci. 37, 133 (1987).