Subatomic Physics 572, Final

This final is a take home problem.

Consider elastic scattering of a relativistic electron from a proton. Show that the Rosenbluth cross section (M.N. Rosenbluth, Phys. Rev. 79 (1950) 615) can be written in the laboratory system (where the proton is at rest) as:

$$\frac{d \sigma}{d \Omega} = \sigma_{Mott} \frac{E^\prime}{E}... ...) + 2 (F_1(Q^2) + F_2(Q^2))^2 \tan^2 \theta/2\right] \right\}$$

where $F_1$ and $F_2$ are the Dirac and Pauli form factors, respectively, and

$$\sigma_{Mott} = \frac{\alpha^2}{4 E^2 \sin^4 \theta/2} \cos^2 \theta/2$$

is the Mott cross section for scattering of a relativistic electron in the Coulomb field of the proton (Mott, 1929).

Guidelines

1) Trace back the calculation done in class for scattering from a point-like spin $1/2$ particle.

2) The coupling $\gamma^\mu$ is now replaced by:

$$\Gamma^\mu = \gamma^\mu F_1(Q^2) + \frac{i \sigma^{\mu \rho} q_\rho}{2M} F_2(Q^2)$$

3) Write down the coordinates of all four-vectors in the reaction; write down the spinors for both the electron and proton, their normalizations, and their completeness relation.

4) Explain what is meant by elastic scattering

5) Explain the points in the calculation where we use the fact that the electron is relativistic

6) Explain where the spin of both the electron and the proton enters the calculation.

7) What would change by varying reference frame, by chossing e.g. the center of mass frame for the virtual photon-proton system?

8) Are we using time ordered perturbation theory in this calculation?