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The calculations of Compton scattering for scalar particles and for electrons are standard examples found in many books; so is Mott scattering. A book with the calculation of a number of QED processes is J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons, Springer-Verlag (1955 & 1976).
Neutron scattering and Čerenkov radiation are included to show how the field theory can offer a vantage point of view for some processes which are usually calculated by other techniques. For scattering from a crystal, see J. Callaway, Quantum Theory of the Solid State, Academic Press (1974). The structure factor, which can be measured by neutron scattering, is useful in some condensed matter contexts, for example, Feynman’s theory of liquid Helium; see R.P. Feynman, Statistical Mechanics, Addison-Wesley Publishing Co. (1972).
The Frank-Tamm result on Čerenkov radiation is worked out classically in J.D. Jackson, Classical Electrodynamics, 3rd edition, Wiley Text Books (1998).
The decay of the neutral pion is included to illustrate how one may calculate with phenomenological Lagrangians. It was first calculated by J. Steinberger, Phys. Rev. 82, 664 (1949). The understanding of pion decay, especially appreciating its role as a Goldstone boson, is in terms of anomalies, calculated by S. Adler, Phys. Rev. 177, 2426 (1969); J. Bell and R. Jackiw, Nuov. Cim. 60A, 47 (1969). The effective Lagrangian is derived from this symmetry point of view.
The dominant decay mode of the ρ-meson is into two pions, not the mode we discuss. This calculation is given as another example of the use of a phenomenological Lagrangian. For ρ-γ mixing and vector dominance, see J.J. Sakurai, Currents and Mesons, University of Chicago Press (1969).
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(2005). Examples of Scattering Processes. In: Quantum Field Theory. Graduate Texts in Contemporary Physics. Springer, New York, NY. https://doi.org/10.1007/0-387-25098-0_7
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