1. See Pais 1986, 60–62 and 188–190.
2. See Pais 1986, 190–192, and Trigg 1971, Chap. 2. Rutherford’s model included an additional term for the shielding by the electrons which turned out to be negligible. For the Coulomb potential the calculation is found in every textbook of nuclear physics. Indeed, Rutherford had good luck with his prediction. Geiger and Marsden performed their scattering experiments with low energy α-particles of around 5 MeV and targets with high nuclear charges. The experiments were sensitive neither to deviations from Rutherford’s formula due to strong interactions between the α-particles and the gold nucleus, nor to any quantum mechanical effects. For the Coulomb potential (and only for the Coulomb potential) the quantum mechanics of scattering results in the same formula; see Sect. 4.3.1.
3. Pais 1986, 408.
4. Pais 1986, 475–478.
5. S-matrix means scattering matrix. The calculation is made within the framework of the quantum theory of scattering. It is usually calculated in the Born approximation, that is, in the lowest order of perturbation theory. For high-precision measurements, higher-order corrections also come into play. The Feynman diagrams are in exact correspondence to the various mathematical terms of the calculations which describe superpositions of quantum theoretical contributions to the interaction. See Brown and Harr’e 1988, Falkenburg 2002a, Fox 2006, and Sect. 6.4.3.