Transitions

A derivation of Fermi’s golden rule is given: this is the interface into which matrix elements from theory can be slotted to provide a prediction testable by experiment. The example of the prediction of the 2p→1s decay in hydrogen is worked through in detail. Selection rules, spectral line shapes (Breit–Wigner and Gaussian) and broadening processes are explained. The formula for the experimental cross-section in terms of the matrix element is produced. The Born approximation is presented and applied to Rutherford scattering. Then the decay rate for allowed β‎-decays is calculated in Fermi’s model and fitted to the observed rates. Low energy s-wave scattering is analysed in terms of phase shift and scattering length. The example of cold alkali metal atom scattering (≤10−6eV) is treated in preparation for use later with gaseous Bose–Einstein condensates. Ramsauer–Townsend effect explained.