Electron impact relativistic excitation 1s − 2p of hydrogen atom

Darwin wave functions, as a quasi-relativistic states describing the hydrogen atom, are used to calculate the differential cross section for inelastic excitation of 2p state hydrogen atom by electronic impact in various electron energy regions. The use of these wave functions gives interesting results so long as the condition Z/c ≪ 1 is verified. The incident and scattered electrons are described by a free Dirac spinor. Relativistic spin effects are taken into account explicitly via the spinorial part. The computed results, in the first Born approximation, are given and discussed by analogy with the non-relativistic regime and the relativistic 1s → 2s. They are also compared with some other available theoretical models and with the experimental results of Williams. The general rule of optically allowed and forbidden transitions is also respected