## Abstract

The dipole radiation emitted by an atom excited by a unidirectional electron beam has a non-uniform angular distribution which is simply related to the percentage polarization P of the radiation emitted perpendicular to the beam. P was first calculated using the Oppenheimer-Penney (O.-P.) theory. In this theory the probability of excitation of an upper quantum state and the probability of subsequent emission of a polarized photon from such a state are considered independently. P is finally expressed in terms of the cross-sections Q$_{|M_{L}|}$ for excitation of states of definite component of angular momentum along the direction of the electron beam. In general, P is dependent on detailed numerical calculations of Q$_{|M\|}$, but the selection rule $\Delta $M$_{L}$ = 0 removes this dependence at threshold. In the O.-P. theory allowance may be made for fine structure and hyperfine structure, but the theory is ambiguous when the f.s. or h.f.s. separations are comparable with the line width. A theory is therefore developed which is based on the calculation of the probability of a polarized photon being emitted by the complete system of atom+electron. The ambiguity of the O.-P. theory is removed by integration over line profiles, but the expressions reduce to O.-P. expressions when the f.s. or h.f.s. separations are much smaller or much larger than the line width. The Ly$\alpha $ line of hydrogen is an intermediate case for which the line widths and the h.f.s. separations are comparable. Assuming the validity of the Born approximation, a simple expression is obtained which allows the Q$_{|M_{L}|}$ to be calculated from the angular distribution of the scattered electrons. Theoretical predictions are compared with experimental results. For the Na D lines the predicted polarization is small enough to escape experimental detection. Polarizations observed by Skinner & Appleyard in 1927 for various Hg lines rise to maxima with decreasing electron energy, and then tend to values close to zero at threshold. These experimental results at low energies appear to be inexplicable in terms of the reactions considered, but if the polarization curve above the maximum is extrapolated to threshold, the theory and experiment are found to be in reasonable agreement. Further experimental work is thought to be desirable.