Electron Impact Broadening of Spectral Lines

Ion densities in electrical discharges and in stars are often determined by observing the widths of spectral lines emitted or absorbed. The Holtsmark theory, usually employed in the interpretation of the data, restricts itself to ions and ignores electron collisions, which are treated in a qualitative way. This paper describes a detailed theory of electron effects upon the Lyman alpha line.A convenient physical classification of the result is as follows. Electrons produce, first of all, what we have called a universal line effect, a broadening occurring regardless of the nature of the atomic transition. Its cause is the transfer of energy from the electrons to one or the other of the two atomic states via scattering. So far as the analogy is proper, this effect is what is sometimes called "second order Stark broadening." It forms the predominating feature when a linear Stark effect is absent.Secondly, electrons can enforce the optical transition by collisions of the second kind. This mechanism, called quenching, broadens the line. It alone has the property of reducing the intensity of the line under normal conditions.A third possible contribution to the line width results from polarization, the counterpart of a first-order Stark effect. It comes about if one of the atomic states (the upper in our example) is degenerate or nearly degenerate. The electron, while flying past the atom, can then induce transitions without much energy transfer, i.e., polarize the atom. A distinction is made between (a) polarization through induction of a temporary dipole moment and (b) polarization through reorientation of an atomic dipole already present by virtue of a neighboring ion. The first of these is a large effect; its calculation requires the removal of divergences which are ordinarily encountered in the matrix elements.The summary at the end of the paper contains numerical results on the broadening of L_α by these several agencies under conditions approximating the solar photosphere. They are all small in comparison with Holtsmark broadening by ions. But the example is unusual; in general the electron effects are far from negligible.