Line-breadths and the theory of magnetism

Abstract

The tradit ional start ing point for any discussion of line breadths is the simple collision theory of Lorentz (1). We can omit radiation damping, for it is un impor tan t in the microwave region. The Lorentz model is basically a harmonic oscillator subject to collisions of exceedingly short duration. At each such impact there is a sudden change in phase. I t is further assumed tha t there is no persistance o r ~ hang-over ~> in phase, so tha t after collision one value of the phase is as likely as another. (Actually, as shown by VAN VLEC~; and WEISSKOPF (2), the various phases should be weighted somewhat unevenly conforming to the Bol tzmann factor for the instantaneous v~lue of the energy in the applied field. The resulting corrections, however, introduce only terms in ]/(~+co0) rather than 1/(o~ O~o), and are of no importance near reso a ce. We shall omit them). The mathemat ica l ~nMysis for the Lo~entz model runs as follows. The differential equation for a harmonic oscillator subject to a periodic field