The Structure of Emission Lines

A method for obtaining the intensity distribution in a spectral line is derived from Dirac's quantum theory of the radiation field. The calculations are carried out for the case of emission from a first excited state (resonance line) and show that the intensity of frequency $\nu$ is, in this case, proportional to $\frac{1}{[4\mathrm{}{\pi }^2{({\nu }_0-\nu )}^2+{\left(A·2\right)}^2]}$ were $A$ is the rate at which atoms are leaving the upper state and ${\nu }_0$ is the frequency of the transition. The half-width is therefore $\frac{1}{2\pi }$ times the Einstein probability coefficient for spontaneous transition to the lower state. The more general case where the lower state has a finite life time is not treated.