THEORETICAL DESCRIPTION OF QUANTUM BEATS OF RECOIL-FREE GAMMA-RADIATION

A classical optical theory is given for the phenomenon of -ray quantum beats observed by Perlow in a study of the Mössbauer effect of a frequency-modulated source. The intensity I(0-0,t) of the radiation from such a source transmitted through a resonant absorber is obtained as a function of 0-0 and t, where 0 is the frequency of an absorber resonance, 0 is the central frequency of the frequency-modulated source, and t is the laboratory time. An average is taken over the unobserved initial formation time of the excited nuclear state in the source. When viewed at fixed 0-0, the calculated intensity displays beats in the time spectrum, and when viewed at fixed t, the intensity shows dispersion at appropriate values of 0-0, responsible for the observed enhancement of intensity above background. The harmonic content of the quantum beats is calculated explicitly in the thin-absorber limit, and the observed linear variation about 0-0=0 of the ratio of Fourier components D1D2 is explained. The use of D1D2 to measure small frequency shifts is analyzed by a statistical comparison with the method of switching between steepest points of the line, as used in gravitational-red-shift measurements. The variances are comparable. The effect on I(0-0,t) of line broadening due to sample inhomogeneities is calculated for a Lorentz distribution of center frequencies in source and absorber, and a prescription is given for modifying the various terms in I(0-0,t) accordingly. Finally, the effect of a distribution of phase and amplitude of the motion of the vibrating source is discussed. © 1979 The American Physical Society.