Precision determination of small energy shifts in Mössbauer spectroscopy

The accuracies of modulation techniques used in Mössbauer spectroscopy to measure small energy shifts between source and absorber line positions are compared. The methods considered are sinusoidal and constant-velocity Doppler modulation at low drive frequencies, and sinusoidal and square wave-shaped phase modulation at high drive frequencies. The use of the transient frequency region is also discussed. The analysis includes corrections due to inhomogeneous line broadenings and electronic absorption. The results depend strongly on the absorber thickness. In many cases high-frequency and transient methods lead to slightly smaller statistical errors than conventional methods. Experimental data from measurements with the isotope ${}_{}{}^{67}{}_{}{}^{}\mathrm{Zn}$ are in agreement with theoretical predictions. The relative energy resolution reached in the measurements is $\sim 3\times {10}^{-18\mathrm{}}$.