Second-order Doppler shift and zero-point motion

32 Second-order Doppler Shift and Zero-point Motion 

The existence of a relativistic temperature-dependent contribution to the chemical isomer shift was pointed out independently by Pound and Rebka [6] and by Josephson [7]. The emitting or absorbing atom is vibrating on its lattice site in the crystal. The frequency of oscillation about the mean position is of the order of 10 per second, so that the average displacement during the Mossbauer event is zero. However, there is a term in the Doppler shift which depends on v, so that the mean value r is non-zero. 

The relativistic equation [8] for the Doppler effect on an emitted photon gives the observed frequency v for a closing velocity v as 

Accordingly, there is a shift in the Mossbauer line given by 

The temperature dependence of this quantity is thus related to the molar heat capacity at constant pressure, Q, 

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SECOND-ORDER DOPPLER SHIFT AND ZERO-POINT MOTION 51... 

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