How does source temperature affect the energy of recoil-free gamma rays?

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In the context of the Mössbauer effect, the energy of a recoil-free gamma ray decreases as the source temperature increases.1

This phenomenon, known as the thermal red-shift, can be interpreted in two primary ways:

  • Relativistic Doppler Effect: It can be viewed as a second-order Doppler effect resulting from the mean square thermal velocity of the atoms within the solid lattice.1
  • Time Dilation: It can be interpreted as a direct demonstration of relativistic time dilation, where the moving atom acts as a clock that appears to slow down when viewed by a stationary observer.1

This thermal red-shift is significant in physics because it provides a direct experimental measurement of the mean square thermal velocity of atoms in a solid.1