Energetics of free-atom recoil and thermal broadening

1 Energetics of Free-atom Recoil and Thermal Broadening 

Let us consider an isolated atom in the gas phase and define the energy difference between the ground state of the nucleus (E ) and its excited state (Ec) as 

The following treatment refers for simplicity to one dimension only, that in which a y-ray photon is emitted and in which the atom recoils. This simplification causes no loss of generality as the components of motion in the other two dimensions remain unchanged. If the photon is emitted from a nucleus of mass M moving with an initial velocity in the chosen direction x at the moment of emission (see Fig. 1.1), then its total energy above the ground 

The difference between the energy of the nuclear transition ( ) and the energy of the emitted y-ray photon (Ey) is 

The y-ray energy is thus seen to differ from the nuclear energy level separation by an amount which depends firstly on the recoil kinetic energy ( r = Mv ) which is independent of the velocity F, and secondly on the term Eo = MvVg which is proportional to the atom velocity F and is a 

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Energetics of free-atom recoil and thermal broadening. 

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