Reduced mass and relativistic recoil

Reduction of the two-body electron-nucleus Schrodinger equation to center of mass coordinates leads to an equivalent one-body problem where the electron mass is replaced by the reduced mass fi — mM/(M -f m). The effect of this replacement is to scale the infinite-mass Rydberg constant by fi/m. The corresponding shift of energy from the infinite-mass value E i is 

The relativistic generalization of the above expression, which has been considered in Refs. [20-23] is difficult in as much as there is no proper relativistic two-body Hamiltonian. One starting point for the discussion of the relativistic electron-nuclear two-body problem is the effective Hamiltonisin 

This expression gives the dominant recoil corrections 

A further relativistic reduced mass correction obtained from QED was given by Lathrup et al. [24] and can be expressed as 

An additional radiative corrections that depends on the finite mass of the nucleus, referred to as a radiative recoil correction , was given in [25] and [26]. The leading terms in the radiative recoil correction are 

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