Darwin Foldy contribution

In the Breit Hamiltonian in (3.2) we have omitted all terms which depend on spin variables of the heavy particle. As a result the corrections to the energy levels in (3.4) do not depend on the relative orientation of the spins of the heavy and light particles (in other words they do not describe hyperfine splitting). Moreover, almost all contributions in (3.4) are independent not only of the mutual orientation of spins of the heavy and light particles but also of the magnitude of the spin of the heavy particle. The only exception is the small contribution proportional to the term Sio, called the Darwin-Foldy contribution. This term arises in the matrix element of the Breit Hamiltonian only for the spin one-half nucleus and should be omitted for spinless or spin one nuclei. This contribution combines naturally with the nuclear size correction, and we postpone its discussion to Subsect. 6.1.2 dealing with the nuclear size contribution. 

The general result for the nuclear charge radius and the Darwin-Foldy contribution for a nucleus with arbitrary spin was obtained in [9]. It was shown there that one may write a universal formula for the sum of these contributions irrespective of the spin of the nucleus if the nuclear charge radius is defined with the help of the same form factor for any spin. However, for historic reasons, the definitions of the nuclear charge radius are not universal, and respective formulae have different appearances for different spins. We will discuss here only the most interesting cases of the spin zero and spin one nuclei. 

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