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QED corrections in many-electron atoms

An effective Hamiltonian, that contains all QED corrections of the order ma aZY including radiative and nonradiative ones, was derived by Araki [48] and Sucher [49 for the helium-like atom. Later it was generalized to the N-electron atom [50]. [Pg.451]

The total relativistic and QED energy shift for many-electron atoms consists of two parts. The first part contains the Bethe logarithm and the other is the average value of some effective potential. Throughout the exact nonrelativistic (Schrddinger) wave functions for the many-electron atom are used. The energy shift is [50]  [Pg.451]

Here P — Pi and the summation is extended over the complete spectrum of nonrelativistic many-electron Hamiltonian. [Pg.451]

The following notations are used in Eq(204). The index 0 corresponds to the nucleus, the electrons are numerated by indices i. N. The nucleus coordinate is fo = 0 the electrons coordinates are fj. The interelectron distances are fjk = rj—fk the electron momenta are f = 1N). The nuclear momentum pb = P in the center of mass frame of reference. The masses of particles are denoted as M for the nucleus and m for the electrons p = mM/ m + M) is the reduced mass. The magnetic moments of the particles are denoted as fij. For the electrons i= I. .., N) are the anomalous magnetic moments  [Pg.452]

The notation l/r (a) = 0(r — a)/r is also used, where 9 r — a) is the step function, C is the Euler s constant. After averaging the potential U with the wave functions the limit a —+ 0 should be taken. The singularities with respect to a should cancel. [Pg.452]


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