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When the hydrogen atom moves, the proton current generates a magnetic field which interacts with the hydrogen electron. A simple analyze shows that this interaction between the hydrogen momentum and the electron is of order of α 3 v c m, where α is the fine structure constant, v is the atom velocity, c is the speed of light, and m is the electron mass. Using the Bethe-Salpeter equation, the two velocity-dependent operators of this order are derived for the hydrogen velocity v c << α. As well known, the degeneracy of the energy levels with the same principal quantum number, n, and the same quantum number of the total angular momentum, j, but the different orbital angular momenta l = j ± 1/2 is removed by the radiative corrections (the Lamb shift) that are proportional to α 5 m. It is shown that the velocity-dependent perturbation interactions remove this degeneracy as well. There is, however, an important difference between the Lamb shifts and the energy-levels shifts induced by the atom motion. The Lamb shift is the diagonal correction to the energy separately for each of the degenerate states. The the velocity-dependent perturbation interactions result in the off-diagonal energy corrections between the mutually degenerate states. The joint effect of these two perturbations which are essentially different in their origin, is analyzed. Given their order of magnitude, the crossover from the Lamb shifts to the motion-induced shifts should occur at the atom velocity v = kα 2 c, where k >> 1 is a numerical factor depended on n and j. An experiment used the orbital motion of the Earth, is proposed to test the theory developed.Keywords: hydrogen-like atom; the energy-level degeneracy; the Bethe-Salpeter equation; the Lamb shift; atom-motion-induced shifts PACS numbers:03.65. Pm, 31.30.jf Here the α e matrix is used in the standard representation, the subscript e means the action of the Pauli matrices on the electron spin, and V (r) = − e 2 r is the Coulomb interaction between the electron and proton.

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Experimental determination of the magnetic moment of the Cooper pairs can shed light on the pairing symmetry in cuprates. We argue that the intrinsic magnetic moments of the Cooper pairs can be detected in experiments with superconducting thin-film rings. At sufficiently low temperatures the magnetic field generated by the supercurrent, can cause the ordering of these magnetic moments that produces changes in the supercurrent and magnetic induction distributions, the heat capacity and magnetic moment of the ring. It is shown that the intrinsic magnetic moment of the Cooper pairs can be extracted from low-temperature behaviours of these measurable quantities of the current-carrying rings made of the cuprate superconductors.

The approach in which the electron and positron are treated as ordinary, different particles, each being characterized by the complete set of the Dirac plane waves, is examined. This completely symmetric representation that is beyond the standard QED makes it necessary to choose another solution of the Dirac equation for the free particle propagator as compared to that used currently. The Bethe-Salpeter equation with these particle propagators is solved in the ladder approximation. A new solution has been found represented by the massless composite bosons formed by the coupled electron-positron pairs with the coupling equal to the fine structure constant. It has been demonstrated that (1) the massless boson states have normalizable complex wave functions which are transversely compressed plane waves; (2) the transverse radius of the wave functions diverges as the boson energy goes to zero; that is, the composite bosons cannot be at rest; (3) increasing the boson energy results in an extension of the transverse wave function in the momentum space and a corresponding contraction of the real space coordinate wave function. The new reaction e-e+→Bγγ is investigated with the products composed of the massless composite boson and two photons. The cross-section of this reaction is derived for nonrelativistic colliding beams of spin-polarized electrons and positrons. In this case the 2γ angular correlation spectrum is characterized by a narrow peak with the full-width-at-half-maximum not exceeding 0.2 mrad. It is shown that in order to distinguish between the conventional annihilation of the singlet electron-positron pair with the two-photon emission and the new examined reaction yielding the three particles, experiments are proposed with the extremely nonrelativistic colliding beams.

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