Quantum electrodynamics nuclear mass

We will review here experimental tests of quantum electrodynamics (QED) and relativistic bound-state formalism in the positron-electron (e+,e ) system, positronium (Ps). Ps is an attractive atom for such tests because it is purely leptonic (i.e. without the complicating effects of nuclear structure as in normal atoms), and because the e and e+ are antiparticles, and thus the unique effects of annihilation (decay into photons) on the real and imaginary (related to decay) energy levels of Ps can be tested to high precision. In addition, positronium constitutes an equal-mass, two-body system in which recoil effects are very important. 

The spectrum of hydrogen and one-electron ions provides a direct test of bound-state quantum electrodynamics. Except for finite nuclear-size and mass (recoil)... 

There have been a number of recent reviews of hydrogenic systems and QED [9]-[12] these proceedings contain the most extensive and recent information. To calculate transition frequencies in hydrogen to an accuracy comparable with the experimental precision which has been achieved [3], it is necessary to take into account a large number of corrections to the values obtained using the Dirac equation. These include quantum electrodynamic (QED) corrections, pure and radiative recoil corrections arising from the finite nuclear mass, and a correction due to the non-zero volume of the nucleus. The evaluation of these corrections is an extremely challenging task. 

Positronium (e+e ) is a purely leptonic system, free of nuclear structure effects, but suffers from reduced corrections in the worst possible case of equal masses. This makes the system difficult to treat, since quantum electrodynamical calculations start from an infinite nuclear mass and treat reduced mass effects as a perturbation. 

In writing equation (4.6), we have assumed that the nuclei can be treated as Dirac particles, that is, particles which are described by the Dirac equation and behave in the same way as electrons. This is a fairly desperate assumption because it suggests, for example, that all nuclei have a spin of 1 /2. This is clearly not correct a wide range of values, integral and half-integral, is observed in practice. Furthermore, nuclei with integral spins are bosons and do not even obey Fermi Dirac statistics. Despite this, if we proceed on the basis that the nuclei are Dirac particles but that most of them have anomalous spins, the resultant theory is not in disagreement with experiment. If the problem is treated by quantum electrodynamics, the approach can be shown to be justified provided that only terms of order (nuclear mass) 1 are retained. 

All science is based on a number of postulates. Quanmm mechanics has also elaborated a system of postulates that have been formulated to be as simple as possible and yet to be consistent with experimental results. Postulates are not supposed to be proved-their justification is efficiency. Quantum mechanics, the foundations of which date from 1925 and 1926, still represents the basic theory of phenomena within atoms and molecules. This is the domain of chemistry, biochemistry, and atomic and nuclear physics. Further progress (quantum electrodynamics, quantum field theory, and elementary particle theory) permitted deeper insights into the structure of the atomic nucleus but did not produce any fundamental revision of our understanding of atoms and molecules. Matter as described by non-relativistic quantum mechanics represents a system of electrons and nuclei, treated as pointlike particles with a definite mass and electric... 

In a similar manner, explicitly correlated calculation of the l/r,ic expectation value leads to an absolute shielding constant for the helium atom of 59.9367794 ppm (Drake 2006) (the most accurate value obtained in a recent study including relativistic, quantum-electrodynamic, and nuclear mass effects is cne = 59.96743 ppm (Rudzifiski et al. 2009)). For all the rare-gas atoms the... 

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