Coupling constant 0 electrodynamics

A systematic development of relativistic molecular Hamiltonians and various non-relativistic approximations are presented. Our starting point is the Dirac one-fermion Hamiltonian in the presence of an external electromagnetic field. The problems associated with generalizing Dirac s one-fermion theory smoothly to more than one fermion are discussed. The description of many-fermion systems within the framework of quantum electrodynamics (QED) will lead to Hamiltonians which do not suffer from the problems associated with the direct extension of Dirac s one-fermion theory to many-fermion system. An exhaustive discussion of the recent QED developments in the relevant area is not presented, except for cursory remarks for completeness. The non-relativistic form (NRF) of the many-electron relativistic Hamiltonian is developed as the working Hamiltonian. It is used to extract operators for the observables, which represent the response of a molecule to an external electromagnetic radiation field. In this study, our focus is mainly on the operators which eventually were used to calculate the nuclear magnetic resonance (NMR) chemical shifts and indirect nuclear spin-spin coupling constants. 

The conference was closed with some general comments by Niels Bohr on the present state of atomic physics in which he referred to the satisfactory situation in quantum electrodynamics, but pointed out that the adimensional coupling constant... 

This discussion of the hyperfine splitting of the hydrogen isotopes was still affected by some uncertainty originating in part from the inaccuracy in the value of the electrodynamic coupling constant a. 

The point we will mainly focus on in this contribution is the coupling constant Za of the electromagnetic nuclear-electron interaction. As a 1 /137, for light nuclei the coupling constant allows a perturbation expansion for all quantum electrodynamical processes under consideration. For heavier nuclei, this is no longer true, because Za approaches unity as Z approaches 137. Already for uranium Za = 0.67. A perturbation expansion in Za is therefore useless, and all quantum electrodynamical processes have to be calculated non-perturbatively, including all orders of Za. 

The leading quantum electrodynamic effects to be accounted for in electronic structure calculations are the radiative corrections known as electron self-energy interaction and vacuum polarization. For the energy of electronic systems, the latter is usually small compared to the former, but only the latter can be expressed in terms of an effective additive potential to be included in the electronic structure calculations. The total vacuum polarization potential can be expanded into a double power series in the fine structure constant a and the external coupling constant Za. The lowest-order term, the Uehling potential, can be expressed as [110-112] ... 

The values of the fundamental constants and the theory of quantum electrodynamics (QED) are cl< ely coupled. This is evident from the fact that the constants appear as parameters in the theoreticjd expressions that describe the physical properties of particles and matter, and most of these theoretical expressions are derived from QED. In practice, values of the constants are determined by a consistent competrison of the relevant measurements and theoretical expressions involving those constants. Such a comparison is being carried out in order to provide CODATA recommended values of the constants for 1997. This review describes some of the advances that have been made since the last set of constants was recommended in 1986. As a result of these advances, there is a significant reduction in the uncertainty of a number of constants included in the set of 1997 recommended values. 

The considerable distinctions between optical spectra of a metal nanostmcture and corresponding bulk metal appear due to surface modes (plasmon-polariton resonances) in nanoparticles and size dependence of their optical constants. In the case of partially-ordered nanoparticle arrays these effects are of the collective nature because of strong electrodynamic coupling. The theoretical approach for regarding... 

The role of the Maxwell pressure residting from a normal gas phase interfacial electric field that scales as /R in elongating the Uquid meniscus into a cylindrical microjet stracture can also be verified through a dynamic simulation in which the equations governing the coupled interactions between the hydrodynamics (Eqs. 1-3) and electrodynamics (Eq. 9) are solved simultaneously for a constant potential liquid meniscus in the longwave limit in axisymmetric polar coordinates (r,0,z), subject to the boundary conditions... 

So far we have neglected the fact that the levels a) and b) are not only coupled by transitions induced by the external field but may also decay by spontaneous emission or by other relaxation processes such as collision-induced transitions. We can include these decay phenomena in our formulas by adding phenomenological decay terms to (2.68), which can be expressed by the decay constant ya and yt (Fig. 2.17). A rigorous treatment requires quantum electrodynamics [2.23]. 

---