Photons, virtual

Virtual Photonics http //www.vpiphotonics.com/photonics home.php... 

The absolute values of the photoabsorption, photoionization, and photodissociation cross sections are key quantities in investigating not only the interaction of photons with molecules but also the interaction of any high-energy charged particle with matter. The methods to measure these, the real-photon and virtual-photon methods, are described and compared with each other. An overview is presented of photoabsorption cross sections and photoionization quantum yields for normal alkanes, C H2 + 2 n = 1 ), as a function of the incident photon energy in the vacuum ultraviolet range and of the number of carbon atoms in the alkane molecule. Some future problems are also given. 

Fast Electron Impact Dipole-Simulation Method (Virtual-Photon Method) and Comparison with Real-Photon Method... 

Brion and co-workers [14,22-25] have extensively used and applied such an experimental approach by using fast electrons as the virtual-photon source. Brion et al. [14,25] pointed out some expected characteristics of the use of synchrotron radiation in comparison with virtual photons in studies of the photoionization and photoexcitation of molecules, and clarified some necessary assumptions to virtual photons instead of real photons. It should be noted here, as described below, that these two methods, real- and virtual-... 

The two parts of this formula are derived from the same QED Feynman diagram for interaction of two electrons in the Coulomb gauge. The first term is the Coulomb potential and the second part, the Breit interaction, represents the mutual energy of the electron currents on the assumption that the virtual photon responsible for the interaction has a wavelength long compared with system dimensions. The DCB hamiltonian reduces to the complete standard Breit-Pauli Hamiltonian [9, 21.1], including all the relativistic and spin-dependent correction terms, when the electrons move nonrelativistically. 

According to QED an electron continuously emits and absorbs virtual photons (see the leading order diagram in Fig. 2.1) and as a result its electric charge is spread over a finite volume instead of being pointlike ... 

In the previous section we presented the semi-classical electron-electron interaction we treated the electrons quantum mechanically but assumed that they interact via classical electromagnetic fields. The Breit retardation is only an approximate treatment of retardation and we shall now consider a more consistent treatment of the electron-electron interaction operator that also provides a bridge to relativistic DFT, which is current-density functional theory. For the correct description we have to take the quantization of electromagnetic fields into account (however, we will discuss only old, i.e., pre-1940 quantum electrodynamics). This means the two moving electrons interact via exchanged virtual photons with a specific angular frequency u>... 

If we now set the frequencies of the exchanged virtual photon to zero, unm —> 0, i.e., if we neglect retardation effects, the energy expectation value reduces to... 

The amplitude contribution from the B(3> field occurs in a second-order process using the sum over all possible fluctuations of B(3> in the virtual photon that causes electron-electron interaction. The amplitude due to B(i) has an ultraviolet divergence [17] described by Crowell. This may be removed by regularization techniques. 

During the transition in any mass to masstime state by reaction of the mass with an observable photon, a myriad of tiny virtual photon interactions involving very tiny (AE)(At) components of size... 

There is no need to worry about the existence of the reciprocal in (4.4) as we are merely concerned with a bookkeeping method for obtaining the successive terms of the cumulant expansion. Nor do we have to worry about the dependence of K on t0, because we have seen that this dependence disappears as soon as t — t0 > tc. After this transient the fluctuations around are determined by A(t) alone and hence also their influence on the evolution of itself. In this regime, u moves surrounded by a cloud of fluctuations, not unlike an electron surrounded by its cloud of virtual photons. 

By that time, the theory of the interactions between electrons and photons had developed to the point where the electrostatic repulsion or attraction between electrically charged particles could be understood in terms of the exchange of photons between diem. In the lowest nontrivial approximation, it gave the Coulomb law for small velocities, The basic interaction was the emission and absorption of virtual photons by charged particles. 

How is this possible Consider the familial- electromagnetic interaction. Two charged particles can be imagined to interact electromagnetically by the emission of virtual photons that are continuously emitted and absorbed by the particles (i.e., exchanged). The Heisenberg uncertainty principle tells us that... 

The emission of a virtual photon by a charged particle violates the law of conservation of energy by the photon energy AE.) If this photon is traveling at the speed of light, it can travel a distance R such that... 

The energy operator considered above is an approximation, in which only the lowest terms of the correction for the retardation of the interaction are taken into account. More general is the formal quantum-electrodynamical interaction energy operator in the approximation of the exchange of one virtual photon [58]... 

These are produced by autoionization transitions from highly excited atoms with an inner vacancy. In many cases it is the main process of spontaneous de-excitation of atoms with a vacancy. Let us recall that the wave function of the autoionizing state (33.1) is the superposition of wave functions of discrete and continuous spectra. Mixing of discrete state with continuum is conditioned by the matrix element of the Hamiltonian (actually, of electrostatic interaction between electrons) with respect to these functions. One electron fills in the vacancy, whereas the energy (in the form of a virtual photon) of its transition is transferred by the above mentioned interaction to the other electron, which leaves the atom as a free Auger electron. Its energy a equals the difference in the energies of the ion in initial and final states ... 

Figure 5. Virtual photon loop correlated with B field fluctuation.

This term is then a sum over all possible fluctuations of the that couple to the virtual photon coupled to the electrons. This means that the propagator is of the form... 

Even if there is no electromagnetic field present, the vector potential exhibits fluctuations A = (4 ) + 84, so that even if there is only the vacuum, physics still involves this fluctuation. This is also seen in the zero-point energy of the harmonic oscillator expansion of the fields. So an electron will interact with virtual photons. If we represent all of these interactions as a blob coupled to the path of an electron, this blob may be expanded into a sum of diagrams where the electron interacts with photons. Each term is an order expansion and contributes... 

The interacting waves from myriads of charge centres constitute the electromagnetic radiation field. In particle physics the field connection between balanced charge centres is called a virtual photon. This equilibrium is equivalent to the postulated balance between classical and quantum potentials in Bohmian mechanics, which extends holistically over all space. 

In the case of an ionic crystal the interacting units are readily identified as cations and anions, which exchange virtual photons. The ions are formed by the transfer of valence electrons to the more electronegative partners. Only a small fraction of the valence density remains in interstitial space. The resulting closed-shell ionic spheres are prevented from interpenetrating by the exclusion principle. 

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