Relativistic electrons

The topological (or Berry) phase [9,11,78] has been discussed in previous sections. The physical picture for it is that when a periodic force, slowly (adiabatically) varying in time, is applied to the system then, upon a full periodic evolution, the phase of the wave function may have a part that is independent of the amplitude of the force. This part exists in addition to that part of the phase that depends on the amplitude of the force and that contributes to the usual, dynamic phase. We shall now discuss whether a relativistic electron can have a Berry phase when this is absent in the framework of the Schrddinger equation, and vice versa. (We restrict the present discussion to the nearly nonrelativistic limit, when particle velocities are much smaller than c.)... 

C. B. Kellogg, An Introduction to Relativistic Electronic Structure Theory in Quantum Chemistry http //zopyros.ccqc.uga.edu/ kellogg/docs/rltvt/rltvt.html (1996). 

Free-Electron Lasers. The free-electron laser (EEL) directly converts the kinetic energy of a relativistic electron beam into light (45,46). Relativistic electron beams have velocities that approach the speed of light. The active medium is a beam of free electrons. The EEL, a specialized device having probably limited appHcations, is a novel type of laser with high tunabiHty and potentially high power and efficiency. 

The limitation of EELs is that they require a high-quaHty beam of relativistic electrons having low angular spreading and a small range of velocities. 

In a synchrotron, electrons are accelerated to near relativistic velocities and constrained magnetically into circular paths. When a charged particle is accelerated, it emits radiation, and when the near-relativistic electrons are forced into curved paths they emit photons over a continuous spectrum. The general shape of the spectrum is shown in Fig. 2.4. For a synchrotron with an energy of several gigaelectronvolts and a radius of some tens of meters, the energy of the emitted photons near the maximum is of the order of 1 keV (i.e., ideal for XPS). As can be seen from the universal curve, plenty of usable intensity exists down into the UV region. With suitable mono-... 

Rose, M. E., Relativistic Electron Theory, John Wiley and Sons, Inc., New York, 1961. 

Synchrotron radiation provides a convenient source of tunable VUV and SXR radiation. Natural synchrotron radiation, emitted by relativistic electrons, is linearly polarized in the plane of their orbit, which is traditionally the configuration used to collect the radiation. However, it is well known that the polarization becomes elliptical if observed above or below the plane of the orbit. 

Schwerdtfeger, P. (ed.) (2002) Relativistic Electronic Structure Theory. Part 1 Fundamentals, Elsevier, Amsterdam. 

Hess, B.A. (1986) Relativistic electronic-structure calculations employing a two-component no-pair formalism with external-field projection operators. Physical Review A, 33, 3742-3748. 

Theory a relativistic electrons-only theory for chemistry. Theoretical Chemistry Accounts, 116, 241-252 and references therein. 

Loucks, T.L. (1966) Relativistic Electronic Structure in Crystals. II. Eermi Surface of Tungsten. Physical Review, 143, 506-512. 

Show that, for f -decay with highly relativistic electrons, the decay rate is proportional to Qp 5 (the Sargent rule). 

Optical guiding in preformed plasmas has been extensively investigated in experiments mainly oriented to demonstrate the production of relativistic electrons in LWF-related schemes. Plasma channel formation has been pursued with a variety of means, ranging from the use of hydrodynamic and shock-wave... 

An Efficient Source of Relativistic Electrons for Medical Applications... 

Figure 2. (lb) Distribution function of the velocity for the relativistic electrons. (2b) Distribution functions of the observable frequencies. (3b) Most probable values of the observable frequencies as a function of b. (4b) Absolute minimal realization of most probable states of system. 

As is well known (Chirikov, 1979 Izrailev, 1990), the phase-space evolution of the norelativistic classical kicked rotor is described by nonrelativistic standard map. The analysis of this map shows that the motion of the nonrelativistic kicked rotor is accompanied by unlimited diffusion in the energy and momentum. However, this diffusion is suppressed in the quantum case (Casati et.al., 1979 Izrailev, 1990). Such a suppression of diffusive growth of the energy can be observed when one considers the (classical) relativistic extention of the classical standard map (Nomura et.al., 1992) which was obtained recently by considering the motion of the relativistic electron in the field of an electrostatic wave packet. The relativistic generalization of the standard map is obtained recently (Nomura et.al., 1992)... 

Rajagopal, A.K. 1978. Inhomogeneous relativistic electron gas. J. Phys. C Solid State Phys. 11 L943-L948. 

Within the Born-Oppenheimer approximation, the non-relativistic electronic Hamiltonian of an A-electron molecular system in the presence of an external potential can be written (in atomic units) as... 

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