Ultrarelativistic Case Research Articles

Inverse scattering problem in the relativistic quasiclassical approximation

We apply the quasipotential approach of quantum field theory to solve the inverse scattering problem in the relativistic quasiclassical approximation. We obtain expressions for reconstructing the quasipotential from the phase shifts and consider both nonrelativistic and ultrarelativistic cases.

Negative absorption near a magnetized black hole: Black hole masers

The mechanism of the energy extraction from charged particles moving in the vicinity of black holes due to the negative absorption of electromagnetic waves is considered. It is shown that there exist a number of resonant frequencies for which the ring of particles circling in the equatorial plane of Kerr black holes amplifies the incident electromagnetic waves. The negative absorption coefficients are calculated both for non-relativistic and ultrarelativistic cases.

Radiative interaction of electrons in a light field

The interaction of electrons in an external light field of arbitrary intensity has been studied. The relative motion of the electrons' rotation centres is supposed to be slow. The adiabatic potential of particle interaction has been found for this case, the effects of retardation being taken into account. In a sufficiently strong field the difference from the Coulomb law of interaction may be rather essential. In particular, bound states may be created. The ultra-relativistic case of electron motion in a field has been considered in detail. The contribution to the light pressure due to collective effects has been found.

The ionisation equation in a relativistic gas

By deriving the relativistic form of the ionisation equation for a perfect gas it is shown that the usual Saha equation is valid to 3% for temperatures below one hundred million Kelvin. Beyond 109K, the regular Saha equation is seriously incorrect and a relativistic distribution function for electrons must be taken into account. Approximate forms are derived when only the electrons are relativistic (appropriate up to 1012K) and also for the ultrarelativistic case (temperatures greater than 1015K).

The rigidly rotating relativistic dust cylinder

The solution of van Stockum (1937) consists of a rotating dust interior, and three exterior metrics referring to different ranges of the mass per unit length. It has been stated in the literature that the exterior in static, but it is proved here that this is so only in the low-mass case. An examination of the Riemann tensor shows that van Stockum's spacetime is free from singularities and matter at radial infinity below a certain value of the mass per unit length. The ultrarelativistic case which has closed timelike lines, can occur at physically possible densities and radii.

The spectrum of synchrotron-transient radiation of a charged particle in plasma with random inhomogeneities

The radiation of a charge rotating in a circle with the constant velocity (in the external magnetic field) in the isotropic plasma with random inhomogeneities of the electron density has been considered. A general expression is obtained for the radiation intensity at thenth harmonic, which is a generalization of the known Shott formula. In the ultra-relativistic case the conditions are clarified under which the inhomogeneity effect on the form of the spectrum of radiation from a particle is essential. An asymptotic formula is derived for the spectral intensity in the region of sufficiently low frequencies. The mechanism of transient radiation in this case is shown to prevail over the synchrotron one.

The radiation wave zone

The criterion for the formation of a radiation wave zone of a charge moving in an arbitrary way is discussed. The appearance of a wave zone is investigated in detail for synchrotron radiation and radiation from a charge moving along a hyperbola. Special attention is given to the ultrarelativistic case.

Compressible Relativistic Flow

The governing equations of compressible relativistic flow are cast in a form suitable for treating the subsonic, transonic, and supersonic regimes by established aerodynamic techniques. Small disturbance solutions are found which are the relativistic generalizations of the well-known aerodynamic laws for these flows. A comparison of present results with the nonrelativistic solutions for pressure coefficient shows significant compressible-relativistic effects for all three flow regimes. In the supersonic regime, the character of the variation of pressure coefficient with Mach number is quite different for the relativistic and nonrelativistic cases. The ultrarelativistic case is found to represent the limit of the compressible-relativistic effect in the three flow regimes.

Bremsstrahlung and pair production of particles of spin [formula omitted

Bremsstrahlung and pair production for spin 3 2 particles are computed in the lowest perturbation theory approximation. THe ultrarelativistic case is considered in detail. The importance of small impact parameters is demonstrated. For a pure Coulomb nuclear field the cross sections are proportional to E 6, where E is the incident particle or proton energy. The effect of deviation of the nuclear electric field from that of a point Coulomb source is discussed.