Relativistic signature

Equations (6.4) describe the balance between two unknowns - the fundamental tensor and the distribution of matter in a system of interest. Although the distribution function is not conditioned by the theory of relativity in any way, it assumes critical importance in deciding the appropriate space-time geometry in cosmological applications. This way the metric tensor is defined, not on the basis of relativistic considerations, but on Newtonian principles. Cosmological models arrived at in this way we consider non-relativistic, unless the metric tensor has the correct relativistic signature. To explain the reasoning we consider a few elementary models. 

EXO 0748-676, Cottam et al. (2002) have found absorption spectral line features, which they identify as signatures of Fe XXVI (25-time ionized hydrogenlike Fe) and Fe XXV from the n = 2 —> 3 atomic transition, and of O VIII (n = 1 —> 2 transition). All of these lines are redshifted, with a unique value of the redshift z = 0.35. Interpreting the measured redshift as due to the strong gravitational field at the surface of the compact star (thus neglecting general relativistic effects due to stellar rotation on the spectral lines (Oezel Psaltis 2003)), one obtains a relation for the stellar mass-to-radius ratio ... 

Abstract. We address the question of the importance of relativity in selected non-linear radiative processes to be observed when an atomic system is submitted to an intense radiation field. To this end, we report on recent results obtained in the theoretical analysis of the following processes i) two-photon transitions in high-Z hydrogenic systems, ii) laser-assisted Mott scattering of fast electrons, and iii) two-colour photoionisation spectra of atoms in the simultaneous presence of two ultra-intense laser fields. In each case, the signature of relativistic effects is evidenced. 

In the present paper, we have reported the results of very recent computations, either analytical or fully numerical, of the transition amplitudes and/or of the cross sections for different phenomena which are expected to be observed when atomic systems experience non-linear radiative processes in intense external fields. In each case, we have addressed the question of the relative importance of the effects of relativity and we have made explicit the conditions in which the signatures of relativistic effects and retardation could be evidenced. 

The experimentally observable effects of the linear relativistic Renner coupling are perturbations in the vibronic spectra of 11 states. Since zero-order energy levels which differ by one quantum of the bending mode, the effects are maximal for o). These perturbations have previously been observed in the Renner spectra of triatomic radicals, such as NCO, NCS and GeCH [40-42] and have been termed Sears resonances [42]. Another signature of the linear relativistic vibronic coupling is intensity transfer to vibronic levels with an odd number of quanta of the bending mode [43,44]. 

Needless to say, many-electron atoms and molecules are much more complicated than one-electron atoms, and the realization of the nonrelativistic limit is not easily accomplished in these cases because of the approximations needed for the description of a complicated many-particle system. However, the signature of relativistic effects (see, for example, Chapter 3 in this book) enables us to identify these effects even without calculation from experimental observation. Two mainly experimentally oriented chapters will report astounding examples of relativistic phenomenology, interpreted by means of the methods of relativistic electronic structure theory. These methods for the theoretical treatment of relativistic effects in many-electron atoms and molecules are the subject of most of the chapters in the present volume, and with the help of this theory relativistic effects can be characterized with high precision. 

The aim of this volume is twofold. First, it is an attempt to simplify and clarify the relativistic theory of the hydrogen-like atoms. For this purpose we have used the mathematical formalism, introduced in the Dirac theory of the electron by David Hestenes, based on the use of the real Clifford algebra Cl(M) associated with the Minkwoski space-time M, that is, the euclidean R4 space of signature (1,3). This algebra may be considered as the extension to this space of the theory of the Hamilton quaternions (which occupies an important place in the resolution of the Dirac equation for the central potential problem). 

Meanwhile, there is no just speed of light if we assume a violation of the relativity. There are many different effects instead. But still we can expect that non-relativistic physics would not change too much. The size of a piece of atomic bulk matter is basically determined by the non-relativistic Coulomb interaction and we can believe that comparing a non-relativistic distance and relativistic propagation of light we should have a clear signature. 

---