Relativistic volume effect

It has been suggested by Brooks (1983) that the deviations from theory observed in Np and Pu may in part be explained by the relativistic volume effect (sect. 3.8). If there is a preferential occupation of the j = f band, there is a 7 = contribution to the pressure in eq. (54), which, in the limit where the spin-orbit interaction is much larger than the 5f bandwidth, vanishes for Mf = 6, i.e. between Pu and Am. It turns out that this limit is not realized in any of the metals Np, Pu or Am, but the effect is sufficiently large to cause deviations from Pauli theory. Even with spin-orbit interaction included, the calculated radii of Np and Pu are too low compared with experiments. The remaining deviation may be due to correlation effects not included in our one-electron scheme. Both Np and Pu are known to be nearly magnetic (Brodsky 1978), which indicates strong f correlations. An additional reason for the discrepancies might be found in the crystal structures. 

Vegard s law, magneto-volume and relativistic volume effects... 

Figure 60 also provides a good example of a large relativistic volume effect (sect. 3.6). The volumes evaluated from the equation of state calculated using the Dirac equation, display a minimum before the middle of the series, which arises from preferential filling of the (5/2 bands and their anti-bonding orbitals. However, the volume increase is too small compared with experiment, as for the elemental metals, and it is quite likely that relativistic effects - correctly treated in the Dirac equation, but in isolation - are suppressed by many-body effects. 

This paper reviews progress in the application of atomic isotope shift measurements, together with high precision atomic theory, to the determination of nuclear radii from the nuclear volume effect. The theory involves obtaining essentially exact solutions to the nonrelativistic three- and four-body problems for helium and lithium by variational methods. The calculation of relativistic and quantum electrodynamic corrections by perturbation theory is discussed, and in particular, methods for the accurate calculation of the Bethe logarithm part of the electron self energy are presented. The results are applied to the calculation of isotope shifts for the short-... 

K. Hirao. Ligand effect on uranium isotope fractionations caused by nuclear volume effects An ab initio relativistic molecular orbital study. /. Chem. Phys.,... 

F. A. Paipia, A. K. Mohanty, E. Qementi. Relativistic calculations for atoms self-consistent treatment of Breit interaction and nuclear volume effect. /. Phys. B At. Mol. Opt. Phys., 25 (1992) 1-16. 

General Equation of Motion. Neglecting relativistic effects, the rate of accumulation of mass within a Cartesian volume element dx-dy-dz must equal the sum of the rates of inflow minus outflow. This is expressed by the equation of continuity ... 

Second, using the fully relativistic version of the TB-LMTO-CPA method within the atomic sphere approximation (ASA) we have calculated the total energies for random alloys AiBi i at five concentrations, x — 0,0.25,0.5,0.75 and 1, and using the CW method modified for disordered alloys we have determined five interaction parameters Eq, D,V,T, and Q as before (superscript RA). Finally, the electronic structure of random alloys calculated by the TB-LMTO-CPA method served as an input of the GPM from which the pair interactions v(c) (superscript GPM) were determined. In order to eliminate the charge transfer effects in these calculations, the atomic radii were adjusted in such a way that atoms were charge neutral while preserving the total volume of the alloy. The quantity (c) used for comparisons is a sum of properly... 

The relativistic EOS of nuclear matter for supernova explosions was investigated recently [11], To include bound states such as a-particlcs, medium modifications of the few-body states have to be taken into account. Simple concepts used there such as the excluded volume should be replaced by more rigorous treatments based on a systematic many-particle approach. We will report on results including two-particle correlations into the nuclear matter EOS. New results are presented calculating the effects of three and four-particle correlations. 

Pulse radiolysis was modeled after flash photolysis. The time resolution of laser flash photolysis has always been better than for pulse radiolysis. There are multiple reasons for this effect. (1) Flash photolysis equipment is cheaper than electron accelerators so there have been many more practitioners of the art. (2) Photons do not repel each other so it is possible to focus a larger number of them in a small volume over a short time period than it is possible to do for electrons. (3) The velocity of relativistic electrons in a dense material is much higher than photons in the same material so sample thicknesses must be much thinner for pulse radiolytic experiments than for flash photolytic experiments, thus meaning that signals would be smaller. 

This volume is based on the work and the reports of the following members of the Schwerpunkt of the German Science Foundation (Deutsche Forschungsgemein-schaft) on Relativistic Effects in Heavy-Element Chemistry and Physics . 

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. 

This short historical introduction to relativistic electronic structure, and even more so the chapters that follow, illustrates a very alive and active field of research whose vigom is illustrated by the increasing number of publications in this field. Indeed, if in 1986 a single volume published by Pyykkp [2] was sufficient to list all the related publications on relativistic quantum theory (about 3 100) over a period of 70 years, the next 15 years required two more volumes to hold the list of almost 8 000 new articles or reviews devoted to this subject. Although inflation in publishing is a common feature of all fields of research, these figures clearly show the importance to take relativistic and QED contributions into account. The need to include relativistic effects in quantum chemical calculations has stimulated both conceptual and numerical developments to finally fulfil the wish of Dirac for "approximate practical methods"... 

In proceeding to the relativistic description of molecular systems, one would like to be able to draw on the advances and developments of the non-relativistic case. However, as we shall show, the relativistic formulation as well as the effects that this formulation place demands on the basis sets that are not necessarily satisfied by a simple transfer of the non-relativistic framework. The subject of our presentation here is therefore to describe the special features and requirements for basis sets to be used in relativistic calculations. As this volume will show, there axe numerous approaches to describing relativity for molecular systems. Here we shall relate our discussion to the conceptually simplest of these, the... 

Although the importance of relativistic effects for chemistry and physics of heavy elements is today generally acknowledged and their discussion even begins to be included in (quantum) chemical textbooks, a brief and incomplete outline of relativistic effects for atoms and some consequences for molecules will be given here. Several excellent review articles, besides the ones collected in this volume, focussing on relativistic effects exist [63-77]. 

A thermal red-shift in /S-Sn was first reported in 1960 [16]. A more accurate study in the range 3-6-90 K has taken into account the contributions due to relativistic time-dilation, temperature dependence of the chemical isomer shift from volume changes, and the effect of unresolved quadrupole asymmetry on the effective line position [208]. 

A basic, old idea of Chemistry is that only a few electrons of an atom or a molecule are directly relevant to its chemical properties. Another basic, newer idea of the Chemistry of heavy elements is that relativity is necessary for its understanding. While the first is a very powerful simplifying idea, the second one increases the complexity of prediction and analysis in Chemistry. The ability of Effective Core Potentials (ECPs) to be, at the same time, the computational realisation of the first idea, and a means to implement very good simplifications of the most rigorous equations of relativistic Quantum Chemistry, lead them to be as popular as they are nowadays. A deep insight into this is offered to the reader in the previous volume of this collection [1]. 

These problems can be solved if one starts from the (untruncated ) Foldy-Wouthuysen transformation for a free particle, the only case for which the transformation is known anal3d ically, and incorporates the effects of the external potential on top. Along these lines, the so-called Douglas-Kroll-HeB (DKH) method [61-64] is constructed which is probably the most successful quasi-relativistic method in wave function based quantum chemistry. No details will be given here since this topic has been extensively discussed in volume 1 [34] of this series. Meanwhile several density functional implementations exist based on the Douglas-Kroll-HeJ3 approach [39-45]. In recent years. 

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