First principles calculation of electronic properties and effective mass of zinc-blende GaN

Based on the first principle pseudopotential plane wave method, the electronic structure of zinc-blende semiconductor GaN is calculated. Using the relativistic treatment of valence states, the spin orbit splitting energy of valence band top near the center of Brillouin region is calculated. Based on the effective mass approximation theory, the effective mass of electrons near the bottom of the conduction band and the effective mass of light and heavy holes near the Γ point along the directions of [100], [110] and [111] are calculated. These parameters are valuable and important parameters of optoelectronic materials.

Relativistic Configuration-Interaction and Perturbation Theory Calculations of the Sn XV Emission Spectrum

Recently, there has been increased interest in developing advanced bright sources for lithography. Sn ions are particularly promising due to their bright emission spectrum in the required wavelength range. Cowan’s code has been used to model the emission; however, it has adjustable parameters, which limit its predictive power, and it has limited relativistic treatment. Here, we present calculations based on ab initio relativistic configuration-interaction many-body perturbation theory (CI-MBPT), with relativistic corrections included at the Dirac-Fock level and core-polarization effects with the second-order MBPT. As a proof of principle that the theory is generally applicable to other Sn ions with proper development, we focused on one ion where direct comparison with experimental observations is possible. The theory can also be used for ions of other elements to predict emissions for optimization of plasma-based bright sources.

Spin tensor and pseudo-gauges: from nuclear collisions to gravitational physics

The relativistic treatment of spin is a fundamental subject which has an old history. In various physical contexts it is necessary to separate the relativistic total angular momentum into an orbital and spin contribution. However, such decomposition is affected by ambiguities since one can always redefine the orbital and spin part through the so-called pseudo-gauge transformations. We analyze this problem in detail by discussing the most common choices of energy-momentum and spin tensors with an emphasis on their physical implications, and study the spin vector which is a pseudo-gauge invariant operator. We review the angular momentum decomposition as a crucial ingredient for the formulation of relativistic spin hydrodynamics and quantum kinetic theory with a focus on relativistic nuclear collisions, where spin physics has recently attracted significant attention. Furthermore, we point out the connection between pseudo-gauge transformations and the different definitions of the relativistic center of inertia. Finally, we consider the Einstein–Cartan theory, an extension of conventional general relativity, which allows for a natural definition of the spin tensor.

Relativistic Bondi accretion for stiff equations of state

ABSTRACT We revisit Bondi accretion – steady-state, adiabatic, spherical gas flow on to a Schwarzschild black hole at rest in an asymptotically homogeneous medium – for stiff polytropic equations of state (EOSs) with adiabatic indices Γ > 5/3. A general relativistic treatment is required to determine their accretion rates, for which we provide exact expressions. We discuss several qualitative differences between results for soft and stiff EOSs – including the appearance of a minimum steady-state accretion rate for EOSs with Γ ≥ 5/3 – and explore limiting cases in order to examine these differences. As an example, we highlight results for Γ = 2, which is often used in numerical simulations to model the EOS of neutron stars. We also discuss a special case with this index, the ultrarelativistic ‘causal’ EOS, P = ρ. The latter serves as a useful limit for the still undetermined neutron star EOS above nuclear density. The results are useful, for example, to estimate the accretion rate on to a mini-black hole residing at the centre of a neutron star.

An effective-gravity perspective on the Sun–Jupiter–comet three-body system

Within the solar system, approximate realizations of the three-body problem occur when a comet approaches a planet while being affected mainly by such a planet and the Sun, and this configuration was investigated by Tisserand within the framework of Newtonian gravity. The exact relativistic treatment of the problem is not an easy task, but this paper develops an approximate calculational scheme which computes for the first time the tiny effective-gravity correction to the equation of the surface for all points of which it is equally advantageous to regard the heliocentric motion as being perturbed by the attraction of Jupiter, or the jovicentric motion as being perturbed by the attraction of the Sun. This analysis completes the previous theoretical investigations of effective-gravity corrections to the Newtonian analysis of three-body systems, and represents an intermediate step towards relativistic effects on cometary motions.