The mass effects on two-dimensional relativistic fermions

We investigate chemical potential, internal energy and specific heat of ideal relativistic fermions in two spatial dimensions taking into account the finite mass effect and the finite carrier concentration. The results show that the heavy mass and low carrier concentration fermions trend to be non-relativistic. The light mass and high carrier concentration lead more relativistic behavior. For massless fermions, the total kinetic energy equals to a constant for a given density (n), which is a function of n^3/2. Meanwhile, the specific heat for massless fermions keeps the linear increasing behavior with temperature with constant slope rather than the slope of zero, which is deduced from the non-relativistic case.     

Special Relativity,the Source of Electron Deep Orbits

In this paper, we explicitly point out the reasons why Special Relativity must be considered as the source of electron deep orbits, and dominates their behavior. We show that the cause is the quadratic form of the relativistic expression of energy, and this clearly appears when we explicitly develop the relativistic Schrödinger equation and compare it with the non-relativistic one.     

Relativistic electron-phonon interaction

On the basis of a new relativistic one-particle equation it is possible to reformulate the problem of the relativistic electron-phonon interaction in terms of “oscillating rigid muffin-tins” such that it can be expressed as in the non-relativistic case. The improvement over the non-relativistic approximation is shown for lanthanum and tungsten.     

Quasiparticle relativistic G-matrix interaction

A quasiparticle G-matrix interaction has been constructed from a three-dimensional integral equation which is a relativistic generalization of the conventional non-relativistic Bethe-Goldstone equation. Relativistic dynamical effects have been discussed by comparing the relativistic and the conventional non-relativistic G-matrices. The Landau theory and, in particular, the quasi-particle current have also been discussed within the present relativistic formulation.

As an example of application, the quasiparticle relativistic G-matrix interaction has been used in the RPA calculation which includes 2p-2h processes.     

Friedel oscillations in a relativistic quantum plasma

The linear responce of a two-component plasma to a static test charge is analyzed at large distances from the impurity. The electrons are considered relativistic and degenerate and the ions classical and non-relativistic. The results show that the electrons give the principal contribution to the response, which is long ranged and characterized by the Friedel oscillatory behavior.     

Shape change in Hf,W and Os-isotopes: A non-relativistic Hartree-Fock versus relativistic Hartree approximation

We have investigated the ground-state structures of even-even Hf, W and Os isotopes within the framework of a deformed non-relativistic Hartree-Fock and a relativistic mean field formalism. A majority of the nuclei are predicted to be prolate in shape in the relativistic calculations. On the other hand, contrary to the relativistic results, we predict a shape change in a cyclic order in the non-relativistic calculations. However, in both the cases, the magnitude of the quadrupole deformation parameter agrees well with the experimental data. We also evaluated the hexadecapole deformation parameter for Hf, W and Os isotopes and irrespective of the shape change in quadrupole moments, we find a cyclic change in hexadecapole shape from positive to negative and vice versa in both the relativistic and non-relativistic formalisms.     

Non-relativistic approximations to the pion production operator in 4He(p,nπ+)4He

Various non-relativistic pion production operators are applied in the study of the ⁴He(p, nπ⁺)⁴He process. We compare their predictions with fully covariant calculations of the external emission graphs both for pseudovector and pseudoscalar coupling. It is found that the non-relativistic pion production operators cannot reproduce the relativistic results quantitatively, in particular for the pseudoscalar case. The simple static pion production operator gives agreement with the relativistic pseudovector results to within a factor three or four. Adding recoil terms to this static operator has a significant effect on the cross section but does not improve the agreement with the relativistic results. The implications of PCAC and the soft-pion theorem for the relativistic calculation are studied. The uncertainty in the cross section in the soft-pion approach is found to be considerably smaller than the difference between pseudovector and pseudoscalar results or between the relativistic pseudovector result and its non-relativistic approximations.     

类Na离子振子强度的相对论效应

 采用相对论和非相对论原子自洽场方法,计算了类Na离子（原子序数为11~92）的3s-np,3p-ns和3p-nd跃迁过程的激发能和光学振子强度;通过比较相对论与非相对论的结果,研究了M壳层电子的相对论效应随原子序数的变化规律。结果表明：对n=3的跃迁过程,相对论效应主要是影响激发能,对线强度(或跃迁矩阵元)的影响不重要;对于n>3的跃迁过程,相对论效应同时影响线强度和激发能,通常对线强度的影响更大。这些结果对惯性约束聚变和X射线激光研究中需要的不透明度参数计算有重要的参考意义。     

On negative refraction in electron optics

Negative refraction is investigated within the context of both relativistic and non-relativistic electron optics. In fact, starting from the de Broglie wave-particle dualism, the negative refractive index as a function of wavelength is determined for both relativistic and non-relativistic electrons. Comparison with photon optics is done. Negative refractive index averaged over both sufficiently small and sufficiently large wavelength ranges is found to be tending to minus unity and minus infinity, respectively. In addition, the sensitivity to wavelength of the negative refractive index is evaluated.     

Relativistic quantum similarities in atoms in position and momentum spaces

A study of different quantum similarity measures and their corresponding quantum similarity indices is carried out for the atoms from H to Lr (Z=1-103). Relativistic effects in both position and momentum spaces have been studied by comparing the relativistic values to the non-relativistic ones. We have used the atomic electron density in both position and momentum spaces obtained within relativistic and non-relativistic numerical-parameterized optimized effective potential approximations.     

Electronuclear sum rules

Generalized sum rules are derived by integrating the electromagnetic structure functions along lines of constant ratio of momentum and energy transfer. For non-relativistic systems these sum rules are related to the conventional photonuclear sum rules by a scaling transformation. The generalized sum rules are connected with the absorptive part of the forward scattering amplitude of virtual photons. The analytic structure of the scattering amplitudes and the possible existence of dispersion relations have been investigated in schematic relativistic and non-relativistic models. While for the non-relativistic case analyticity does not hold, the relativistic scattering amplitude is analytical for time-like (but not for space-like) photons and relations similar to the Gell-Mann-Goldberger-Thirring sum rule exist.     

Relativistic sum rule for the total binding energies of nuclei

A relativistic form of the Koltun sum rule is derived. The possibility that the neglected relativistic terms may account for the experimental failure of the non-relativistic form of the sum rule is discussed.     

Electronic structure of CsAu

Self-consistent non-relativistic and relativistic LMTO band structure calculations have been carried out for CsAu. In the non-relativistic model CsAu is a metal, whereas — in agreement with experiments — the relativistic calculations predict CsAu to be a semiconductor. The gap is not caused by the spin-orbit coupling. The importance of the core-like Cs-5s and Cs-5p states for the alloy formation is discussed, and charge distribution calculations are used to illustrate the ionic nature of the bonding.     

Relativistic lattice gas hydrodynamics

Non-relativistic cellular automata can model non-relativistic hydrodynamical flows. In this article we show that if the hopping occurs on a space-time lattice which is generated by discrete subgroups of the Poincaré group and if the collision rules embody the relativistic conservation laws, we can modelrelativistic flows. The simplest version of the relativistic model is formally isomorphic with the non-relativistic Hardy, de Pazzis and Pomeau (HPP) lattice model, provided we reinterpret the various quantities that appear there. This observation explains the non-Galilean invariant results of HPP.     

Lorentz Boosted Potential for a Two-Body System with Unequal Masses

We produce a Lorentz boosted two-body potential for particles of different mass that is phase equivalent to a given realistic non-relativistic two-body potential. The relativistic potential is related to the nonrelativistic potential using the Coester–Pieper–Serduke scheme, which ensures that the same scattering wave functions are obtained from the relativistic and non-relativistic potentials. This implies that the phase shifts are identical functions of the relative momentum. To construct the potential we use an iterative scheme that generalizes one that has been applied successfully to two-body systems with equal masses.     

电子与原子、离子碰撞过程的相对论效应

在玻恩近似下,建立了高能电子与原子、离于非弹性碰撞过程的相对论性理论计算方法,并以类Li等电子系列为例,阐明了电子与原子、离子非弹性碰撞过程的相对论效应.它包括:1.靶原子的相对论效应,它随原子序数的增加而增大.低z靶(如Li)的相对论效应可以忽略;对Au~(+76)靶的2_3—3p跃迁,广义振子强度相对论性计算值比相应的非相对论性值小27.1%.2.入射电子的相对论效应,它随入射电子能量的增加而增大.对高能入射电子,在特殊角度,要考虑广义振子强度横场项对微分截面的影响.在极端相对论情况下,如入射电子动能 关键词：     

A non-relativistic bandstructure calculation for silver

Preliminary results of a non-relativistic bandstructure calculation for silver are compared with the relativistic calculations of Christensen. It is concluded that it is not necessary to include relativistic effects as stated by Christensen, in order to obtain agreement with optical data.     

A Study of Electromagnetic Transition of △（1232） Resonance

Point form relativistic dynamics of relativistic quantum mechanics is employed to estimate the photon and electroproduction amplitudes of A(1232) resonance. Results are compared with the non-relativistic work, and the differences between the two frame works are discussed.     

Single-nucleon model of nucleus II

The paper solves the relativistic equations of motion of a single-nucleon model of the atomic nucleus. The nucleon moves in a central field which is given by a mixture of scalar, pseudo-vector and pseudo-scalar coupling. A comparison between the results and experiment and between the results and the non-relativistic theory of the shell model shows that the relativistic theory offers practically as much as the non-relativistic theory, although it differs both in the formal and physical aspects.In conclusion the authors thank M. Plchová for carefully performing the numerical calculations.