A new result under weak and non-relativistic approximation from general theory of relativity

We have derived a metric field equation in the locally inertial coordinate system from Einstein's field equation considering the energy density of the moving particle with the approximations that the force field under which the particle is moving is weak and the velocity of the particle is non-relativistic. We study the motion of different microscopic systems using this metric equation and compared the results with the experimentally measured values and we find that the results are identical.

Spin 3/2 particle: Puali – Fierz theory, non-relativistic approximation

The relativistic wave equation is well-known for a spin 3/2 particle proposed by W. E. Pauli and M. E. Fierz and based on the 16-component wave function with the transformation properties of the vector-bispinor. In this paper, we investigated the nonrelativistic approximation in this theory. Starting with the first-order equation formalism and representation of Pauli – Fierz equation in the Petras basis, also applying the method of generalized Kronecker symbols and elements of the complete matrix algebras, and decomposing the wave function into large and small nonrelativistic constituents with the help of projective operators, we have derived a Pauli-like equation for the 4-component wave function describing the non-relativistic particle with a 3/2 spin.

Geometric aspects of certain second order differential systems in particle physics

We consider the problem of the spin 1 particle with anomalous magnetic moment in an external Coulomb field, in non-relativistic approximation. The structural stability of the extended second order ODE system is studied.

Relativistic Completion of Schrodinger’s Quantum Mechanics by the Ether Theory

One recalls that we have shown in our precedent publications that the ether is an elastic isotropic medium. One presents the exact equation and its non-relativistic approximation that govern the ether in presence of a Schwarzschild-Coulomb field to which is submitted a Par(m,e)  (particle of mass m  and of electric charge e ). We present the exact relativistic solution of this exact equation in the circular case. We prove that the Schrödinger equation is such a non-relativistic approximation, that is, is a particular case of the ether elasticity theory. One recalls that the Schrödinger equation was obtained by the use of operators and not from the theory of elasticity. It follows that this manner of obtaining this equation from operators is arbitrary and does not permit to obtain its complete relativistic form, but permits to reach absurd conclusions as, e.g., the cat that, at the same moment, is alive and dead. One shows then that other results ensuing from the Schrödinger equation are particular cases of the non-relativistic equation that governs the elastic ether, like for example: the Bohr-Sommerfeld condition, and the eigenstates function equation.

Expectation Values of the Neutral Chromium Radius

Neutral Chromium (Cr I) is an important element in many laboratory plasma applications. In this work, expectation values of the radius for Cr I are calculated. These atomic data are calculated with three different atomic codes: Cowan code using the Hartree–Fock Relativistic approximation, SUPERSTRUCTURE and AUTOSTRUCTURE codes using scaled Thomas–Fermi–Dirac–Amaldi potential. Relativistic corrections are introduced according to the Breit–Pauli approach. The 3 d 5 4 s , 3 d 4 4 s 2 , 3 d 5 4 d , 3 d 5 4 p and 3 d 4 4 s 4 p configurations are included to obtain the expectation values of radius of Cr I and compared with available data. The novelty of our work is to obtain new values of < 1 r > , < r > , and < r 2 > for the configuration of 4 p and 4 d and the values of < r 3 > for all orbitals configurations considered in this work.

Relativistic Rotation of the Rigid Body in the Rodrigues – Hamilton Parameters: Lagrange Function and Equations of Motion

The main purposes of this research are to obtain Lagrange function for the relativistic rotation of the rigid body, which is generated by metric properties of Riemann space of general relativity and to derive the differential equations, determining the rigid body rotation in the terms of the Rodrigues - Hamilton parameters. The Lagrange function for the relativistic rotation of the rigid body is derived from the Lagrange function of the nonrotation point of masses system in the relativistic approximation.

Absence of the Rashba Splitting of Au(111) Surface Bands

The electronic structure of Au(111) films is studied by means of relativistic DFT calculations. It is found that the twinning of the surface bands, observed in photoemission experiment, does not necessarily correspond to the spin-splitting of the surface states caused by the break of the inversion symmetry at the surface. The twinning of the bands of clean Au(111) films can be obtained within nonrelativistic or scalar-relativistic approximation, so that it is not a result of spin-orbit coupling. However, the spin-orbit coupling does not lead to the spin-splitting of the surface bands. This result is explained by Kramers’ degeneracy, which means that the existence of a surface itself does not destroy the inversion symmetry of the system. The inversion symmetry of the Au(111) film can be broken, for example, by means of adsorption, and a hydrogen monolayer deposited on one face of the film indeed leads to the appearance of the spin-splitting of the bands.

MRS2016: Rigid Moon Rotation Series in the Relativistic Approximation

The rigid Moon rotation problem is studied for the relativistic (kinematical) case, in which the geodetic perturbations in the Moon rotation are taken into account. As the result of this research the high-precision Moon Rotation Series MRS2016 in the relativistic approximation was constructed for the first time and the discrepancies between the high-precision numerical and the semi-analytical solutions of the rigid Moon rotation were investigated with respect to the fixed ecliptic of epoch J2000, by the numerical and analytical methods. The residuals between the numerical solution and MRS2016 in the perturbing terms of the physical librations do not exceed 80 mas and 10 arc seconds over 2000 and 6000 years, respectively.