Relativistic Mass of Gravitational Field

It is discovered that the gravitational field on the surface of a neutron star is with a relativistic mass density of 2.65*1016~5.87*1018kgm-3 which can be larger than the mass density of the neutron star (~1017kgm-3). And, the total relativistic mass of the gravitational field of the Sun is ~107 times the mass of the Sun. For different stars, the relativistic mass of the gravitational field is larger as the mass density of the star is larger. In the Milky Way, the total relativistic mass of the gravitational fields is much larger than the total mass of the stars, planets and gas. And, the relativistic mass density of the observed strongest magnetic field is 2.17*108kgm-3. This discovery should be a new frame to understand the fundamental problem of physics.

Gravitational Field and Mass

It is extremely fascinating and astonishing that the gravitational field on the surface of a neutron star is with a relativistic mass density of 2.65*1016~5.87*1018kgm-3 which can be larger than the mass density of the neutron star (~1017kgm-3).Therefore, it is the author’s first intuitional imagining that this field could directly convert into mass. In so strong a gravitational field, electron and proton could be produced directly from graviton–photon collision. The gravitational field exists in everywhere in our universe. No vacuum that the region of a space is “empty” does exist. A particle is clearly always being acted on by the gravitational field. The quantum vacuum fluctuation and vacuum polarization need be re-understood with the interaction between photon and gravitational field. Therefore, the gravitational field is naturally one of the foundations of modern physics.

A study of elliptic biquaternionic angular momentum and Dirac equation

In this paper, we deal with the Dirac equation and angular momentum, which have an important place in physics in terms of elliptic biquaternions. Thanks to the elliptic biquaternionic representation of angular momentum, we have expressed some useful mathematical and physical results. We obtain the solutions of the Dirac equation with the help of Dirac matrices with elliptic biquaternionic structure. Then, we have expressed the elliptic biquaternionic rotational Dirac equation. This equation could be interpreted as the combination of rotational energy and angular momentum of the particle and anti-particle. Therefore, we also discuss the elliptic biquaternionic form of rotational energy–momentum and of the relativistic mass. Further, we express the spinor wave function by elliptic biquaternions. Accordingly, we also show elliptic biquaternionic rotational Dirac energy–momentum solutions through this function.

High-precision calculation of relativistic corrections for hydrogen-like atoms with screened Coulomb potentials

The first-order relativistic corrections to the non-relativistic energies of hydrogen-like atom embedded in plasma screening environments are calculated in the framework of direct perturbation theory by using the generalized pseudospectral method. The standard Debye-Hückel potential, exponential cosine screened Coulomb potential, and Hulthén potential are employed to model different screening conditions and their effects on the eigenenergies of hydrogen-like atoms are investigated. The relativistic corrections which include the relativistic mass correction, Darwin term, and the spin-orbit coupling term for both the ground and excited states are reported as functions of screening parameters. Comparison with previous theoretical predictions shows that both the relativistic mass correction and spin-orbit coupling obtained in this work are in good agreement with previous estimations, while significant discrepancy and even opposite trend is found for the Darwin term. The overall relativistic-corrected system energies predicted in this work, however, are in good agreement with the fully relativistic calculations available in the literature. We finally present the scaling law of the first-order relativistic corrections and discuss the validity of the direct perturbation theory with respect to both the nuclear charge and the screening parameter.

A Mathematical Modelling with Zakharov System for Langmuir Wave in Unmagnetized Plasma

In this article we present a discussion and overview of mathematical result of the self-focusing of a Langmuir wave which governs Zakharov system and has studied the self- focusing of a Langmuir wave following by Gaussian distribution. Langmuir wave propagates through uncharged plasma which governed by Zakharov systems. The phenomenon plays a vital role in the Dynamics. We present the article mathematical model with effect of Landou damping. Relativistic mass oscillation and ponderomotive force on electrons of the ionized plasma encouraged the Langmuir wave which resists the self-focusing effect when damping is ignored. The Beam radius gets narrow. when it further propagates considering the paraxial ray’s approximation, the self-focusing length Rn. It shows that characteristics of varying bandwidth distance of propagation in relativistic plasma.

Analytical method for calculating atomic structures based on the variational method for many-electron atomic structure in plasmas

Within the framework of the Hartree–Fock method and the irreducible tensor theory, we have proposed an analytic formula for calculating the nonrelativistic energies of many-electron atoms. The relativistic mass, the one- and two-body Darwin, the spin–spin contact interaction, and the orbit–orbit interaction corrections to the energies are considered to make the results more precise. The angular interactions and spin sums involved in the formula are worked out explicitly using the irreducible theory. A program based on the variational method is developed to calculate the wave functions and atomic structure properties. The energies of the 1sns 1,3S (n = 1–4) and 1snp 1,3P (n = 2–4) states of the exemplary ions Ar16+, Fe24+, and Kr34+ in both Debye plasma and quantum plasma environments are given. Moreover, we analyzed the evolution of plasma screening parameters and provided some rules for practical and rapid evaluation in plasma applications.

An alternative way to derive equation of relativistic mass

Till now we did see many derivations of equation of relativistic mass using various methods. In this article we are going to see an alternate method to derive the same

Approximate Relativistic Mass-Formulae for the Ground State Binding Energy of a Λ in Hypernuclei

The Dirac equation with potentials having attractive and repulsive parts is con­ sidered in a simplified model and approximate semiempirical mass formulae for the ground state binding energy of a Λ in hypernuclei are derived and discussed.