Form Invariance and Noether Symmetries of Rotational Relativistic Birkhoff Systems

Under the infinitesimal transformations of groups,a form invariance of rotational relativistic Birkhoff systems is studied and the definition and criteria are given,In view of the invariance of rotational relativistic Pfaff-Birkhoff-D‘ Alembert principle under the infinitesimal transformations of groups,the theory of Noether symmetries of rotational relativistic Birkhoff systems are constructed.The relation between the form invariance and the Noether symmetries is studied ,and the conserved quantities of rotational relativistic Birkhoff systems are obtained.     

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.     

Collective Oscillation of Relativistic Electrons in Hot Plasma

The interactions between relativistic electrons in a hot plasma are analysed theoretically. By splitting the electron density fluctuations into the individual part and the collective part, we are concerned with the collective oscillation of the relativistic electrons resulting from the Coulomb interactions. Consequently, we derive the frequency of the hot plasma and the “Debye length“ with relativistic modification.     

Form Invariance and Noether Symmetries of Rotational Relativistic Birkhoff Systems

Under the infinitesimal transformations of groups, a form invariance of rotational relativistic Birkhoffsystems is studied and the definition and criteria are given. In view of the invariance of rotational relativistic PfaffBirkhoff D‘Alcmbert principle under the infinitesimal transformations of groups, the theory of Noether symmetries ofrotational relativistic Birkhoff systems are constructed. The relation between the form invariance and the Noethersymmetries is studied, and the conserved quantities of rotational relativistic Birkhoff systems are obtained.     

Current Filamentation and Resonant Transport of the Relativistic Electron Beam in Dense Plasmas

The transport of a relativistic electron beam in dense plasmas with a cold return electron current is examined by two-dimensional particle-in-cell simulation.The filamentation and coalescence of currents and related magnetic field patterns,caused by the electromagnetic-benm-plasma instability,are observed.In the later simulation time,the electrons of the relativistic electron beam are trapped into the potential wells of the wave excited by the instability,and transport resonantly with the wave.     

First Integrals and Integral Invariants of Relativistic Birkhoffian Systems

For a relativistic Birkhoflan system, the first integrals and the construction of integral invariants are studied. Firstly, the cyclic integrals and the generalized energy integral of the system are found by using the perfect differential method. Secondly, the equations of nonsimultaneous variation of the system are established by using the relation between the simultaneous variation and the nonsimultaneous variation. Thirdly, the relation between the first integral and the integral invariant of the system is studied, and it is proved that, using a t~rst integral, we can construct an integral invarlant of the system. Finally, the relation between the relativistic Birkhoflan dynamics and the relativistic Hamilton;an dynamics is discussed, and the first integrals and the integral invariants of the relativistic Hamiltonian system are obtained. Two examples are given to illustrate the application of the results.     

Theory of symmetry for a rotational relativistic Birkhoff system

The theory of symmetry for a rotational relativistic Birkhoff system is studied. In terms of the invariance of the rotational relativistic Pfaff－Birkhoff－D'Alembert principle under infinitesimal transformations, the Noether symmetries and conserved quantities of a rotational relativistic Birkhoff system are given. In terms of the invariance of rotational relativistic Birkhoff equations under infinitesimal transformations, the Lie symmetries and conserved quantities of the rotational relativistic Birkhoff system are given.     

Importance of Relativistic Effects for Intermediate-Z Elements： Photoionization Process of Excited Na

Using a modified R-matrix code, the fine-structure-resolved partial photoionization cross sections of excited Na （Z = 11） are calculated within the Breit-Pauli approximation. Our calculated energy levels of Na＋ and Na are in good agreement with the experimental values within 1% and the branching ratios of the J-resolved partial cross sections are consistent with the recent measurements within the experimental uncertainties. The agreements are impossible to be obtained without adequately taking into account the relativistic effects and the electron correlations together. Therefore, even for the intermediate-Z elements （e.g. Na with Z = 11）, the relativistic effects （mainly the spin-orbit interactions） should not be neglected.     

Density Dependence of the Detailed Spectral Line Effects on the Opacity of Astrophysical Abundant Elements： oxygen

A full relativistic detailed-level-accounting approach has been developed independently to deal with the detailed spectral line effects on the opacity of the third most abundant element in stars: oxygen. The atomic energy levels and the oscillator strengths of the radiative transitions between the energy levels are obtained by carrying out the full relativistic one-configuration Dirac-Fock calculations. The photoionization cross sections are obtained via an average atom scheme with a consideration for the splitting of the ionization threshold due to the ionization stages and the term-couplings. As an example, the spectra resolved opacities and the mean opacities of oxygen are calculated to show the importance of the detailed spectral line profiles with the density of the matter.     

First-Principles Calculations of Elastic Constants of Superconducting MgB2

The five independent elastic constants of superconducting MgB2 are obtained using the first-principles plane wave method with the new relativistic analytic pseudopotential of the Hartwigsen-Goedecker-Hutter (HGH) scheme in the frame of local density approximation. The dependences of bulk modulus on temperature and pressure are also obtained. It is suggested that the HGH-type pseudopotentials are successful in investigating the ground-state mechanical properties of any solids.     

High-order Effects of Symmetry Energy in Proton Fraction of Neutron Stars

Many theoretical methods, such as the non-relativistic Brueckner approach, relativistic Brueckner approach, variational many body, the relativistic mean field theory, non-relativistic many body theory and the quarkmeson coupling model, have been used to explore the properties of neutron stars. In the present work, we shall study the properties of neutron stars within the framework of Hartree-Fock theory using the extended Skyrme effective interaction[1]. Many theoretical studies indicate that the relation between the single nucleon energy and the relative neutron excess satisfies the parabolic law approximately when δ and density p is not too high, the δ^4 and higher-order terms of δ are negligible, we shall show the higher-order terms of symmetry energy are important in studying neutron stars.     

Noether‘s theorem of a rotational relativistic variable mass system

Noether‘s theory of a rotational relativistic variable mass system is studied.Firstly,Jourdain‘s principle of the rotational relativistic variable mass system is given.Secondly,on the basis of the invariance of the Jourdain‘s principle under the infinitesimal transformations of groups,Noether‘s theorem and its inverse theorem of the rotational relativistic variable mass system are presented.Finally,an example is given to illustrate the application of the result.     

Mei Symmetry and Lie Symmetry of the Rotational Relativistic Variable Mass System

The Mei symmetry and the Lie symmetry of a rotational relativistic variable mass system are studied. The definitions and criteria of the Mei symmetry and the Lie symmetry of the rotational relativistic variable mass system are given. The relation between the Mei symmetry and the Lie symmetry is found. The conserved quantities which the Mei symmetry and the Lie symmetry lead to are obtained. An example is given to illustrate the application of the result.     

New Types of the Lie Symmetries and Conserved Quantities for a Relativistic Hamiltonian System

For a relativistic Hamiltonian system,two new types of the Lie symmetries and conservation laws are given under infinitesimal transformaitons of groups.On the basis of the theory of invariance of the relativistic Hamiltonian equations under infinitesimal transformations and introducing infinitesimal transformations for time t,generalized coordinates qs and generalized monenta ps,we obtain the determinging equations,the structure equations and the conserved quantities of the Lie symmetries.Introducing infinitesimal transformation for generalized coordinates qs and generalized momenta ps,we construct the Lie symmetrical transformations of the system,which only depend on the canonical variables.A set of conserved quantities are directly obtained from the Lie symmetries of the syste.An example is given to illustrante the application of the results.     

Study of the Lie symmetries of a relativistic variable mass system

The differential equations of motion of a relativistic variable mass system are given.By using the invariance of the differential equations under the infinitesimal transformations of groups,the determining equations and the restriction equations of the Lie symmetries of a relativistic variable mass system are built,and the structure equation and the conserved quantity of the Lie symmetries are obtained.Then the inverse problem of the Lie symmetries is studied.The corresponding Lie symmetries are found according to a known conserved quantity.An example is given to illustrate the application of the result.     

Relativistic density functional investigation of UX6（X=F,Cl,Br and I）

The molecular structures and the vibrational frequencies of uranium hexahalides UX 6(X=F,Cl,Br and I) molecules are investigated by using local density approximation(LDA) and generalised gradient approximation(GGA) functions(BP,BLYP and RPBE) in combination with two different relativistic methods(scalar and scalar+spin-orbit relativistic effects).The calculated results show that the differences are trivial between scalar and scalar+spin-orbit relativistic methods.The vibrational frequencies are also compared with existing experimental values,and overall,the RPBE approach gives the smallest error.The bond dissociation energies(BDEs) of UX 6 are computed by using the RPBE function,thereby obtaining exact vibrational frequencies.In addition,the calculated magnitudes of the spin-orbit effect on the BDE of UX 6(X=F,Cl,Br,and I) are found to be approximately-0.3198,-0.3218,-0.3609 and-0.4415 eV,respectively.     

Lie symmetry and Mei symmetry of a rotational relativistic system in phase space

The Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are studied. The definition, criterion and conserved quantity of the Lie symmetry and the Mei symmetry of a rotational relativistic system in phase space are given. The relation between the Lie symmetry and the Mei symmetry is found. An example is given to illustrate the application of the result.     

A new type of conserved quantity of Mei symmetry for relativistic nonholonomic mechanical system in phase space

In this paper, a new type of conserved quantity induced directly from the Mei symmetry for a relativistic nonholonomic mechanical system in phase space is studied. The definition and the criterion of the Mei symmetry for the system are given. The conditions for the existence and form of the new conserved quantity are obtained. Finally, an example is given to illustrate the application of the result.     

Relativistic effects on the back-to-back correlation functions of boson-antiboson pairs in high energy heavy ion collisions

We calculate the back-to-back correlation(BBC) functions of relativistic boson-antiboson pairs in high energy heavy ion collisions using the Monte Carlo method. The relativistic effects on the BBC functions of φφ and K~+K~- pairs are investigated. The investigations indicate that the relativistic effects on the BBC functions of K~+K~- pairs with large momenta are significant, and the effect is sensitive to the particle freeze-out temperature.