Relativistic effects in nuclear motions

Using the wave functions of the relativistic equivalent harmonic oscillator recently proposed, elastic electron scattering cross sections have been calculated in the Born approximation for helium and lead. Calculations have also been made with the non-relativistic isotropie oscillator wave functions. Comparison with high-energy electron scattering experiments shows that relativistic effects may be significant in a heavy nucleus like lead.     

相对论高次谐波的蒙特卡罗模拟

 根据相对论条件下的经典电磁辐射理论,采用蒙特卡罗计算方法对类氢离子在强激光场下辐射的高次谐波进行了模拟计算,获得了相对论领域内激光参数（频率、脉冲波形、强度等）对高次谐波影响的各种计算结果,并对结果进行了理论分析。     

On the thermodynamic properties of the quantum vacuum

Several thermodynamic relations for the vacuum state have been derived by assuming that it behaves like a relativistic perfect simple fluid. Unlike the usual fluids, the vacuum becomes hotter when it undergoes an adiabatic expansion (TV ⁻¹=const). A new Lorentz-invariant spectrum for the vacuum is also suggested which is compatible with the usual equation of statep=−ρ and the other thermodynamic constraints. Some cosmological consequences of these results have also been discussed.     

Au等离子体M带5f-3d跃迁的电子离子碰撞激发速率系数

电子离子碰撞激发速率系数在超组态碰撞辐射模型中真实模拟非局域热动力学平衡Au激光等离子体M带谱5f-3d跃迁中各种复杂电荷态离子的电离态特性(譬如离子的平均电离度,相对丰度和能级布居数)是必不可少的。基于准相对论多组态Hartree Fock方法和扭曲波玻恩交换近似,采用自编的扭曲波程序ACDW（9）和Fit(9),从头计算了Au等离子体M带5f-3d电子离子碰撞激发速率系数。结果表明：在“神光II”实验装置诊断的电子温度约2keV,电子密度约 6×1021cm-3范围内,这些电子离子碰撞激发参数有利于采用超组态碰撞辐射模型模拟Au的激光等离子体M带5f-3d细致谱的平均电离度和电荷态分布。     

Influence of a relativistic kinematics on s-wave KN phase shifts in a quark model

The I=1 and I=0 kaon-nucleon s-wave phase shifts have been calculated in a quark potential model using the resonating group method (RGM) and a relativistic kinematics. The spinless Salpeter equation has been solved numerically using the Fourier grid Hamiltonian method. The results have been compared to the non relativistic ones. For each isospin channel the phase shifts obtained are not so far from the non relativistic results.     

组态相互作用和相对论修正对类He离子双电子谱的影响

研究了组态相互作用和相对论修正对低Z(原子序数)及中等Z类He离子双电子谱的影响,使用准相对论及非相对论的Hartree-Fock自洽场方法计算了描写双电子伴线的原子参数。计算结果表明,(1)组态相互作用对类He离子双电子诺有显著影响;(2)对中等Z的类He离子,仅以能量微扰的形式计入相对论修正是不足够的,为了获得更加精确的计算结果,不仅要考虑相对论修正对单、双激发态能量的影响,而且要考虑该效应对径向波函数的影响。     

A Numerical Investigation of the Pinning Phenomenon in Quasi-Periodic Frenkel Kontrova Model Under an External Force

We derive the relativistic Vlasov equation from quantum Hartree dynamics for fermions with relativistic dispersion in the mean-field scaling, which is naturally linked with an effective semiclassic limit. Similar results in the non-relativistic setting have been recently obtained in Benedikter et al. (Arch Rat Mech Anal 221(1): 273–334, 2016). The new challenge that we have to face here, in the relativistic setting, consists in controlling the difference between the quantum kinetic energy and the relativistic transport term appearing in the Vlasov equation.     

Obliquely propagating quantum solitary waves in quantum‐magnetized plasma with ultra‐relativistic degenerate electrons and positrons

The oblique propagation of the quantum electrostatic solitary waves in magnetized relativistic quantum plasma is investigated using the quantum hydrodynamic equations. The plasma consists of dynamic relativistic degenerate electrons and positrons and a weakly relativistic ion beam. The Zakharov‐Kuznetsov equation is derived using the standard reductive perturbation technique that admits an obliquely propagating soliton solution. It is found that two types of quantum acoustic modes, that is, a slow acoustic mode and fast acoustic mode, could be propagated in our plasma model. The parameter that determines the nature of soliton, that is, compressive or rarefactive soliton, for slow mode is investigated. Our numerical results show that for the slow mode, the determining parameter is ion beam velocity in the case of relativistic degenerate electrons. We also have examined the effects of plasma parameters (like the beam velocity, the density ratio of positron to electron, the relativistic factor, and the propagation angle) on the characteristics of solitary waves.     

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.     

激光金等离子体的电子离子碰撞电离速率系数

电子离子碰撞电离过程在超组态碰撞辐射(SCROLL)模型中真实模拟非局域热动力学平衡(non-LTE)高Z材料Au激光等离子体M带谱5f-3d跃迁中各种复杂离子的电离态特性,诸如离子的平均电离度和电荷态分布是一个主要过程.基于准相对论扭曲波玻恩交换近似,采用组态平均的方法,从头计算了金M带类铁金离子-类锗金离子的电子离子碰撞电离速率系数,其中电离截面的高能行为由Bethe系数决定.结果表明:在"神光Ⅱ"实验装置诊断的电子温度～2keV,电子密度～6×1021cm-3范围内,这些参数有利于使用超组态碰撞辐射模型拟Au的激光等离子体M带细致谱5f-3d跃迁的平均电离度和电荷态分布.     

On the widths ofK levels of heavy elements

The ratios of the widths ofK levels of heavy elements with atomic number 70 to 92 have been calculated with relativistic wave functions, retardation, screening and field theoretical corrections to relativistic energy. The calculated values have been compared with the available observed data and good agreement has been obtained.     

Strong lensing of a regular black hole with an electrodynamics source

In this paper we have investigated the gravitational lensing phenomenon in the strong field regime for a regular, charged, static black holes with non-linear electrodynamics source. We have obtained the angle of deflection and compared it to a Schwarzschild black hole and Reissner Nordström black hole with similar properties. We have also done a graphical study of the relativistic image positions and magnifications. We hope that this method may be useful in the detection of non-luminous bodies like this current black hole.     

Relativistic energies and transition probabilities for some highly excited levels in singly ionized indium

For some excited levels (n?8), the energies, wavelengths, oscillator strengths and transition probabilities calculations in singly ionized indium have been calculated within the framework of multiconfiguration Hartree-Fock approximation with relativistic corrections (Breit-Pauli Hamiltonian). The wavefunctions and some relativistic corrections have been obtained using MCHF-BP atomic package. Comparisons with other calculations and experiments are presented.     

A generalized quantum kinetic equation for models of relativistic nuclear dynamics

Zubarev’s method of non-equilibrium statistical operator is applied to problems of relativistic kinetic theory. Within this method, a generalized relativistic quantum kinetic equation for the relativistic Wigner function is derived with taking into account the drift term of the Vlasov type and the collision integral of the second order in particle interaction. It is shown that this result holds as well for gauge invariant theories in the case of slowly changing fields. An advantage of the developed approach is exemplified by the consideration of relativistic nuclear matter within the Walecka and Nambu-Jona-Lasinio models. Typical relativistic effects like retardation, spin degrees of freedom and antiparticle evolution are taken into consideration.     

Classical tests of general relativity in the Newtonian limit of the Schwarzschild–de Sitter spacetime

Recently it has been shown that despite previous claims the cosmological constant affects light bending. In the present article we study light bending and the advance of Mercury’s perihelion in the context of the Newtonian limit of the Schwarzschild–de Sitter spacetime employing the special relativistic equivalence of mass and energy. In both cases, up to a constant factor, we find the same results as in the full general relativistic treatment of the same phenomena. These approximate and intuitive arguments demonstrate clearly what effects should have been expected from the presence of Λ in the general relativistic treatment of these phenomena.     

KⅧ—TbLⅣ离子3s3p 3P1—3s21S0 的自旋禁戒跃迁

在对KⅧ—TbLⅣ离子3s3p3P1能级结构的多组态相互作用理论HXR方法计算的基础上, 分析了各种效应对等电子序列离子能级结构的影响, 找出了能级沿等电子序列变化的规律性. 预测计算了KⅧ—TbLⅣ离子3s3p3P1的能级. 由此进一步计算了KⅧ—TbLⅣ离子自旋禁戒跃迁3s3p3P1—3s21S0的谱线波长、 振子强度和跃迁概率. We have calculated the energy levels of 3s3p3P1 for magnesium like sequence ions from KⅧ—TbLⅣ by HXR (Hartree Forck plus statistical exchange potential with relativistic corrections) method. With the important effects taken into account, we have made a systematic fit for the energy levels of the ions mentioned above. We predicted here the energy levels which have not been observed in experiments for ions from KⅧ to TbLⅣ.The wavelengths, oscillator strengths and probabilities of intercombination transitions 3s3p 3P1—3s21S0 are computed too.     

New representation for energy-momentum and its applications to relativistic dynamics

In this paper we introduce the concept counterpart of rapidity and define energy and momentum of the relativistic particle as functions of the counterpart of rapidity. Formulae of the relativistic mechanics defined in such a way are regular near the zero-mass and speed of light state. This representation admits to attain a correct limit of the formulae of the relativistic mechanics, including the Dirac equation, at zero-mass point and explains violation of the parity at this state. On the other hand, the representation for energy-momentum can be realized as a mapping from the massless state onto the massive one which looks like a “q deformation”. Hypothesis on quantization of the energy-momentum and the velocity near the light speed is suggested. The group of transformations using the counterpart of rapidity as a parameter of transformation is constructed.     

Isotopic production cross sections of residues in reactions induced by relativistic heavy ions with protons and deuterons

The isotopic production cross sections of heavy residues in relativistic heavy-ion collisions have been investigated in inverse kinematics. The primary reaction products were fully identified in mass and atomic number prior to beta decay using the fragment separator FRS. The huge collection of data obtained helps in the understanding of the two main reaction mechanisms involved: fragmentation and fission. These data provide basic information for future radioactive ion beam facilities and for technical applications like intense neutron sources by means of spallation targets.     

Time Asymmetry and Quantum Theory of Resonances and Decay

These notes review a consistent and exact theory of quantum resonances and decay. Such a theory does not exist in the framework of traditional quantum mechanics and Dirac's formulation. But most of its ingredients have been familiar entities, like the Gamow vectors, the Lippmann-Schwinger (in- and out-plane wave) kets, the Breit-Wigner (Lorentzian) resonance amplitude, the analytically continued S-matrix, and its resonance poles. However, there are inconsistencies and problems with these ingredients: exponential catastrophe, deviations from the exponential law, causality, and recently the ambiguity of the mass and width definition for relativistic resonances. To overcome these problems the above entities will be appropriately defined (as mathematical idealizations). For this purpose we change just one axiom (Hilbert space and/or asymptotic completeness) to a new axiom which distinguishes between (in-)states and (out)observables using Hardy spaces. Then we obtain a consistent quantum theory of scattering and decay which has the Weisskopf-Wigner methods of standard textbooks as an approximation. But it also leads to time-asymmetric semigroup evolution in place of the usual, reversible, unitary group evolution. This, however, can be interpreted as causality for the Born probabilities. Thus we obtain a theoretical framework for the resonance and decay phenomena which is a natural extension of traditional quantum mechanics and possesses the same arrow-of-time as classical electrodynamics. When extended to the relativistic domain, it provides an unambiguous definition for the mass and width of the Z-boson and other relativistic resonances.     

Electron,Proton, Neutron as Spheroidical Particles

It is shown that it is possible to describe the electron and the proton at rest within the framework of Dirac's relativistic theory of particles as electro-magnetic stable, spheroidical particles like balloons with very thin envelopes. Their properties, especially their spins and their magnetic momenta, are exactly those, which have been measured at first and later on derived by Dirac. In this picture the neutron plays the rǒle of a system of two concentric and synchronically rotating balloons with a small distance between them at a positive energetic minimum of balance at 1.26 MeV. The magnetic moment of this particle has a negative sign and is of the correct size.