Thermodynamic quantities for gases in static spherically symmetric backgrounds possessing a horizon

The brick-wall method is used to study the thermodynamic quantities for perfect relativistic gases in generic spherically symmetric and static background spacetimes possessing a horizon. The Wentzel-Kramers-Brillouin (WKB) approximation is employed for the Teukolsky-type master equation. It is shown that the entropy density, energy density, pressure, and state equation all contain a subleading term, which depends on the spins of the particles of the gases. When particularizing to the Schwarzschild and Reissner-Nördstrom geometries, the results previously found in the literature for those geometries are recovered.     

变形对称双阱势

利用变形双曲函数,将对称双阱势推广为变形对称双阱势模型.证明了该势模型是五参量指数型势模型的特例.运用超对称WKB近似和五参量指数型势模型的能谱公式,获得了变形对称双阱势模型的能谱公式.     

氢及类氢离子光谱精细结构理论计算的改进

原子光谱数据是研究原子结构的重要参数,氢及类氢离子是原子物理和量子力学研究的理想体系.通过对氢及类氢离子光谱精细结构数据的研究发现,需要对Dirac提出的有关理论公式进行改进.本文在考虑了电子的自旋角动量与轨道角动量的耦合作用后,通过对Bohr理论中的电子运动角动量的修改,推导出单电子体系的电子速度公式,结合对Schr dinger的原子轨道能级表达式相对论效应修正,从而得出本文的氢及类氢离子光谱精细结构值的理论计算公式,应用此改进公式,所得的计算值与实验观测值符合得很好,计算结果也反映了氢及类氢离子光谱精细结构数据变化的规律性.     

The neutron halo in heavy nuclei calculated with the Gogny force

The proton and neutron density distributions, one- and two-neutron separation energies and radii of nuclei for which neutron halos are experimentally observed, are calculated using the self-consistent Hartree-Fock-Bogoliubov method with the effective interaction of Gogny. Halo factors are evaluated assuming hydrogen-like antiproton wave functions. The factors agree well with experimental data. They are close to those obtained with Skyrme forces and with the relativistic mean-field approach.     

New approaches to the study of properties of the generalized WKB approximation. IV

The problem of evaluating partial scattering phases of particles by spherically symmetric potentials is treated by the new formulation of the generalized WKB method. The error committed in calculating scattering phases in the zeroth approximation is estimated.     

Analytically solving the relativistic Dirac-Coulomb equation for atoms and molecules

A method of solving the Schr?dinger equation in an analytically expanded form reported previously is extended to the relativistic case and a general method of exactly solving the Dirac-Coulomb equation has been proposed for atoms and molecules. Some problems characteristic of the relativistic case are discussed. Test applications to the hydrogen-like, helium-like atoms are satisfactory, implying a high potentiality of the proposed method also for the relativistic case.     

Charged anisotropic matter with quadratic equation of state

We extend the work of Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) by considering quadratic equation of state for the matter distribution to study the general situation of a compact relativistic body. Presence of electromagnetic field and anisotropy in the pressure are also assumed. Some new classes of static spherically symmetrical models of relativistic stars are obtained. All the results given in Thirukkanesh and Maharaj (Class Quantum Gravity 25:235001, 2007) and there in can also be recovered as a particular case of our work.     

原子内壳层双光子衰变的相对论效应和屏蔽效应

本文系统地计算了H原子,类H-Xe离子及Xe原子内壳层的双光子衰变速率。阐明其相对论效应和电子屏蔽效应。并与最新的实验结果和他人的理论计算结果进行了比较和分析讨论。 关键词：     

Using a new method to solve the single-electron atom problem

A new relativistic method of one-component wave functions applicable for describing fields with arbitrary spins is suggested. This method is used to solve the problem of energy states of hydrogen-like atoms with different required accuracies and under differing conditions (rough estimate, relativistic correction, fine structure, Zeeman effect in a magnetic field, or hyperfine splitting with account of nucleus spin)     

一般球对称带电蒸发黑洞的熵

从一般球对称带电蒸发黑洞的时空线元和零曲面方程出发,得到了该黑洞的视界;利用KleinGordon方程求得波数,进而采用WenzelKramersBrillouin近似方法和薄膜brickwall模型,求出了一般球对称带电蒸发黑洞的熵,所得的熵正好与该黑洞的视界面积成正比 关键词： 黑洞 KleinGordon方程 熵 薄膜brickwall模型 视界     

类氢及碱金属原子激发态寿命的半经典计算公式

根据对应原理,得到了类氢原子能态平均寿命半经典的计算公式τ(n,l),然后利用相对论单通道量子数亏损理论进行推广,得到用来计算考虑总角动量J的激发态寿命公式τ(n,l,l+1/2)和τ(n,l,l-1/2),利用单通道量子数亏损理论得到了碱金属原子n、l远大于1时激发态寿命的半经典公式τ(n.l)=τ0(m+M/nm/v/+M)2v7l(l+1/2)/n4,其计算结果和实验数据符合的很好.     

Inelastic processes in the interaction of an atom with an ultrashort electromagnetic pulse

Electron transitions occurring during the interaction of a heavy relativistic atom with a spatially inhomogeneous ultrashort electromagnetic pulse are considered by solving the Dirac equation. The corresponding transition probabilities are expressed in terms of known inelastic atomic form factors, which are widely used in the theory of relativistic collisions between charged particles and atoms. By way of example, the inelastic processes accompanying the interaction of ultrashort pulses with hydrogen-like atoms are considered. The probabilities of ionization and production of a bound-free electron-positron pair on a bare nucleus, which are accompanied by the formation of a hydrogen-like atom in the final state and a positron in the continuum, are calculated. The developed technique makes it possible to take into account exactly not only the spatial inhomogeneity of an ultrashort electromagnetic pulse, but also the magnetic interaction.     

Modeling of a Wide Class of Static Stars Within the Framework of a Unified Approach

A class of static spherically symmetrical models of relativistic stars with a preset energy density distribution is examined. An analytical expression for an approximate solution of the Einstein equations is derived by the method of successive approximations in terms of a small parameter determining the star compactness. Equilibrium star configurations are constructed for a family of models and their stability and basic physical characteristics are investigated. The results of modeling of three different astrophysical objects (a neutron star, a white dwarf (Sirius B), and a star of the main sequence (Sun)) have been compared with the available observational data. This allows us to conclude that the suggested model approach is applicable to a wide class of stars.     

Internal conversion in hydrogen-like ions

The probability of internal gamma-ray conversion is theoretically investigated for hydrogen-like ions versus the corresponding neutral atoms. The relevant calculations are performed by the relativistic Dirac-Fock method. The results reveal that the effect of multiple ionization on the coefficients of internal conversion in the K shell is maximal near the ionization threshold and for transitions of high multipole order, where this effect can be as great as a few orders of magnitude. The distinction between the coefficient of internal conversion in the K shell of a neutral atom and that in the respective hydrogen-like ion decreases with increasing transition energy, but it remains sizable for transitions of practical importance. It is found that the ionization of an atom to a hydrogen-like ion with allowance for conversion in external atomic shells may change significantly (by up to eight orders of magnitude) the lifetime of the nucleus being considered. The predicted effects can be observed in experiments with beams of relativistic heavy ions.     

Ni27+ 离子Kα和Kβ 型衰变的双电子复合速率系数的计算

用HFR波函数对低密度类氢Ni²⁷⁺等离子体与电子相互作用的KLn和KMn共振激发的双电子复合过程进行了细致的理论计算研究.根据可能的重要辐射衰变通道，分析了Ni²⁷⁺等离子体Kα 型和Kβ 型辐射衰变的双电子复合速率系数随旁观电子主量子数n和轨道角动量量子数l与电子温度的变化行为，计算了Ni²⁷⁺等离子体双电子复合过程的总速率系数.研究结果表明，在低密度条件下，Kα 型和Kβ型辐射衰变的分支双电子复合速率系数与旁观电子主量子数n和轨道角动量量子数l有重要关系，前者的分支速率系数远大于后者. 关键词： 27+离子')" href="#">Ni²⁷⁺离子 Kα型和Kβ型辐射衰变')" href="#">Kα型和Kβ型辐射衰变 双电子复合 速率系数     

WKB approach to calculating the lifetime of quasistationary states

A novel WKB approach to calculating the lifetime of quasistationary states in the potential wells of the form V(x)=P(x)-muQ(x), where P(x) is the radial part of the potential for the spherically symmetric harmonic oscillator or the hydrogen atom and Q(x) is a polynomial, is suggested. In this approach, the usual explicit procedure of the asymptotic matching of the perturbative and WKB wave functions is avoided and a simple formula for the imaginary part of the energy is found. The leading and the first correction terms for the imaginary part of the energy and the related lifetime are analytically calculated.     

Eigenvalue Spectrum of a Dirac Particle in Static and Spherical Complex Potential

It has been observed that a quantum theory need not be Hermitian to have a real spectrum. We study the non-Hermitian relativistic quantum theories for many complex potentials, and obtain the real relativistic energy eigenvalues and corresponding eigenfunctions of a Dirac-charged particle in complex statically and spherically symmetric potentials. Complex Dirac–Eckart, complex Dirac–Rosen–Morse II, complex Dirac–Scarf and complex Dirac–Poschl–Teller potential are investigated.     

Nuclear size correction to the hyperfine splitting in low- hydrogen-like atoms

The finite nuclear size effect on the hyperfine splitting of low-Z hydrogen-like atoms is studied in the external field approximation. A simple non-relativistic formula is proposed which expresses the nuclear size correction to the hyperfine splitting in terms of moments of the nuclear charge and magnetization distribution. The numerical results obtained via this formula are compared with corresponding results derived by means of the Zemach formula. A relativistic formula for the nuclear size correction to the hyperfine splitting is also derived. Received 18 March 2002 / Received in final form 14 November 2002 Published online 28 January 2003 RID="a" ID="a"e-mail: plunien@physik.tu-dresden.de     

Applicability of first and second order WKB approximation to elastic scattering of two particles interacting by long-range forces

The accuracy of the first and second order WKB approximation in describing sub-Coulomb elastic scattering of ions is investigated. Thereby the scattering of non-identical as well as of identical particles is taken into consideration. It is shown that in cases where the behaviour of the scattered ions is not quasi-classical and therefore the first order WKB approximation fails, the second order WKB will be in most cases still a quite good approximation.     

Relativistic nonlinearity and wave-guide propagation of rippled laser beam in plasma

In the present paper we have investigated the self-focusing behaviour of radially symmetrical rippled Gaussian laser beam propagating in a plasma. Considering the nonlinearity to arise from relativistic phenomena and following the approach of Akhmanov et al, which is based on the WKB and paraxial-ray approximation, the self-focusing behaviour has been investigated in some detail. The effect of the position and width of the ripple on the self-focusing of laser beam has been studied for arbitrary large magnitude of nonlinearity. Results indicate that the medium behaves as an oscillatory wave-guide. The self-focusing is found to depend on the position parameter of ripple as well as on the beam width. Values of critical power has been calculated for different values of the position parameter of ripple. Effects of axially and radially inhomogeneous plasma on self-focusing behaviour have been investigated and presented here.