Bethe logarithm and QED shift for lithium

A novel finite basis set method is used to calculate the Bethe logarithm for the ground 2 (2)S(1/2) and excited 3 (2)S(1/2) states of lithium. The basis sets are constructed to span a huge range of distance scales within a single calculation, leading to well-converged values for the Bethe logarithm. The results are used to calculate an accurate value for the complete quantum electrodynamic energy shift up to order alpha(3) Ry. The calculated 3 (2)S(1/2)-2 (2)S(1/2) transition frequency for 7Li is 27 206.092 6(9) cm(-1), and the ionization potential for the 2 (2)S(1/2) state is 43 487.158 3(6) cm(-1). The 7Li-6Li isotope shift is also considered, and all the results compared with experiment.     

Thermodynamic Bethe ansatz for generalized extensive statistics

We investigate properties of the entropy density related to a generalized extensive statistics and derive the thermodynamic Bethe ansatz equation for a system of relativistic particles obeying such a statistics. We investigate the conformal limit of such a system. We also derive a generalized Y-system. The Gentile intermediate statistics and the statistics of γ-ons are considered in detail. In particular, we observe that certain thermodynamic quantities for the Gentile statistics majorize those for the Haldane–Wu statistics. Specifically, for the effective central charges related to affine Toda models we obtain nontrivial inequalities in terms of dilogarithms.     

Scattering tightly bound dimers off a scattering potential

The motion of two attractively interacting atoms in an optical lattice is investigated in the presence of a scattering potential. The initial wavefunction can be prepared by using tightly bound exact two-particle eigenfunction for vanishing scattering potential. This allows to numerically simulate the dynamics in the generation of two-particle Schrödinger cat states using a scheme recently proposed for scattering of quantum matter wave solitons.     

Transitions between bound states for axially channeled MeV electrons

Photon lines emitted in the forward direction from 2.0–4.5 MeV electrons channeled along a 〈110〉 axis in a 3400 Å Si crystal have been measured and compared with calculations and with previous results from a 12 000 Å Si 〈111〉 crystal. Nearly all features agree with predictions based on an isolated string.     

Scattering of relativistic electrons by high-power laser light tightly focused

We obtain an approximate solution for the drift and oscillatory components of the motion of relativistic electrons in the field of temporally extended high-power laser light under strong focusing of the light (the size of the focal region is of the order of the light wavelength). This makes it possible to start numerically integrating the equations of electron motion near the focal region. We estimate the impact parameters of the electrons when they are still efficiently accelerated in the focal region. Zh. éksp. Teor. Fiz. 111, 1554–1562 (May 1997)     

Estimating the bound for the generalized Lorenz system

A chaotic system is bounded, and its trajectory is confined to a certain region which is called the chaotic attractor. No matter how unstable the interior of the system is, the trajectory never exceeds the chaotic attractor. In the present paper, the sphere bound of the generalized Lorenz system is given, based on the Lyapunov function and the Lagrange multiplier method. Furthermore, we show the actual parameters and perform numerical simulations.     

Continuous growth models in terms of generalized logarithm and exponential functions

Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are suitable to describe and unify the great majority of continuous growth models, which we briefly review. Physical interpretation to the generalization function parameter is given for the Richards’ model, which has an underlying microscopic model to justify it.     

Weakly bound electrons in an external magnetic field

The electron behavior in a spherical symmetric potential well in the presence of an external magnetic field is studied. The transcendental equation for the energy spectrum is derived. The energy of the bound state is approximately calculated. The electron wave function and the probability current are found.     

The Bethe ansatz equations for reflecting magnons

We derive the Bethe ansatz equations on the half line for particles interacting through factorized S-matrices invariant relative to the centrally extended su(2|2) Lie superalgebra and su(1|2) open boundaries. These equations may be of relevance for the study of the spectrum of open strings on AdS₅×S⁵ background attached to Y=0 giant graviton branes. A one-dimensional spin chain Hamiltonian associated to this system is also derived.     

The role of bound electrons in the non-local surface response of metals

P-polarized light has the unique feature of probing the surface region of a metal which gives rise to effects not taken into account in a classical (Fresnel) treatment. Previous calculations of this non-local effect have been restricted to free-electron metals. Within a simple framework we will here consider the modifications because of the presence of bound electrons. The somewhat surprising result is that a system with both free and bound electrons will still be possible to analyze in free-electron terms, provided we plot the experimental results with a normalization which removes all dependence of the angle of incidence.     

The Bethe approximation for lattice gauge theories

The Bethe approximation is defined for general lattice gauge theories. It amounts to solving the model on an infinite Cayley lattice of cubes. The approximation is tested on the 4-d Z₄ model, where it is shown to reproduce accurately most of the phase diagram. It also suggests which mass vanishes in the Coulomb phase.     

Support of generalized parton distributions in Bethe–Salpeter models of hadrons

The proper support of generalized parton distributions from relativistic constituent quark models with pointlike constituents is studied. The correct support is guaranteed when the vertex function does not depend on the relative minus-momentum. We show that including quark interactions in models with pointlike constituent quarks might lead to a support problem. A computation of the magnitude of the support problem in the Bonn relativistic constituent quark model is presented.     

Energies of electrons bound to nitrogen pairs in GaP

The binding energies of electrons bound to nitrogen pairs in GaP are evaluated by use of the effective mass theory with a suitable model potential. The variational procedure yields (i) satisfactory agreement with previous experimental values for nitrogen pairs and (ii) no bound state for the isolated nitrogen atom. Our results suggest the electron to be bound in a potential with strain-like contributions which approaches earlier ideas of Allen.     

Solution of lattice gas models in the generalized ensemble on the Bethe lattice

We present the exact Bethe lattice solution for a lattice gas Potts model defined in the generalized ensemble which was previously studied in elucidating the anomalous thermodynamic properties of water. For this model the locus of density maxima (TMD), the locus of isothermal compressibility extrema, (TEC), the spinodal curve, and the percolation curve for four hydrogen bonded molecules are calculated using the Bethe lattice solution. The results confirm qualitative relationships between the TMD, the TEC, and the percolation curve obtained previously from a mean field calculation.     

Exact thermodynamic behavior of a generalized spin-isospin ising system on the Bethe lattice

We study a generalized Ising system consisting of a Bethe lattice on every site of which two spin-1/2 and two isospin-1/2 (or atomic species A) states can be realized, the spin-species interacting with appropriate nearest neighbor couplings. The system is equivalent to that of four states per site and we obtain its exact thermodynamic behavior. The case of a fixed concentration of species is the annealed or liquid magnetic binary alloy. The temperature dependence of the short-range-order (SRO) parameter of such systems is obtained as an application of the theory and discussed in connection with relevant material from the literature. When fixing both the concentration and the nearest neighbor spatial correlation of the species, we obtain Eggarter's formulas for the frozen-in species problem, which therefore are only approximately valid even on the Bethe lattice.     

Incoherent scattering of 279 keV gamma rays by bound electrons

The differential cross section for 279 keV gamma rays scattered incoherently from K-shell electrons of thorium is determined experimentally at six angles from 30° to 150° and expressed in terms of the free electron scattering cross section. Two NaI(T1) scintillation spectrometers and a fast-slow coincidence circuit are employed. The scattered gamma rays are detected in coincidence with the fluorescent K X-rays. The bound-to-free electron cross section ratios are compared with those calculated from different non-relativistic theories. The bound electron cross sections are also directly compared with the Klein-Nishina values. At low scattering angles the experimental results agree well with those incoherent scattering function values based on the Thomas-Fermi model, while at large scattering angles there is no good agreement between the experimental values and any of the theories discussed in the text.