Note on relativistic coulomb wave functions

Some results on the wave functions of a Dirac particle in a point charge Coulomb field are presented. Angular momentum and parity eigenfunctions are tabulated and used to construct solutions representing asymptotically a plane wave plus incoming or outgoing spherical waves. The solutions forr → 0 are exhibited in a form closely similar to the corresponding free particle spinors and are used to construct generalizations of the Casimir projection operators for positive or negative energy particles. The various wave functions presented are useful in calculations such as nuclear beta decay in which it is necessary to take into account final (or initial) state Coulomb interactions. Because of the similarity of the wave functions to those of a free particle, calculations including rigorously all Coulomb corrections for such processes as allowed beta decay can be performed with little more effort than is involved in a calculation using only plane waves.     

New summation rules for coulomb wave functions

Sums of products of the Coulomb wave functions over degenerate manifolds have been obtained in a closed form. These sums appear in many atomic and molecular problems. The sums have been obtained making use of the properties of the Coulomb Green's function G(r, r('),E), in the limit E-->E(n), where E(n) is the eigenenergy of the hydrogenlike atomic ion. The closed Hostler-Pratt form of G in the coordinate representation has been used. The sums calculated are a consequence of the n degeneracy of the Coulomb atomic energy levels. This itself, as is well known, follows from the four-dimensional symmetry of the Coulomb problem for the hydrogen atom.     

Kinetic theory of charge-density wave systems in the presence of long-range coulomb forces

The coupling between the charge-density weve condensate, and the quasiparticles and normal electrons, due to long-range Coulomb forces is investigated within the framework of the kinetic theory, for finite temperatures and in the presence of impurity scattering. The temperature dependence of the parameters, which enter the phenomenological equations for the transport in CDW systems, is determined. In the absense of normal electrons, a strong enhancement of the damping and the velocity of the phase mode is found for low temperatures, which is due to the freezing out of quasiparticles.     

氩原子基态波函数和能量的解析计算

以第一性原理和变分原理为基础,给出了氩原子基态波函数的一种解析表达式,计算了基态氩原子(含类氩离子)的能量,导出了所涉及的所有积分的解析表达式.对氩原子,所得到的能量理论值与实验值的相对误差为0.22%.     

The high-momentum components in the wave functions of the few-body systems

Provided that final-state interactions and meson-exchange currents are fully taken into account, the analysis of recent (e, e′p) reactions provides us with the strongest constraint on the high-momentum part of the wave functions of the few-nucleon systems.     

Precise calculation of coulomb binding energies of mesomolecules

The best variational energies obtained to date for the ground states of all -mesomolecules are presented. The results are of rather high accuracy and can serve as a theoretical basis for the experimental study of three-body systems. The energies of thee ^– e ⁺ e ^–,H^– and 1¹ S, 2³ S, 2³ P, 2³ P states ofHe are calculated using the same method.     

Exact wave functions for atomic electron interacting with photon fields

Many nonlinear quantum optical physics phenomena need more accurate wave functions and corresponding energy or quasienergy levels to account for. An analytic expression of wave functions with corresponding energy levels for an atomic electron interacting with a photon field is presented as an exact solution to the Schrödinger-like equation involved with both atomic Coulomb interaction and electron-photon interaction. The solution is a natural generalization of the quantum-field Volkov states for an otherwise free electron interacting with a photon field. The solution shows that an Nlevel atom in light form stationary states without extra energy splitting in addition to the Floquet mechanism. The treatment developed here with computing codes can be conveniently transferred to quantum optics in classical-field version as research tools to benefit the whole physics community.     

New formula for calculating coulomb energies in the liquid-drop model

A new transformation of double volume integrals into double surface integrals is presented. A simple regular method for deriving integrands in a surface integral is proposed. This method is used to calculate the Coulomb energy of a nucleus within the model of a liquid drop with a sharp boundary. Numerical results obtained on the basis of the new formula are compared with those calculated by one of the formulas employed previously.     

Temperature dependence of the giant magnetoresistance in Fe-Cr multilayers—Intralayer and interlayer exchange energies

We present field and temperature dependence data on giant magnetoresistive (GMR) ion-beam sputtered Fe-Cr multilayers of varying Cr thickness. We show that the decrease in GMR with temperature is related to the decrease in sublattice magnetization due to thermal excitation of magnons in the antiferromagnetic configuration. The intralayer and the interlayer exchange energies thus obtained vary systematically as the Cr thickness increases. The corresponding decrease in the measured saturation field further supports our interpretation leading to a better understanding of the physics of GMR.     

Impact picture in the coulomb interference region at high energies

We present the predictions on pp̄ elastic differential cross sections in the Coulomb interface region for energies 0.546 to 2.0 TeV on the basis of the impact picture.     

Exponential wave functions for atomic-molecular systems

Geometric properties of correlated exponential basis functions for n-particle Coulomb systems are studied. Using a system of model Schrödinger equations, the relations between the average values of Coulomb interaction energies of pairs of the particles and average values of cosines of the angles of mutual tilt of interparticle bonds are derived. The use of these relations significantly simplifies calculations of the energy operator matrix of many-particle systems by reducing them to evaluation of the Coulomb and normalization integrals. Geometric inequalities are established that allow one to estimate the many-particle Coulomb interaction integrals that are hard to evaluate. The results obtained can be used in calculations of atomic-molecular systems.     

Analytical structure and properties of Coulomb wave functions for real and complex energies

The radical Coulomb wave functions are analysed in their dependence on the energy E considered as a complex parameter. Repulsive and attractive fields are both considered. First turning to the function Φ_l ∝ r^?l?1F_l introduced by Briet, slightly modifying its definition, and assuming that the angular momentum is also a complex parameter, for which the notation L is used, it is proved that Φ_L is an entire function of both E and L. From an expansion of the regular Whittaker function given by Buchholz, the Taylor expansion of Φ_L in powers of E and a simple recurrence relation for its coefficients are easily obtained. The expansion of the regular function F_l is readily obtained from that of Φ_L for L = l, but the irregular function G_l contains Φ_l and $\text{?Φ}{}_{\mathrm{L}}\text{?L}$ for L = l and ?l?1. Having proved that the expansion obtained for Φ_L in powers of E can also be regarded as a uniformly convergent series of entire functions of L, the derivative $\text{?Φ}{}_{\mathrm{L}}\text{?L}$ can be obtained by term-by-term derivation. This method for obtaining the expansion of G_l is straightforward and leads to a final result involving essentially: (i) the conventional function $\text{h(η) =}\text{1}\text{2}\text{ψ(1 + iη) +}\text{1}\text{2}\text{ψ(1 ? iη) ?}\text{ln}\text{η}$ which is singular at η = ∞, i.e., at k = 0; (ii) two entire functions of E, namely Φ_l and Ψ_l; the terms of the expansion of the latter in powers of E contain only Bessel functions multiplied by Bernoulli numbers and coefficients easily obtained from a simple recurrence relation. As an application of the above results, the last sections contain: (i) an alternate from of G_l expansion useful in numerical computations; (ii) the definition and expansion of two linearly independent solutions of the Coulomb equation which are entire in E; (iii) the expansion and threshold properties of the outgoing and incoming solutions, O_l and I_l, corresponding to those we have obtained for F_l and G_l.     

Smoothed wave functions of chaotic quantum systems

It is shown that wave functions of quantum systems as ħ → 0 have an extra density near unstable periodic trajectories of the classical problem. The averaged wave function square is represented as the sum over a finite number of periodic trajectories. The contribution of each trajectory is expressed through the elements of the monodromy matrix of the trajectory. The results are compared with the numerical calculations of the wave functions for the stadium billiard.     

Use of Furry-Sommerfeld-Maue wave functions in pair production at medium and high energies

The analytic expression for the differential pair production cross section, obtained using full Furry-Sommerfeld-Maue wave functions for the electron and positron, is integrated numerically over angles without further approximation. The resulting Coulomb corrections to the total pair production cross section are compared with existing interpolations in the energy range 10 MeV to 50 MeV, and their experimental relevance is discussed.     

Direct coulomb and exchange interaction in artificial atoms

We determine contributions from the direct Coulomb and exchange interactions to the total interaction in artificial semiconductor atoms. We tune the relative strengths of the two interactions and measure them as a function of the number of confined electrons. The electrons tend to have parallel spins when they occupy nearly degenerate single-particle states. We use a magnetic field to adjust the single-particle-state degeneracy, and find that the spin configurations in an arbitrary magnetic field are well explained in terms of two-electron singlet and triplet states.     

Robustness of wave functions of interacting many bosons in a leaky Box

We study the robustness, against the leakage of bosons, of wave functions of interacting many bosons confined in a finite box by deriving and analyzing a general equation of motion for the reduced density operator. We identify a robust wave function that remains a pure state, whereas other wave functions, such as the Bogoliubov's ground state and the ground state with a fixed number of bosons, evolve into mixed states. Although these states all have the off-diagonal long-range order, and the same energy, we argue that only the robust state is realized as a macroscopic quantum state.     

Exponential-trigonometric basis functions in the coulomb four-body problem

Basis functions of a new type—specifically, exponential-trigonometric functions depending on all six interparticle distances—have been proposed for the Coulomb four-body problem. A method has been developed for computing nine-dimensional integrals determining the matrix elements of the Hamiltonian for a four-body system and featuring these functions. The efficiency of the approach that relies on the proposed basis functions has been tested by calculating the e ⁺ e ^? e ⁺ e ^?, p ⁺μ^? p ⁺μ^?, μ⁺ e ^?μ⁺ e ^?, and p ⁺ e ^? p ⁺ e ^? molecules.     

Nuclear and coulomb interaction in 8B breakup at sub-coulomb energies

The angular distribution for the breakup of 8B-->7Be+p on a 58Ni target has been measured at an incident energy of 25.75 MeV. The data are inconsistent with first-order theories but are remarkably well described by calculations including higher-order effects. The comparison with theory illustrates the importance of the inclusion of the exotic proton halo structure of 8B in accounting for the data.