Helium-like System Research Articles

Co-spherical electronic configuration of the helium-like atomic systems

The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius r, and angle θ characterizes their positions on sphere, are investigated. Unlike the previous studies, r is considered as a quantum mechanical variable but not a parameter. It is important that the “co-spherical” and the “collinear” configuration are coincident in two points. For θ=0 one obtains the state of the electron–electron coalescence, whereas the angle θ=π characterizes the e − n − e configuration when the electrons are located at the ends of the diameter of sphere with the nucleus at its center. The Pekeris-like method representing a fully three-body variational technique is used for the expedient calculations. Some interesting features of the expectation values representing the basic characteristics of the “co-spherical” electronic configuration are studied. The unusual properties of the expectation values of the operators associated with the kinetic and potential energy of the two-electron atom/ion possessing the “co-spherical” configuration are found. Refined formulas for calculations of the two-electron Fock expansion by the Green’s function approach are presented. The model wave functions of high accuracy describing the “co-spherical” electronic configuration are obtained. All results are illustrated in tables and figures.

Single electron capture cross sections for collisions of multi-charged ions with helium-like atomic system

SynopsisA four-body distorted wave method (DW-4B) is applied to calculate the total cross section for single electron capture in the collisions of multi-charged ions with helium-like atomic system. The proper long range behavior of the Coulomb potential is introduced. The present theoretical method is satisfactory in the intermediate and high-energy regime and is quite reliable compared to other theoretical methods.

A Branching Random Walk Method for Many-Body Wigner Quantum Dynamics

A branching random walk algorithm for the many-body Wigner equation and its numerical applications for quantum dynamics in phase space are proposed and analyzed. After introducing an auxiliary function, the (truncated) Wigner equation is cast into the integral formulation as well as its adjoint correspondence, both of which can be reformulated into the renewal-type equations and have transparent probabilistic interpretation. We prove that the first moment of a branching random walk happens to be the solution for the adjoint equation. More importantly, we detail that such stochastic model, associated with both importance sampling and resampling, paves the way for a numerically tractable scheme, within which the Wigner quantum dynamics is simulated in a time-marching manner and the complexity can be controlled with the help of an (exact) estimator of the growth rate of particle number. Typical numerical experiments on the Gaussian barrier scattering and a Helium-like system validate our theoretical findings, as well as demonstrate the accuracy, the efficiency and thus the computability of the Wigner branching random walk algorithm.

The Wigner Branching Random Walk: Efficient Implementation and Performance Evaluation

To implement the Wigner branching random walk, the particle carrying a signed weight, either $-1$ or $+1$, is more friendly to data storage and arithmetic manipulations than that taking a real-valued weight continuously from $-1$ to $+1$. The former is called a signed particle and the latter a weighted particle. In this paper, we propose two efficient strategies to realize the signed-particle implementation. One is to interpret the multiplicative functional as the probability to generate pairs of particles instead of the incremental weight, and the other is to utilize a bootstrap filter to adjust the skewness of particle weights. Performance evaluations on the Gaussian barrier scattering (2D) and a Helium-like system (4D) demonstrate the feasibility of both strategies and the variance reduction property of the second approach. We provide an improvement of the first signed-particle implementation that partially alleviates the restriction on the time step and perform a thorough theoretical and numerical comparison among all the existing signed-particle implementations. Details on implementing the importance sampling according to the quasi-probability density and an efficient resampling or particle reduction are also provided.

Three charges on a plane in a magnetic field: Special trajectories

As a generalization and extension of Escobar-Ruiz and Turbiner [J. Math. Phys. 54, 022901 (2013)], the classical dynamics of three non-relativistic Coulomb charges (e1, m1), (e2, m2), and (e3, m3) on the plane placed in a perpendicular constant magnetic field is considered. Special trajectories for which the distances between the charges remain unchanged are presented and their corresponding constants of motion are indicated. For these special trajectories, the number of constants of motion is larger than the dimension of the configuration space and hence they can be called particularly superintegrable. Three physically relevant cases are analyzed in detail, namely, that of three electrons, a neutral system, and a helium-like system. The n-body case is discussed as well.

Application of the Hylleraas- B -spline basis set: Static dipole polarizabilities of helium

The Hylleraas-B-splines basis set is introduced in this paper, which can be used to obtain the eigenvalues and eigenstates of helium-like system's Hamiltonian. Comparing with traditional B-splines basis, the rate of convergence of our results has been significantly improved. Through combine this method and pseudo-states sum over scheme, we obtained the high precision values of static dipole porlarizabilities of the $1{}^1S-5{}^1S$, $2{}^3S-6{}^3S$ states of helium in length and velocity gauges respectively, and the results get good agreements. The final extrapolate results of porlarizabilities in different quantum states arrived eight significant digits at least, which fully illustrates the advantage and convenience of this method in the problems involving continuous states.

An Advective-Spectral-Mixed Method for Time-Dependent Many-Body Wigner Simulations

As a phase space language for quantum mechanics, the Wigner function approach bears a close analogy to classical mechanics and has been drawing growing attention, especially in simulating quantum many-body systems. However, deterministic numerical solutions have been almost exclusively confined to one-dimensional one-body systems and few results are reported even for one-dimensional two-body problems. This paper serves as the first attempt to solve the time-dependent many-body Wigner equation through a grid-based advective-spectral-mixed method. The main feature of the method is to resolve the linear advection in $(\boldsymbol{x},t)$-space by an explicit three-step characteristic scheme coupled with the piecewise cubic spline interpolation, while the Chebyshev spectral element method in $\boldsymbol{k}$-space is adopted for accurate calculation of the nonlocal pseudo-differential term. Not only is the time step of the resulting method not restricted by the usual CFL condition and thus a large time step is allowed, but also the mass conservation can be maintained. In particular, for the system consisting of identical particles, the advective-spectral-mixed method can also rigorously preserve physical symmetry relations. The performance is validated through several typical numerical experiments, like the Gaussian barrier scattering, electron-electron interaction and a Helium-like system, where the third-order accuracy against both grid spacing and time stepping is observed.

On the high-energy limits for the double-to-single ionization ratio of helium and helium-like ions in collisions with charged and neutral particles

We compare ionization of helium and helium-like ions in collisions with highly charged ions and neutral atoms in the asymptotic high-energy limit γ→∞, where γ is the collisional Lorentz factor. In the case of ionization of helium and helium-like ions by charged particles, the asymptotic high-energy double-to-single ionization ratio is independent of the properties of the ionizing agent and depends on the nuclear charge of the helium-like system. In contrast to that, in the case of ionization of helium-like ions by neutral atoms, this ratio is nearly independent of the nuclear charge of the helium-like ion but strongly depends on the atomic number of the ionizing agent (neutral atom), provided the condition Z1Z2>0.4c is fulfilled where Z1 is the nuclear charge of the helium-like ion, Z2 is the atomic number of the neutral atom, and c=137 is the speed of light.

Measurement of the spectral shape for the two-photon decay in heliumlike gold

Progress on a measurement of the spectral distribution of the two-photon decay of the 1s2s 1S0 level in the strong central fields of heavy heliumlike ions is reported. A measurement of the exact shape of the continuous spectrum of the two-photon decay in heavy heliumlike ions provides a sensitive test of the details of the complete structure of a heliumlike system. In our experiment at GSI, a beam of 106.6 MeV/u Au77+ ions was excited by a thin Aluminum foil and the subsequent decays were observed in an array of Ge(i) detectors.

The two-photon decay in helium-like gold

Progress on a measurement of the spectral distribution of the two-photon decay of the 21S0 level in helium-like gold is reported. A measurement of the exact shape of the continuous spectrum of the two-photon decay in heavy helium-like ions provides a sensitive test on the details of the complete structure of a helium-like system. In our experiment at GSI, a beam of 106.6 MeV/u Au77+ ions is excited by a thin Aluminum foil and the subsequent decays are observed in an array of Ge(i) detectors.

Explicitly correlated trial functions in relativistic variational calculations

We report the first successful extension of the Hylleraas-type variational expansion to the relativistic Hamiltonian for a helium-like system. The explicitly correlated trial functions are introduced within the minimax variational finite basis set technique for the relativistic energy functional.

Relativistic corrections to Ps -

Explicit calculations were performed to verify that a previously derived relativistic three-fermion equation [Phys. Lett. A 158 (1991) 361] contains the complete O(α 4) physics. Perturbative solutions of the ground state eigenenergy, to O(α 4), are presented for equal mass systems, such as Ps -, as well as for helium-like systems. Results for the helium-like system agree with those obtained from the Breit equation in the Pauli approximation. The relativistic corrections to the Ps - energy are very small.

The Effect of Adsorbeb Oxygen Ions on the Inelastic Scattering of Photo-Electrons at the Metal-Vacuum Interface

AbstractMeasurements of uv photoemission from evaporated aluminum films were made at photon energies 7.7–11 eV as a function of time after film deposition. Evidence of the initial stage of chemisorption of oxygen can be seen in the uv photoelectron spectra. The spectra taken immediately after film deposition showed a smooth energy distribution characteristic of clean aluminum. Structure in the spectra was found to appear at approximately 60 minutes after deposition at 10−9 Torr. Three noticeable features were observed at 1.0, 1.3, and 2.5 eV above the vacuum level. They appeared stationary with increasing photon energy. The structure can be attributed to inelastic scattering of photoelectrons into resonant states associated with oxygen ions on the metal surface. The energy levels of the calculated resonant states of a helium-like system are compared with the energy of the observed structure. The agreement suggests that there are adsorbed 0− ions to which photoelectrons can be scattered at the metal-vacuum interface.

The spectrum and dipole and quadrupole moments of hydrogen-like and helium-like ions in superstrong fields

The properties of hydrogen-like and helium-like systems in superstrong magnetic field are studied at field values characteristic for white dwarfs and pulsars. Calculated values of the energy levels and matrix elements of dipole and quadrupole moments of systems with an arbitrary nucleus charge Z in field interval 0.05Z2<or=B<or=Z2 are given. The evolution of lines of equal electron density for hydrogen-like and helium-like systems as the field is increased is analysed. The helium-like system in a strong magnetic field was treated by perturbation theory for the inter-electron interaction.

Vacuum Polarization in Heavy-Ion Collisions

The results of a study on vacuum polarization, orders $\ensuremath{\alpha}{(Z\ensuremath{\alpha})}^{n}$, $n&gt;~3$, for large-$Z$ systems encountered in heavy-ion collisions are presented. It is shown that the higher-order vacuum polarization cannot prevent the $1{S}_{\frac{1}{2}}$ state from reaching the lower continuum, $E=\ensuremath{-}{m}_{e}{c}^{2}$, for some critical charge ${Z}_{\mathrm{cr}}\ensuremath{\sim}170$. In addition, the stability and localization of a heliumlike system for $Z&gt;{Z}_{\mathrm{cr}}$ is demonstrated.

Convergence and energy bounding properties of the Nosanow cluster expansion

We consider a one-dimensional linear lattice of particles whose mass, pair potential, and nearest neighbor separation are those of a real rare gas crystal. Numerical solution of the Hartree equation shows that the model behaves as a quantum crystal in the low mass, weak attraction case. In the basic Nosanow cluster approximation the cohesive energy of this helium-like system drops from 6.903°K/N (Hartree) to 3.64°K/N. When all except nearest neighbor correlations in the Jastrow function are taken as unity, the result is 3.69°K/N. For the case of nearest neighbor correlations only, we introduce a positive integral operator with properties akin to those of a transfer matrix and thus form a rigorous upper bound on the cohesive energy of the model system. The convergence rate of the Nosanow expansion is shown to depend on the ratio of the two highest eigenvalues of this operator.