Related papers: Evaluation of three-center two-electron repulsion …
Spherical Harmonic Gaussian type orbitals and Slater functions can be expressed using spherical coordinates or a linear combinations of the appropriate Cartesian functions. General expressions for the transformation coefficients between the…
We point out that a typical two-electron distribution function in atoms and molecules often called the intracule depends sensitively on the electron-electron repulsion which leads to the so-called Coulomb correlation. The difference between…
An analytic reversible Hamiltonian system with two degrees of freedom is studied in a neighborhood of its symmetric heteroclinic connection made up of a symmetric saddle-center, a symmetric orientable saddle periodic orbit lying in the same…
The first integrals of the Kepler problem are used to compute preliminary orbits starting from two short observed arcs of a celestial body, which may be obtained either by optical or radar observations. We write polynomial equations for…
An analysis of single-electron orbits in combined coaxial wiggler and axial guide magnetic fields is presented. Solutions of the equations of motion are developed in a form convenient for computing orbital velocity components and…
We report on electron removal calculations for 2.81 keV/amu Li$^{3+}$ and O$^{3+}$ ion collisions with neon dimers. The target is described as two independent neon atoms fixed at the dimer's equilibrium bond length, whose electrons are…
Closed orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high resolution spectral analyzer to obtain the…
The calculation of the two-loop corrections to the three-jet production rate and to event shapes in electron--positron annihilation requires the computation of a number of two-loop four-point master integrals with one off-shell and three…
The oscillator parameter in nuclei is refitted to reproduce the available charge radius data. As an important improvement, we include the Coulomb term evaluated within the assumption of a uniformly charged sphere, and take into account the…
A fully analytical approach based on the equation of motion technique to investigate the spectral properties and orbital occupations in an interacting double quantum dot in equilibrium is presented. By solving a linear system for the…
A hybrid lattice-statistical model on doubly decorated planar lattices, which have localized Ising spins at their nodal lattice sites and two itinerant electrons at each pair of decorating sites, is exactly solved by the use of a…
Separating the Coulomb potential into short-range and long-range components enables the use of different electron repulsion integral algorithms for each component. The short-range part can be efficiently computed using the analytical…
The goal of this article is to review the progress of three-electron spin qubits from their inception to the state of the art. We direct the main focus towards the resonant exchange (RX) qubit and the exchange-only qubit, but we also…
We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where…
We study a one-dimensional model of interacting conduction electrons with a two-fold degenerate band away from half filling. The interaction includes an on-site Coulomb repulsion and Hund's rule coupling. We show that such one-dimensional…
We construct product formulas for exponentials of commutators and explore their applications. First, we directly construct a third-order product formula with six exponentials by solving polynomial equations obtained using the operator…
Comet-type periodic orbits of the circular restricted three-body problem (CR3BP) are periodic solutions that are generated from very large retrograde and direct circular Keplerian motions around the common center of mass of the primaries.…
The analysis of correlation energy of the simplest first approximation of a variational method for the intrashell states of two-electron atoms is the purpose of the present work. This method allows to divide energy of atom on Coulomb and…
Within the framework of the Composite Operator Method, a three-pole solution for the two-dimensional Hubbard model is presented and analyzed in detail. In addition to the two Hubbard operators, the operatorial basis comprises a third…
The strong-coupling perturbation theory (SCPT) for correlated electron systems is extended to the case of full Coulomb interaction. The Coulomb mechanism of the orbital polarization is discussed and attention is paid to the importance of…