NUMERICAL STUDYING ENERGY PARAMETERS OF MULTIELECTRON ATOM IN A MAGNETIC FIELD: HELIUM

There are presented the results of calculating the energies of the helium atom energy in a homogeneous magnetic field on the basis of the new numerical quantum-mechanical approach. The approach is based on the numerical difference solution of the Schrödinger equation, the model potential method and the operator perturbation theory formalism. The obtained results on energy of the helium atom in dependence upon the magnetic field strength are compared with available theoretical results, obtained on the basis of alternative numerical Hartree-Fock and diagonalization methods.

Movement and Diffusion of the Helium Atom in Nanostructures (in Pores) with Water

The influence of water-filled nanoscale defects on the total movement of helium atoms through a quartz crystal is considered. The approximation of local chains is used, the interaction constant of which characterizes the interaction of the helium atom with the environment. The appearance of water molecules in defects (pores) leads to the renormalization of this interaction. The D'Alembert principle is used to evaluate this renormalization. The effect of such a renormalization of the interaction on the diffusion coefficient of helium through a crystal with defects filled with water is considered.

Plasma Confined Ground and Excited State Helium Atom: A Comparison Theorem Study Using Variational Monte Carlo and Lagrange Mesh Method

The energy eigenvalues of the ground state helium atom and lowest two excited states corresponding to the configurations 1s2s embedded in the plasma environment using Hulthén, Debye–Hückel and exponential cosine screened Coulomb model potentials are investigated within the variational Monte Carlo method, starting with the ultracompact trial wave functions in the form of generalized Hylleraas–Kinoshita functions and Guevara–Harris–Turbiner functions. The Lagrange mesh method calculations of energy are reported for the He atom in the ground and excited 1S and 3S states, which are in excellent agreement with the variational Monte Carlo results. Interesting relative ordering of eigenvalues are reported corresponding to the different screened Coulomb potentials in the He ground and excited electronic states, which are rationalized in terms of the comparison theorem of quantum mechanics.

About calculation of the ground-state energy of the helium atom

Two versions of the numerical calculation of the ground state energy of the helium atom are compared. First, the nonrelativistic Schrödinger equation with a fixed nucleus is solved, and then the perturbation theory is used. Another version solves this problem exactly. Comparison shows that the difference between the calculation results is 94 kHz.

Hyperfine structure S state of muonic helium atom

In this work the nonrelativistic ionization energies 3He2+μ−e− and 4He2+μ−e− of helium-muonic atoms are calculated for S states.The estimates are based on the variational principle of exponential expansion. Convergence of the numerical values of variational energies is studied by increasing a number of the basis functions N. That allows to claim that the obtained energy values have 30-33 significant digits for S states

A compactness theorem for Frozen planets

In this paper, we study the moduli space of frozen planet orbits in the Helium atom for an interpolation between instantaneous and mean interactions and show that this moduli space is compact.