The helium atom in a strong magnetic field

Abstract

We investigate the electronic structure of the helium atom in a magnetic field between B = 0 and B = 100a.u.. The atom is treated as a nonrelativistic system with two interacting electrons and a fixed nucleus. Scaling laws are provided connecting the fixed-nucleus Hamiltonian to the one for the case of finite nuclear mass. Respecting the symmetries of the electronic Hamiltonian in the presence of a magnetic field, we represent this Hamiltonian as a matrix with respect to a two-particle basis composed of one-particle states of a Gaussian basis set. The corresponding generalized eigenvalue problem is solved numerically, providing in the present paper results for vanishing magnetic quantum number M = 0 and even or odd z-parity, each for both singlet and triplet spin symmetry. Total electronic energies of the ground state and the first few excitations in each subspace as well as their one-electron ionization energies are presented as a function of the magnetic field, and their behaviour is discussed. Energy values for electromagnetic transitions within the M = 0 subspace are shown, and a complete table of wavelengths at all the detected stationary points with respect to their field dependence is given, thereby providing a basis for a comparison with observed absorption spectra of magnetic white dwarfs.

Spectra and correlated wave functions of two electrons confined in a quasi-one-dimensional nanostructure

“…A c-aniGTO basis set can be transformed into a set of eigenfunctions of the corresponding three-dimensional anisotropic harmonic oscillator [19]. Therefore it would be useful also for calculating with high accuracy eigenvalues and eigenfunctions of atoms in strong magnetic fields [38][39][40][41] and of semiconductor quantum dots [42,43]. In the present study a c-aniGTO basis set has been placed at the center of the confining potential, i.e.…”

High-field impurity magneto-optics of Si:Se

“…Lowest energy states of helium from Ref. [10]. Energies are in atomic units and are relative to the double-ionization threshold.…”

“…In what follows the ground state is always the singlet, and we investigate only electric dipole transitions that conserve spin. We therefore use the common simplified notation from the semiconductor literature, e.g., 2p + refers to 2 1 P +1 or 1 1 (+1) + [10].…”

“…The helium crossover occurs at 0.76 B 0 , which would be at around 50 T in silicon and is In the case of H we took the spin down binding energy from Ref. [10] and added 0.5 B to remove the effect of spin, and in the case of He we took the binding energy from Refs. [17] and [18] and subtracted it from the zero-field first ionization threshold followed by an additional 0.5 B for the continuum shift.…”

Distribution of oscillator strength in Gaussian quantum dots: An energy flow from center-of-mass mode to internal modes

“…(4). Since a c-aniGTO basis set can be transformed into a set of eigenfunctions of the corresponding anisotropic harmonic oscillator [27], it should be also useful in the studies of atoms in strong magnetic fields [28,29] and of semiconductor quantum dots [30,31] for calculating eigenvalues and eigenfunctions with high accuracy [32][33][34].…”