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Physical Review A

Atomic ground states in strong magnetic fields: Electron configurations and energy levels

C. Schimeczek, Sebastian Boblest, Dirk Meyer, Günter Wunner

Published Jul 12, 2013• 16 citations
Publisher

Abstract

Using a combination of a fast two-dimensional-Hartree-Fock-Roothaan method and highly accurate fixed-phase diffusion quantum Monte Carlo simulations, we analyze the electronic structure and calculate the energy of the ground states of atoms with nuclear charges $Z=2--26$ in very strong magnetic fields $B={10}^{7}--5\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0.28em}{0ex}}\mathrm{T}$, relevant for astrophysical problems, e.g., the thermal emission of strongly magnetized isolated neutron stars.

DOI
10.1103/physreva.88.012509

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Using a combination of a fast two-dimensional-Hartree-Fock-Roothaan method and highly accurate fixed-phase diffusion quantum Monte Carlo simulations, we analyze the electronic structure and calculate the energy of the ground states of atoms with nuclear charges Z=2−−26Z=2--26Z=2−−26 in very strong magnetic fields B=107−−5\ifmmode×\else\texttimes\fi108TB={10}^{7}--5\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0.28em}{0ex}}\mathrm{T}B=107−−5\ifmmode×\else\texttimes\fi108T, relevant for astrophysical problems, e.g., the thermal emission of strongly magnetized isolated neutron stars.
We use the combination of a two-dimensional Hartree-Fock and a diffusion quantum Monte Carlo method, both of which we recently presented in this journal [C. Schimeczek et al., Phys. Rev. A 88, 012509 (2013)], for a thorough investigation of the ground state configurations of all atoms and ions with Z=2Z=2Z=2--10 with the exception of hydrogen-like systems in strong magnetic fields. We obtain the most comprehensive data set of ground state configurations as a function of the magnetic field strength currently available and hence are able to analyze and compare the properties of systems with different core charges and electron numbers in detail.
The electronic structure of the ground state and some excited states of neutral atoms with the nuclear charge numbers 1< Z< 101<~Z<~101< Z< 10 and their singly positive ions are investigated by means of our two-dimensional mesh Hartree-Fock method for strong magnetic fields $0.5<~\ensuremath{\gamma}<~10000.$ For $\ensuremath{\gamma}=10000$ the ground-state configurations of all the atoms and ions considered are given by fully spin-polarized configurations of single-electron orbitals with magnetic quantum numbers ranging from m=0m=0m=0 to $m=\ensuremath{-}N+1,$ where N is the number of the electrons. Focusing on the fully spin-polarized situation, we provide critical values of the magnetic-field strength for which crossovers with respect to the spatial symmetries of the ground state take place. It is found that the neutral atoms and singly charged positive ions with 2< Z< 52<~Z<~52< Z< 5 have one fully spin-polarized ground-state configuration, whereas for 6< Z< 106<~Z<~106< Z< 10 one intermediate fully spin-polarized configuration with an orbital of 2p0{2p}_{0}2p0​ type occurs.
The energy levels of hydrogen and helium atoms in strong magnetic fields are calculated in this study. The current work contains estimates of the binding energies of the first few low-lying states of these systems that are improvements upon previous estimates. The methodology involves computing the eigenvalues and eigenvectors of the generalized two-dimensional Hartree-Fock partial differential equations for these one- and two-electron systems in a self-consistent manner. The method described herein is applicable to calculations of atomic structure in magnetic fields of arbitrary strength as it exploits the natural symmetries of the problem without assumptions of any basis functions for expressing the wave functions of the electrons or the commonly employed adiabatic approximation. The method is found to be readily extendable to systems with more than two electrons.
The ground and a few excited states of the beryllium atom in external uniform magnetic fields are calculated by means of our 2D mesh Hartree-Fock method for field strengths ranging from zero up to 2.35*10^9T. With changing field strength the ground state of the Be atom undergoes three transitions involving four different electronic configurations which belong to three groups with different spin projections S_z=0,-1,-2. For weak fields the ground state configuration arises from the 1s^2 2s^2, S_z=0 configuration. With increasing field strength the ground state evolves into the two S_z=-1 configurations 1s^22s 2p_{-1} and 1s^2 2p_{-1}3d_{-2}, followed by the fully spin polarised S_z=-2 configuration 1s2p_{-1}3d_{-2}4f_{-3}. The latter configuration forms the ground state of the beryllium atom in the high field regime \\gamma>4.567. The analogous calculations for the Be^+ ion provide the sequence of the three following ground state configurations: 1s^22s and 1s^22p_{-1} (S_z=-1/2) and 1s2p_{-1}3d_{-2} (S_z=-3/2).
We calculate the binding energies of atoms and molecular chains in 1012{10}^{12}1012 G magnetic fields using the Hartree-Fock method. For Z>2 (4) at 1\ifmmode\times\else\texttimes\fi{}1012{10}^{12}1012 (5\ifmmode\times\else\texttimes\fi{}1012{10}^{12}1012), the isolated atom is energetically favored over the molecular chain.