Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:physics/9910017 · Physical Review A

Ground states of H, He,…, Ne, and their singly positive ions in strong magnetic fields: The high-field regime

Mikhail Ivanov, Peter Schmelcher

Published Jan 11, 2000• 60 citations
arXivHTMLPDF

Abstract

The electronic structure of the ground state and some excited states of neutral atoms with the nuclear charge numbers $1<~Z<~10$ 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 $m=0$ 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 $2<~Z<~5$ have one fully spin-polarized ground-state configuration, whereas for $6<~Z<~10$ one intermediate fully spin-polarized configuration with an orbital of ${2p}_{0}$ type occurs.

DOI
10.1103/physreva.61.022505

Related papers

Ground states of helium to neon and their ions in strong magnetic fields

Sebastian Boblest, C. Schimeczek, Günter Wunner

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 $Z=2$--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.

Physical Review A•Jan 10, 2014•17 citations

The beryllium atom and beryllium positive ion in strong magnetic fields

Ivanov, M V, Schmelcher, P

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).

•Sep 1, 2000•11 citations

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

C. Schimeczek, Sebastian Boblest, Dirk Meyer +1 more

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.

Physical Review A•Jul 12, 2013•16 citations

Exchange and correlation energies of ground states of atoms and molecules in strong magnetic fields

Peter Schmelcher, Mikhail Ivanov, W. Becken

Using a Hartree-Fock mesh method and a configuration-interaction approach based on a generalized Gaussian basis set, we investigate the behavior of the exchange and correlation energies of small atoms and molecules, namely, the helium and lithium atoms as well as the hydrogen molecule, in the presence of a magnetic field covering the regime $B=0--100 \mathrm{a}.\mathrm{u}.$ In general, the importance of the exchange energy to the binding properties of atoms or molecules increases strongly with increasing field strength. This is due to the spin-flip transitions, and in particular due to the contributions of the tightly bound hydrogenic states which are involved in the corresponding ground states of different symmetries. In contrast to the exchange energy the correlation energy becomes less relevant with increasing field strength. This holds for the individual configurations constituting the ground state and for the crossovers of the global ground state.

arXiv:physics/9902060•Physical Review A•May 1, 1999•28 citations

Ground states of atoms and molecules in strong magnetic fields

P. Schmelcher

The ground states of small atoms and molecules, namely those of the hydrogen, helium, and lithium atoms and the hydrogen molecular ion and hydrogen molecule, are studied in the presence of an external magnetic field. For the one-electron systems the ground state is of the same symmetry for arbitrary field strengths, and the corresponding binding energy shows a monotonic increase with increasing field strength. More interesting, the two- and three-electron systems show ground-state transitions which involve both transitions in the spin multiplicity and spatial quantum numbers. An outlook on the expected cascade of transitions in many electron atoms and molecules is provided. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 789–795, 1998

International Journal of Quantum Chemistry•Jan 1, 1998•5 citations

The HeH+molecular ion in a magnetic field

A V Turbiner, N L Guevara

A detailed study of the low-lying electronic states 1 Σ, 3 Σ, 3 Π, 3 Δ of the HeH + molecular ion in parallel to a magnetic field configuration (when α-particle and proton are situated on the same magnetic line) is carried out for B = 0 − 4.414 × 10 13 G in the Born–Oppenheimer approximation. The variational method is employed using a physically adequate trial function. It is shown that for the Σ states the parallel configuration is stable with respect to small deviations. The quantum numbers of the ground state depend on the magnetic field strength. The ground state evolves from the spin-singlet 1 Σ state for small magnetic fields B ≲ 0.5 au to the spin-triplet 3 Σ (unbound or weakly bound) state for intermediate fields and to the spin-triplet strongly bound 3 Π state for B ≳ 15 au. When the HeH + molecular ion exists, it is stable with respect to dissociation.

arXiv:physics/0703090•Journal of Physics B Atomic Molecular and Optical Physics•Aug 6, 2007•10 citations
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< \ensuremathγ< 10000.0.5<~\ensuremath{\gamma}<~10000.0.5< \ensuremathγ< 10000. For \ensuremathγ=10000\ensuremath{\gamma}=10000\ensuremathγ=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,m=\ensuremath{-}N+1,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.
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 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).
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 $B={10}^{7}--5\ifmmode\times\else\texttimes\fi{}{10}^{8}\phantom{\rule{0.28em}{0ex}}\mathrm{T}$, relevant for astrophysical problems, e.g., the thermal emission of strongly magnetized isolated neutron stars.
Using a Hartree-Fock mesh method and a configuration-interaction approach based on a generalized Gaussian basis set, we investigate the behavior of the exchange and correlation energies of small atoms and molecules, namely, the helium and lithium atoms as well as the hydrogen molecule, in the presence of a magnetic field covering the regime B=0−−100a.u.B=0--100 \mathrm{a}.\mathrm{u}.B=0−−100a.u. In general, the importance of the exchange energy to the binding properties of atoms or molecules increases strongly with increasing field strength. This is due to the spin-flip transitions, and in particular due to the contributions of the tightly bound hydrogenic states which are involved in the corresponding ground states of different symmetries. In contrast to the exchange energy the correlation energy becomes less relevant with increasing field strength. This holds for the individual configurations constituting the ground state and for the crossovers of the global ground state.
The ground states of small atoms and molecules, namely those of the hydrogen, helium, and lithium atoms and the hydrogen molecular ion and hydrogen molecule, are studied in the presence of an external magnetic field. For the one-electron systems the ground state is of the same symmetry for arbitrary field strengths, and the corresponding binding energy shows a monotonic increase with increasing field strength. More interesting, the two- and three-electron systems show ground-state transitions which involve both transitions in the spin multiplicity and spatial quantum numbers. An outlook on the expected cascade of transitions in many electron atoms and molecules is provided. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 789–795, 1998
A detailed study of the low-lying electronic states 1 Σ, 3 Σ, 3 Π, 3 Δ of the HeH + molecular ion in parallel to a magnetic field configuration (when α-particle and proton are situated on the same magnetic line) is carried out for B = 0 − 4.414 × 10 13 G in the Born–Oppenheimer approximation. The variational method is employed using a physically adequate trial function. It is shown that for the Σ states the parallel configuration is stable with respect to small deviations. The quantum numbers of the ground state depend on the magnetic field strength. The ground state evolves from the spin-singlet 1 Σ state for small magnetic fields B ≲ 0.5 au to the spin-triplet 3 Σ (unbound or weakly bound) state for intermediate fields and to the spin-triplet strongly bound 3 Π state for B ≳ 15 au. When the HeH + molecular ion exists, it is stable with respect to dissociation.