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

Open Journal of Microphysics

Ground State, Isoelectronic Ions and Low-Lying Excited States of Lithium Atom in Strong Magnetic Field

Khadija Abdelhassan Kharroube

Published Jan 1, 2021• 1 citation
Publisher

Abstract

In the framework of the variational Monte Carlo method, the ground states of the lithium atom and lithium like ions up to Z = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states , and of the lithium atom in strong magnetic field are also investigated. Simple trial wave functions for lithium are used.

DOI
10.4236/ojm.2021.113004

Related papers

Variational Monte Carlo calculations of lithium atom in strong magnetic field

Salah Badawi Doma, M. O. Shaker, A. M. Farag +1 more

The variational Monte Carlo method is applied to investigate the ground state and some excited states of the lithium atom and its ions up to Z = 10 in the presence of an external magnetic field regime with γ = 0–100 arb. units. The effect of increasing field strength on the ground state energy is studied and precise values for the crossover field strengths were obtained. Our calculations are based on using accurate forms of trial wave functions, which were put forward in calculating energies in the absence of magnetic field. Furthermore, the value of Y at which ground-state energy of the lithium atom approaches to zero was calculated. The obtained results are in good agreement with the most recent values and also with the exact values.

Journal of Experimental and Theoretical Physics•Jan 1, 2017•14 citations

The beryllium atom, ions, and iso-electronic ions in magnetic field using the variational Monte Carlo method

Salah Badawi Doma, Gamal D. Roston, M. F. Ahmed

Abstract The variational Monte Carlo method is applied to investigate several properties of the beryllium atom, ions, and its iso-electronic ions. For the ground and the excited states of the beryllium atom and ions, the energy eigenvalues were evaluated freely and under the influence of magnetic field. Furthermore, the iso-electronic ions (B+ and C2+) are also investigated under the influence of the external magnetic field. Suitable trial wave functions including the spin and the correlated parts are used in these investigation. Some new excited states were included in the present work, such as the low-lying states (1s22s3s and 1s22s3p) and the core states (1s2s23s and 1s2s3s2). For the spin functions of these states, we used two different functions for the singlet and the triplet excited states. Moreover, the energies of the beryllium ions (Be+ and Be2+) were evaluated freely and in the presence of magnetic field. The obtained results are in good agreement with the corresponding results of other works. Graphical abstract

The European Physical Journal D•Aug 1, 2023•4 citations

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

Hydrogen Atom and Hydrogen Molecule Ion in Homogeneous Magnetic Fields of Arbitrary Strength

Ranjan Bhaduri, Yozo Nogami, Chindhu S. Warke

A simple and accurate variational method is formulated and applied to the ground and excited states of the hydrogen atom as well as the hydrogen molecule ion in a homogeneous magnetic field of arbitrary strength. For the ground state, the electronic wave function o is assumed to be a function of a single, appropriately chosen variable R which contains a variational parameter. The functional form of o, and the corresponding energy, are determined by solving a Schr6dinger- like equation, in which the variational parameter appears explicitly in the kinetic and potential energy terms. The variational parameter is optimized by minimizing the lowest eigenvalue of the equation. Excited states may also be obtained by a slight modification of the method, and explicit calculations are carried out for the m1 = - 1 first excited state of hydrogen and the ( )-state of H2 +. Numerical comparisons are made with some recent papers in the literature. Subject headings: atomic processes - magnetic fields - molecular processes - quantum mechanics

The Astrophysical Journal•Oct 1, 1977•36 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

One-electron atomic–molecular ions containing lithium in a strong magnetic field

Horacio Olivares‐Pilón, D. Baye, Alexander V. Turbiner +1 more

The one-electron lithium-containing Coulomb systems of atomic type Li 2 + and molecular type Li 5 + 2 , LiHe 4 + and LiH 3 + are studied in the presence of a strong magnetic field B ⩽ 10 7 au in a non-relativistic framework. They are considered at the Born–Oppenheimer approximation of zero order (infinitely massive centres) within the parallel configuration (molecular axis parallel to the magnetic field). The variational and Lagrange-mesh methods are employed, complementing each other. It is demonstrated that the molecular systems LiH 3 + , LiHe 4 + and Li 5 + 2 can exist for sufficiently strong magnetic fields B ≳ 10 4 au and that Li 5 + 2 can even be stable at magnetic fields typical of magnetars.

arXiv:0912.1043•Journal of Physics B Atomic Molecular and Optical Physics•Mar 9, 2010•8 citations
In the framework of the variational Monte Carlo method, the ground states of the lithium atom and lithium like ions up to Z = 10 in an external strong magnetic field are evaluated. Furthermore, the two low-lying excited states , and of the lithium atom in strong magnetic field are also investigated. Simple trial wave functions for lithium are used.
The variational Monte Carlo method is applied to investigate the ground state and some excited states of the lithium atom and its ions up to Z = 10 in the presence of an external magnetic field regime with γ = 0–100 arb. units. The effect of increasing field strength on the ground state energy is studied and precise values for the crossover field strengths were obtained. Our calculations are based on using accurate forms of trial wave functions, which were put forward in calculating energies in the absence of magnetic field. Furthermore, the value of Y at which ground-state energy of the lithium atom approaches to zero was calculated. The obtained results are in good agreement with the most recent values and also with the exact values.
Abstract The variational Monte Carlo method is applied to investigate several properties of the beryllium atom, ions, and its iso-electronic ions. For the ground and the excited states of the beryllium atom and ions, the energy eigenvalues were evaluated freely and under the influence of magnetic field. Furthermore, the iso-electronic ions (B+ and C2+) are also investigated under the influence of the external magnetic field. Suitable trial wave functions including the spin and the correlated parts are used in these investigation. Some new excited states were included in the present work, such as the low-lying states (1s22s3s and 1s22s3p) and the core states (1s2s23s and 1s2s3s2). For the spin functions of these states, we used two different functions for the singlet and the triplet excited states. Moreover, the energies of the beryllium ions (Be+ and Be2+) were evaluated freely and in the presence of magnetic field. The obtained results are in good agreement with the corresponding results of other works. Graphical abstract
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.
A simple and accurate variational method is formulated and applied to the ground and excited states of the hydrogen atom as well as the hydrogen molecule ion in a homogeneous magnetic field of arbitrary strength. For the ground state, the electronic wave function o is assumed to be a function of a single, appropriately chosen variable R which contains a variational parameter. The functional form of o, and the corresponding energy, are determined by solving a Schr6dinger- like equation, in which the variational parameter appears explicitly in the kinetic and potential energy terms. The variational parameter is optimized by minimizing the lowest eigenvalue of the equation. Excited states may also be obtained by a slight modification of the method, and explicit calculations are carried out for the m1 = - 1 first excited state of hydrogen and the ( )-state of H2 +. Numerical comparisons are made with some recent papers in the literature. Subject headings: atomic processes - magnetic fields - molecular processes - quantum mechanics
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
The one-electron lithium-containing Coulomb systems of atomic type Li 2 + and molecular type Li 5 + 2 , LiHe 4 + and LiH 3 + are studied in the presence of a strong magnetic field B ⩽ 10 7 au in a non-relativistic framework. They are considered at the Born–Oppenheimer approximation of zero order (infinitely massive centres) within the parallel configuration (molecular axis parallel to the magnetic field). The variational and Lagrange-mesh methods are employed, complementing each other. It is demonstrated that the molecular systems LiH 3 + , LiHe 4 + and Li 5 + 2 can exist for sufficiently strong magnetic fields B ≳ 10 4 au and that Li 5 + 2 can even be stable at magnetic fields typical of magnetars.