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Journal of Experimental and Theoretical Physics

Variational Monte Carlo calculations of lithium atom in strong magnetic field

Salah Badawi Doma, M. O. Shaker, A. M. Farag, F. N. El‐Gammal

Published Jan 1, 2017• 14 citations
Publisher

Abstract

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.

DOI
10.1134/s1063776117010034

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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 calculate the ground-state energy and the effective spin Land\'e g factor (g∗{\mathit{g}}^{\mathrm{*}}g∗) of a two-dimensional electron gas in strong magnetic fields using a variational Monte Carlo method and many-body trial wave functions composed of the Jastrow correlation factor and the Laughlin-type functions. We find that g∗{\mathit{g}}^{\mathrm{*}}g∗ increases with decreasing of electron density and also shows increasing behavior as the filling factor \ensuremath{\nu} decreases in the region of 12. At \ensuremath{\nu}=1.0, g∗{\mathit{g}}^{\mathrm{*}}g∗ is estimated to be about 11 for a dimensionless parameter rs{\mathit{r}}_{\mathit{s}}rs​=1.33, as compared to the measured value of 7.3, while considering impurity and phonon scatterings gives a better agreement of g∗{\mathit{g}}^{\mathrm{*}}g∗=9. \textcopyright{} 1996 The American Physical Society.
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 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).
Abstract The problem of the hydrogen atom in a magnetic field can be treated satisfactorily by approximate methods which are quite accurate for very low or very high magnetic field strengths. Before this paper the only useful treatments for intermediate field strengths were variational methods giving upper bounds to the energies. As described in the paper the diffusion QMC method was applied in the same way as in earlier solutions for the hydrogen atom, but with additional magnetic terms added to the Hamiltonian expression. These include complex expressions and the required wavefunction includes a corresponding factor. With the magnetic field aligned along one axis, integration over the angle ϕ in (r, θ, ϕ) coordinates reduces the additional terms to real functions of r and z as well as the magnetic quantum number m. In the diffusion/multiplication processes of a random walk procedure these may be simply included with the potential energy term. In this study the energy at each step was determined from the average multiplication factor for the walkers. Importance sampling was not used. Results were obtained for quantum numbers m = 0, 1 at each of three magnetic field strengths. A comparison of results showed good agreement with the lowest values obtained in several of the earlier analytic variational calculations.