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Physical Review A

Three-electron atoms and ions in a magnetic field

Jorge A. Salas, Isabelle M. Pelaschier, Kálmán Varga

Published Sep 2, 2015• 12 citations
Publisher

Abstract

The energies and physical properties of three-electron systems are studied using an explicitly correlated Gaussian basis optimized by the stochastic variational method. The stability of the system as a function of the nuclear charge is analyzed. The role of the Coulomb and magnetic interactions in shaping the structure of these systems is discussed. The accuracy of the energies is substantially improved for high magnetic fields.

DOI
10.1103/physreva.92.033401

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The European Physical Journal D•Aug 1, 2023•4 citations
The energies and physical properties of three-electron systems are studied using an explicitly correlated Gaussian basis optimized by the stochastic variational method. The stability of the system as a function of the nuclear charge is analyzed. The role of the Coulomb and magnetic interactions in shaping the structure of these systems is discussed. The accuracy of the energies is substantially improved for high magnetic fields.
The energy of the ${\mathrm{He}}^{\ensuremath{-}}$ ion in a magnetic field is calculated using the stochastic variational method with a deformed correlated Gaussian basis. The energy levels and the stability domains are calculated and the accuracy of the approach is shown by comparison to previous calculations. The structure of these states is studied by calculating the electron-electron and electron-nucleus distances. In the weak field case, these systems have a pronounced inert He core plus a weakly bound electronlike structure. Stronger fields lead more compact systems unless the stability is lost due to level crossings.
The electronic, magnetic, and structural properties of small clusters are studied in the framework of the single-band Hubbard Hamiltonian. Results for various ground-state and excited-state many-body properties are presented, which were calculated exactly by means of Lanczos's numerical diagonalization method. A full geometry optimization is performed for N\ensuremath{\le}8 atoms by considering all possible nonequivalent cluster structures with fixed nearest-neighbor bond lengths. The most stable structure and the corresponding total spin S are obtained rigorously as a function of the Coulomb interaction strength U/t and number of electrons \ensuremath{\nu}. The resulting interplay between electron correlations, magnetism, and cluster structure is analyzed and the main trends as a function of N, U/t, and \ensuremath{\nu} are derived. The stability of cluster ferromagnetism is studied from two complementary points of view. First, for N\ensuremath{\le}8 and \ensuremath{\nu}=N+1, we determine exactly the stability of the ferromagnetic ground state with respect to electronic excitations and structural changes. It is shown that in small clusters the structural changes can be as important to the temperature dependence of the magnetization as the purely electronic excitations. Second, we determine the stability of the saturated ferromagnetic state with respect to single spin flips as a function of the band filling \ensuremath{\nu}/N. In this case a few selected larger clusters (7\ensuremath{\le}N\ensuremath{\le}43) in the strongly correlated limit (U/t\ensuremath{\rightarrow}+\ensuremath{\infty}) are considered. It is shown that the \ensuremath{\nu}/N dependence of the spin-flip energy \ensuremath{\Delta}${\mathrm{\ensuremath{\varepsilon}}}_{\mathrm{sf}}$ shows interesting electronic-shell-like oscillations, which reflect the characteristics of the single-particle energy-level structure and its dependence on the symmetry and size of the cluster. Finally, we conclude by discussing some of the limitations of the model together with relevant extensions. \textcopyright{} 1996 The American Physical Society.
Variational solutions are given for problems involving diverse fermionic and bosonic N=2--7-body systems. The trial wave functions are chosen to be combinations of correlated Gaussians, which facilitate a fully analytical calculation of the matrix elements. The nonlinear parameters of the trial function are selected by a stochastic technique. The method has proved efficient, accurate, and seems feasible for any few-body bound-state problems emerging in atomic or nuclear physics. \textcopyright{} 1996 The American Physical Society.
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.
In this review we discuss quantum phase transitions and the mapping between symmetry breaking of electronic structure configurations at the large-dimension limit and mean-field theory of phase transitions. We show that the finite size scaling method can be used for the calculations of the critical parameters of the few-body Schrodinger equation. In this approach, the finite size corresponds to the number of elements in a complete basis set used to expand the exact eigenfunction of a given Hamiltonian. The critical parameters such as the critical nuclear charges will be used to explain and predict the stability of atomic and molecular negative ions. For N-electron atoms with 2 N 86, results show that, at most, only one electron can be added to a free atom in the gas phase. However, doubly charged atomic negative ions might exist in a strong magnetic field.
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