Marc Vincke

Hydrogen atom in crossed electric and magnetic fields: transition from weak to strong electron-proton decentring

The hydrogen atom in crossed electric and magnetic fields is studied, taking full account of centre-of-mass effects and using a variational basis which does not depend on the choice of a canonical representation, in particular of a gauge. Spectra and wavefunctions are computed for strong magnetic fields. From the analysis of results, general properties for arbitrary crossed fields are deduced. For small electric fields, the most strongly bound states remain essentially centred in the Coulomb well and show only perturbative departure from cylindrical symmetry, while highly excited states may reveal a partial decentring of the electron with respect to the proton, leading to a significant electric dipole moment. Increasing the electric field induces a transition to strong decentring with a very large dipole moment. Above a state-dependent critical electric field, only strongly decentred states remain bound.

Analysis of the R-matrix method on Lagrange meshes

The R-matrix method on a Lagrange mesh is a very simple approximation of the R-matrix method with a basis. By analysing an exactly solvable example, we observe that the mesh approximation does not reduce the accuracy of the R-matrix bound-state energies and phase shifts. This property is obtained with two different meshes, the shifted Legendre and shifted Jacobi meshes, which correspond to equivalent polynomial bases. Their comparison shows that the orthogonality of the Lagrange basis functions is not as crucial as was previously assumed: the Legendre mesh, which corresponds to a nonorthogonal Lagrange basis, is at least as accurate as the Jacobi mesh based on an orthogonal basis. We also emphasize the surprising origin of a known property of the R-matrix method: the results are much more accurate with basis functions without uniform boundary conditions because the quality of the matching is realized by a few highly excited eigenfunctions, with weak physical content, of the sum of the Hamiltonian and Bloch operators.

Centre-of-mass effects on the hydrogen atom in a magnetic field

With a canonical transformation, the Hamiltonian of a neutral system of charged particles in a homogeneous magnetic field is transformed into the sum of an internal Hamiltonian, a CM kinetic energy operator and a term coupling the internal and CM motions. When the magnetic quantum number m of a hydrogen atom state differs from zero, its binding energy is qualitatively affected by the existence of a transverse motion, even a very small one. The number of bound states with a given m not=0 becomes finite and vanishes beyond a critical magnetic field. For any m, the binding energies are reduced by a transverse collective energy which is conveniently expressed as a function of an effective mass. Several effective masses are calculated with a second-order perturbation method in the strong-field region.

Hydrogen molecular ion in an aligned strong magnetic field by the Lagrange-mesh method

The hydrogen molecular ion in an aligned strong magnetic field is studied in prolate spheroidal coordinates with the Lagrange-mesh method. Different variants of the regularization of singularities are described in detail and tested. The simple resulting equations provide a high accuracy with small computing times. At fixed fields and basis sizes, the accuracy on energies decreases with increasing |m| values. At γ = 1, accuracies from 10−12 for m = 0 to 10−9 for m = −4 in positive parity and 10−7 in negative parity are obtained with various bases. Energies at equilibrium for m = 0 can be determined with at least 12 significant digits up to γ = 1000. Equilibrium distances are calculated with at least six significant digits.

Lagrange-mesh calculation of a three-body model for 6He

Abstract The regularized Lagrange-mesh technique is applied to a calculation of the α + n + n three-body system with effective α-neutron and neutron-neutron forces. With a mixed expansion in terms of spherical harmonics for the angular parts of the ground-state wave function, and of Lagrange functions for the radial parts, a variational calculation takes the form of a mesh calculation with the help of the Gauss-Laguerre quadrature. The resulting eigenvalue problem is simple to program and involves large but sparse matrices. With matrices of dimension 3400, the binding energy is obtained within 0.02 MeV of the extrapolated value 0.75 MeV for the considered forces.

Variational study of H- and He in strong magnetic fields

Two-electron systems in strong magnetic fields (>or=1 MT) are studied with a simple Slater-determinant basis which allows different types of configuration mixing. Variational energies of the lowest singlet and triplet bound states are obtained for values 0 to -2 of the magnetic quantum number. They improve previous results and show the importance of correlations. The order of the -2T+ and -2S+ states is found to be different in the H- and He spectra.

Delocalized states of atomic hydrogen in crossed electric and magnetic fields

Abstract The hydrogen atom in crossed electric and magnetic fields is studied in an approximate but purely quantal way, with exact treatment of gauge invariance and centre-of-mass motion. Under some conditions, a triaxial harmonic motion appears where the electron average location is strongly delocalized with respect to the proton.

Magnetized hydrogen atom on a Laguerre mesh

Without any analytic calculation of a matrix element, energies and root-mean-square radii of the hydrogen atom in low and intermediate magnetic fields are calculated with high accuracy. With the Lagrange functions technique, the Schrodinger equation in semiparabolic coordinates is discretized on a small modified Laguerre mesh involving ten points for each coordinate. The mesh equations approximate a variational calculation with at most 55 basis functions. For a reduced field gamma =0.001 or 0.01, the accuracy of the energies is better than 10-12 for a number of low-lying m=0 and +or-1 states of both parities. At gamma =0.1, the accuracy starts decreasing beyond the second excited state because the dominant spherical symmetry of the basis becomes less appropriate.

Centre-of-mass corrections on atomic binding energies in a magnetic field

Centre-of-mass corrections on the total energies of general atomic systems are investigated in the presence of a homogeneous magnetic field. Threshold energies can easily be defined from the ground-state energy of the subsystem. The general form of binding energies with respect to single-electron ionisation is then established as a function of binding energies obtained in an approximation where the nucleus mass is considered as infinite. A transverse collective motion of the atomic system is shown to reduce the binding energies, especially in the case of negative ions. Expressions for ionisation energies of one-electron and two-electron atoms are derived as examples. A detailed quantitative study of the H- and He atoms in very strong magnetic fields is presented. The H- binding energies are very sensitive to centre-of-mass effects. In particular, the H- bound spectrum becomes finite, in opposition to its properties in the infinite-protons-mass approximation.

A simple variational basis for the study of hydrogen atoms in strong magnetic fields

A variational basis with cylindrical symmetry is shown to provide highly accurate results for the lowest m=0 to -4 levels of a hydrogen atom in a strong magnetic field (B>2.35*105 T). The simplicity of the calculation and formulae summarising the behaviour of the variational parameters make the results easy to reproduce.