Atoms In Strong Magnetic Fields Research Articles

Center-of-mass corrections to the electromagnetic transitions of hydrogen atoms in strong magnetic fields.

The influence of center-of-mass corrections on transition probabilities in the hydrogen spectrum is studied in a homogeneous magnetic field with the help of canonical transformations. To a good approximation, only energy differences are modified but in an unexpected way for electric quadrupole transitions. Center-of-mass corrections mainly affect the lifetimes of the tightly bound states with {ital m}{lt}0. Dipole transitions remain dominant for reduced fields {gamma} up to at least 1000. Quadrupole transitions should dominate the lifetimes of even-parity {ital m}=0 states at higher fields.

Relativistic calculations for hydrogenic atoms in strong magnetic fields with Slater-type basis functions.

Relativistic calculations for hydrogenic atoms in strong magnetic fields with Slater-type basis functions.

Chaos and Atoms in Strong Magnetic Fields

In the presence of a strong state magnetic field, the classical dynamics of a Rydberg atomic state turns chaotic. This has important consequences on the energy levels and eigenstates of the quantum system. These are analysed in connection with the recent experimental results.

Analysis of quantum manifestations of chaos in general Rydberg atoms in strong magnetic fields.

We present a method for calculating quantum spectra of arbitrary highly excited atoms in strong magnetic fields at fixed scaled energy \ensuremath{\varepsilon}=E/${\mathit{B}}^{2/3}$. Since classical dynamics depends exclusively on \ensuremath{\varepsilon}, this approach is most suited to analyzing the quantum manifestations of classical chaos. We find that modulations of the spectra associated with classical periodic orbits depend strongly on the quantum defect \ensuremath{\mu}. In particular, the spectra at given \ensuremath{\varepsilon} are most (least) modulated for integer (half-integer) values of \ensuremath{\mu}. We also find that the energy-level statistics tend more closely towards the Wigner (``chaotic'') limit for half-integer \ensuremath{\mu}.

Finite-temperature density functional theory of atoms in strong magnetic fields

The density functional theory of atomic electrons in strong magnetic fields is generalized to finite-temperature systems. General integral formulations are developed in the format of Mermin-Kohn-Sham finite-temperature density functional theory. The lowest order of the general theory leads to a temperature-dependent extended Thomas-Fermi (TETF)-like functional, which is simple enough to be analyzed. The general theory provides a new way of calculating the equilibrium properties of many-electron systems in strong magnetic fields.

Density-functional theory of atoms in strong magnetic fields.

A density-functional model of atoms in strong magnetic fields is proposed along lines parallel to Hohenberg-Kohn-Sham density-functional theory. We derive a Thomas-Fermi-Weiz\acker-like (TFW) functional by using the classical-path approximation to the relevant one-particle Green's function. We also address the correlation effect between the effective potential and the magnetic field. The TFW-like model provides a simple way of calculating ground-state energies and charge densities of atoms in magnetic fields, and can be systematically improved.

SPECTRUM DISTRIBUTION OF RESONANCE FLUORESCENCE FOR ATOMS IN STRONG MAGNETIC FIELD

A theory describing the resonance fluorescance of atoms in strong magnetic field is proposed. A general expression of spectrum distribution for this resonance fluorescence is given and the relation between the spectrum and the magnitude of the magnetic field is examined.

Hydrogenic Rydberg atoms in strong magnetic fields: Theoretical and experimental spectra in the transition region from regularity to irregularity

For deuterium Rydberg atoms in a magnetic field of ∼6 T we compare the complete experimental spectrum in the range −190 cm−1 to −20 cm−1 with the positions and oscillator strengths of the corresponding quantum theoretically calculated photoabsorption lines. The agreement is excellent. The range of energy covered extends from the end of thel-mixing regime up to the regions where the approximate integrability of the problem is completely lost, and the corresponding classical system undergoes a transition to chaos.

Atoms in strong magnetic fields

We review recent results of investigations of hydrogen-like systems at magnetic field strengths where the Lorentz forces are comparable to, or larger than, the Coulomb binding forces. This situation is realized for low-lying states at field strengths typical of magnetic white dwarfs and neutron stars, while for Rydberg states already laboratory field strengths are sufficient. We discuss the wavelength spectrum of the hydrogen atom in magnetic fields of arbitrary strength, and describe in which way the spectroscopy of "stationary lines", which appear in this spectrum, has made possible the detection of the largest magnetic field strength ever found in a white dwarf star to date. For Rydberg states in strong laboratory fields we perform a quantitative comparison between experimental and theoretical spectra, and demonstrate that symptoms of "quantum stochasticity" are recovered in the spectra of magnetized Rydberg atoms. In particular we point out that the breakdown of quasi-separability in the quantal problem is closely related to the disappearance of regular orbits in the classical problem. We conclude that magnetized Rydberg atoms lend themselves as ideal objects in which to study, theoretically and experimentally, manifestations of quantum stochasticity.

Rydberg atoms in uniform magnetic fields: Uncovering the transition from regularity to irregularity in a quantum system.

We investigate the eigenvalue spectra of hydrogen Rydberg atoms in strong magnetic fields for manifestations of quantum stochasticity and find (i) a smooth transition from a Poisson-type to a Wigner-type distribution of level spacings in the range of energy where classical motion becomes increasingly chaotic, (ii) the occurrence of multiple avoided crossings, and (iii) connected with this, an extreme sensitivity of oscillator strengths, and thus of observable spectra, with respect to small variations of an external parameter, viz., the magnetic field strength.

Note of the usefulness of perturbation theory in calculating energy levels and transitions of hydrogen Rydberg atoms in strong magnetic fields

The author investigates in quantitative terms, how far a standard perturbation calculation can produce reliable results at the principal quantum numbers and magnetic field strengths for which quite recent experiments with magnetised hydrogen atoms in highly excited states have successfully been performed (n approximately 25, B<or approximately=6 T). Energy levels and oscillator strengths of the states originating from the n=22-26 manifolds are determined for B=4.7 T using perturbation theory and are compared with corresponding results obtained previously by Clark and Taylor (1980-2) in the framework of a far more sophisticated numerical method. An unexpected finding is that their Sturmian approach is not able to reproduce the oscillator strength patterns of Balmer transitions to m=0 even-parity states predicted by perturbation theory. The author traces this back to a phase error which seems to occur, in their calculation, in the coherent superposition of the dipole contributions from the s and d partial waves of the Rydberg states. Furthermore, he checks the quality of approximate analytical formulae for the diamagnetic energies in perturbation theory which have recently become available through the exact separation of the diamagnetic interaction in momentum space.

"Circular" states of Rydberg atoms in strong magnetic fields.

Using the numerical techniques that have been successful in elucidating the low-lying part of the level scheme of atoms in magnetic fields pertaining to white dwarf stars and neutron stars, we have computed the energies and wave functions of ``circular'' Rydberg states (i.e., with \ensuremath{\Vert}m\ensuremath{\Vert}=n-1) with \ensuremath{\Vert}m\ensuremath{\Vert}=24--35 for laboratory fields up to several tens of teslas. We can, therefore, follow a number of physical properties, such as transition frequencies and radiative decay times, of circular states as functions of the magnetic field strength and make predictions that should be verifiable experimentally.

Hydrogen and helium atoms in strong magnetic fields

The behaviour of atoms in strong magnetic fields of the order of 106–1012 G is investigated, and ground-state energies of hydrogenlike and heliumlike atoms are calculated and compared with earlier results. For the hydrogen atom, we make a variational calculation for so-called hydrogenlike states, where we assume the solution in the direction of the field corresponds to the solution of a one-dimensional Schrödinger equation with a truncated Coulomb potential. For the helium atoms we also try a variational approach where the trial wave functions are products of single-particle "orbitals," which are mainly magnetic in their spatial form.Ground-state energies and ionization energies are tabulated for field strengths ranging from 106 to 1012 G. At 1012 G, for instance, the binding energy of a hydrogen atom is changed from −13.6 eV to approximately −150 eV, which is in reasonable agreement with other calculations. The corresponding result for the ground-state energy of a helium atom is a change from −78 eV to approximately −730 eV, also in fair agreement with other calculations. Ionization energies for the outer electron are found to be approximately 50 eV for H− atoms and 350 eV for He atoms in a magnetic field of 1012 G.

Pseudoatoms and atoms in strong magnetic fields

An algorithm is developed for dealing with n electron atoms in strong magnetic fields based on the eigenstates of a system called a pseudoatom in which all Coulomb interactions are replaced by oscillator interactions, attractive or repulsive as the case may be. All matrix elements required in this algorithm are given in explicit and closed analytic form. Furthermore, as the eigenvalues and eigenstates of the pseudoatom can be obtained analytically, this model sharpens our intuition on the changes in configuration that can be expected in the presence of strong magnetic fields.

Pseudoatoms and atoms in strong magnetic fields: M, Moshinsky, Instituto de Fisica, UNAM, Apdo, Postal 20-364, México, D.F. 01000, México; and N. Méndez and E. Murow, Facultad de Ciencias, UNAM, México

Pseudoatoms and atoms in strong magnetic fields: M, Moshinsky, Instituto de Fisica, UNAM, Apdo, Postal 20-364, México, D.F. 01000, México; and N. Méndez and E. Murow, Facultad de Ciencias, UNAM, México

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&gt;2.35*105T). The simplicity of the calculation and formulae summarising the behaviour of the variational parameters make the results easy to reproduce.

Asymptotic solution of coupled equations for electron scattering

The basic theory of electron-atom/ion scattering and computer programs implementing this in the close-coupling and related approximations are described. Adaptations made to these codes enabling them to take advantage of the vector processing features on the CRAY-1 are given, together with details of calculations thus amde possible. An approach to solving the equations of electron-molecule scattering that specially makes use of vector machines is described. Current areas of interest in atomic physics such as atoms in strong magnetic fields, electron impact ionisation of atoms and ionic recombination in an ambient gas, where access to CRAY-1 machines has stimulated progress are mentioned.

Hartree-Fock calculations for atoms in strong magnetic fields. I. Energy levels of two-electron systems

A general approach to N-electron systems in superstrong magnetic fields (B>or approximately=5*105 T) is presented within Hartree-Fock theory. Starting from Slater determinants with single-particle wavefunctions that are products of Landau states and arbitrary longitudinal functions gmi(z), the system of equations for self-consistently determining the gmi(z) is derived, and the expansions of the matrix elements of the electron-nucleus and electron-electron interaction which occur between arbitrary Landau states are given in terms of numerically feasible basis functions. The well known Froese-Fischer code had to be modified considerably to solve the HF equations, and the numerical stability and accuracy are carefully checked. As a first application the ground-state energies of helium-like systems with nuclear charges up to Z=26 are calculated for magnetic field strengths in the range 5*105 to 5*109 T.

Atomic collision calculations

The basic theory of electron-atom/ion scattering and computer programs implementing this in the close-coupling and related approximations are described. Adaptations made to these codes enabling them to take advantage of the vector processing features on the CRAY-1 are given, together with details of calculations thus amde possible. An approach to solving the equations of electron-molecule scattering that specially makes use of vector machines is described. Current areas of interest in atomic physics such as atoms in strong magnetic fields, electron impact ionisation of atoms and ionic recombination in an ambient gas, where access to CRAY-1 machines has stimulated progress are mentioned.

On the validity of perturbation calculations of energy levels and transitions of hydrogen atoms in strong magnetic fields

By comparing the numerical results of various authors, the authors have investigated magnetic field strengths up to which a standard perturbation calculation can produce reliable results. Energy levels and transition probabilities for 14 low-lying states of the H atom are determined for B=103 T using perturbation theory and are discussed in relation to previously published numerical values. Discrepancies up to five orders of magnitude in earlier results for transition probabilities are cleared up by their approach.