Heinz Herold

Hydrogen atoms in arbitrary magnetic fields: I. Energy levels and wavefunctions?

The energy values of many low-lying states of the one-electron problem in the presence of a homogeneous magnetic field of arbitrary strength (0<B<or=4.7*108 T) are calculated with high numerical accuracy for a sufficiently dense mesh of B. The wavefunctions are expanded either in terms of spherical harmonics (weak and moderate fields) or in terms of Landau states (strong and very strong fields), with r- or z-dependent expansion functions that are determined with the use of an adopted version of the MCHF code of Froese Fischer (1978). At intermediate field strengths up to 24 expansion terms are included. The structural change of the wavefunctions with magnetic field is discussed quantitatively for a few representative states. As an application, the splittings of the components of the Lyman- alpha , beta , and the Balmer- alpha lines of the hydrogen atom are presented (including the effects of the finite proton mass) as continuous functions of the field strength over the whole range of B considered.

Hydrogen atoms in arbitrary magnetic fields. II. Bound-bound transitions

For pt.I see ibid., vol.17, p.29-52 (1984). Wavelengths, dipole strengths, oscillator strengths and transition probabilities for electromagnetic transitions between low-lying states of the hydrogen atom embedded in a magnetic field of arbitrary strength (0<B<or=4.70*108T) are calculated with high numerical accuracy for a sufficiently dense mesh of B values using the wavefunctions and energy values determined in paper I by expanding the wavefunctions in terms of spherical harmonics (weak and moderate fields), or in terms of Landau states (strong and very strong fields). Effects caused by the finiteness of the proton mass are taken into account, and the scaling laws are quoted by the aid of which the results presented can be utilised to cover quantitatively the whole hydrogenic sequence in intense magnetic fields; finally, the quality of the results of previous calculations is checked.

Numerical aspects of the smoothed particle hydrodynamics method for simulating accretion disks

The derivation of the Smoothed Particle Hydrodynamics (SPH) method is reviewed. In particular, the problem of second-order derivative terms is investigated. Applying these considerations to the Navier-Stokes equations, a physical viscosity is constructed which can be used to perform simulations of viscous fluids within the framework of SPH. With such a viscous stress tensor the energy balance and the angular momentum conservation for the particle and the continuum representations are compared. An SPH code based on these results is tested on different problems, especially on an analytically solvable problem, namely the spreading of a ring of gas moving with Keplerian speed around a point mass. Additionally, some examples for the dynamics of accretion disks in close binary systems are presented. Finally, the efficient implementation of this SPH code is discussed in some detail, in particular by a comparison between scalar and vector computers.

Hartree-Fock calculations for excited states of two-electron systems in strong magnetic fields

The Hartree-Fock method with single-particle wavefunctions adapted in symmetry to the respective regimes, i.e. spherical wavefunctions for dominating Coulomb forces ( beta z=B/(Z24.7010*105 Tesla) or approximately=1), has been employed to determine wavefunctions, energies and oscillator strengths of helium-like atoms for magnetic field strengths in the range 4.7*101 to 4.7*108 T. In addition, the problem of level correspondence between the low-field and high-field domains is solved.

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.

Local particle simulations of viscous self-gravitating disks

Abstract We present the results of a particle simulation studying the local flow of a viscous, self-gravitating disk in Keplerian motion. Our method is based on Wisdom and Tremaines (Astron. J. 95.3, 925–940, 1988) local simulation of planetary rings, but includes self-gravity. We implement a new numerical prescription of interparticle viscosity that formally reduces to Navier-Stokes stresses. Inclusion of hydrodynamic Navier-Stokes-type viscous friction is essential for the system to develop a secular instability for high values of the stability parameter ( Q > 1). In the framework of a linear perturbation theory wavelength and growth time of the most unstable mode are derived for a “softened” potential that is used in the simulation. The objectives of this paper are twofold: predictions regarding wavelength and growth time of a secular ring instability can be confirmed numerically. Moreover the relative density enhancement in the perturbed regions can be determined in the nonlinear particle simulation; it reaches values twice the unperturbed density. The possible relevance of this mechanism for structuring protoplanetary accretion disks and planetary rings is briefly discussed.

Decay of positronium in strong magnetic fields

We investigate the decay of bound electron-positron pairs (positronium) in strong magnetic fields (of order 1012 Gauss, which are assumed for neutron stars) on the basis of a correct treatment of the two-body problem, thus improving previous work by Carr and Sutherland (1978). We find that, even in the presence of a strong magnetic field, the decay of the ground state of positronium must be momentum conserving, whereby the possibility of the one-photon decay is ruled out. We calculate the transition rate for the two-photon annihilation process which turns out to be larger than the field free transition rate by a factor (1/α)2B/Bcr (where α is the electromagnetic coupling constant, andBcr=me2c2/(eħ)=4.41×1013 Gauss).

Comment on the effect of the proton mass on the spectrum of the hydrogen atom in a very strong magnetic field

Abstract Contrary to a recent claim, we point out that, in the problem of a hydrogen atom in a strong magnetic field, the effect of the finite proton mass on the level scheme as well as on electromagnetic transitions is non-neligible.

Bremsstrahlung in strong magnetic fields. I. The elementary process

Analyses the elementary electron-ion bremsstrahlung process for magnetic field strengths of the order 107-109 T, which are present in plasmas in the vicinity of neutron stars. The general expressions of the (non-relativistic) cross section is given, assuming electrons in the ground-state Landau level, and various approximations to it are discussed. Detailed results are presented for the dependence of the cross section on the magnetic field strength, the primary electron energy, and the energy, polarisation, and solid angle of the emitted bremsstrahlung photons.

Line-of-sight integration: A powerful tool for visualization of three-dimensional scalar fields

An easy conceivable but very powerful method for the visualization of three-dimensional scalar fields is described. The way this method works is illustrated by some examples and the computed pictures are compared with the results of other methods of representation.