2.6M - 1. Institut für Theoretische Physik - Universität Stuttgart

Summary
The topic of this thesis is ’Diffusion Quantum Monte Carlo simulations for many-electron
atoms in neutron star magnetic fields’.
Introduction: Since the discovery of large magnetic fields (B ≈ 10 5 −10 9 T) in neutron
stars in the late seventies [28] atoms in strong magnetic fields have become a hot topic of
research [28]. Neutron stars are stellar remnants of supernovae explosions. In principle
the quantitative analysis of their electromagnetic spectrum permits the determination of
its parameters, e.g. surface temperature, mass, radius and magnetic field strength. From
these data the internal structure and the physics of the cosmic object can be deduced.
The spectroscopic investigation of these faint objects became only possible by means
of large telescopes of the 10m-class (VLT, Keck) and space-based X-ray observatories
(XMM, Chandra).
Hydrogen and helium in very strong magnetic fields were already examined extensively
in the past [28]. By contrast reliable data for the higher elements are still missing. It is
assumed that the atmosphere of neutron stars consists of atoms and ions created during
the lifetime of the star. In this regard all elements up to a nuclear charge number of
Z = 26 are of interest. The computation of synthetic spectra is done at the University
of Tübingen in the group of K. Werner [34]. This thesis presents for the first time the
possibility of treating medium-Z atoms in selected magnetic fields using the application
of the Diffusion Quantum Monte Carlo method which yields the correct ground state
energy.
In this thesis Schrödinger’s equation is solved for many-electron atoms in very strong
magnetic fields by a simulation method. On the one hand the Variational, and on the
other hand the Diffusion, Quantum Monte Carlo method is used. The general idea of
these two methods is described in chapter 2. The guiding wavefunction which must
be carefully chosen to obtain good results is of crucial importance. Not even an educated
guess leads to the goal. Chapter 3 describes how the guiding wavefunction is
constructed for the unsolved problem of treating atoms up to Z = 26 in strong magnetic
fields. The computing time increases rapidly with the number of electrons. Therefore
the simulation was implemented on a computing cluster. Important information which
has to be considered for parallelism is given in chapter 4. In chapter 5 the results are
compared with other methods by means of tables and diagrams. This chapter considers,
additionally, the error estimate and the computing time. Chapter 6 follows which gives a
summary of this thesis and an outlook. Further thoughts on the solution of the questions
pointed out in the outlook are given. The appendix contains general information about
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