W. Schweizer

On the theory of collective motion in nuclei. III. From Hamiltonian dynamics to vortex-free fluidity

Abstract It is assumed that the Hamiltonian for collective motion in nuclei is invariant under the orthogonal group O(n, R ). For degenerate orbits in phase space it is shown that the classical Hamiltonian equations reduce to the equations of a vortex-free fluid with a velocity field determined by independent equations of motion.

Discrete variable and finite element techniques applied to simple atomic systems

We present effective numerical algorithms based on discrete variable techniques and finite elements for solving the non-separable three-dimensional Schrodinger equation and a method for the solution of the two electron problem in a strong magnetic field, that combines the hyperspherical close coupling and the Finite Element method. As an example we will present some atomic data for the hydrogen and the helium atom in external fields relevant for magnetic white dwarf stars.

A geometric classical model of collective motion in nuclei

Abstract A collective phase space of dimension 12 is introduced to study a classical model of nuclear collective motion. The model employs the 6 components of the coordinate quadrupole and 6 corresponding generalized momenta and can be related to properties of closed-shell nuclei. Vibrational and rotational coordinates are introduced, and purely rotational solutions are studied. The model demonstrates hamiltonian non-rigid motion with a fixed shape of the nucleus. The relation between the coordinate quadrupole tensor and the ellipsoids related to the angular momentum and angular velocity is analyzed for simple forms of the collective potential.

Hydrogen Atoms in Strong Magnetic Fields — in the Laboratory and in the Cosmos

Recent years have seen tremendous progress in studies of the properties of hydrogen atoms in strong magnetic fields. Decisive stimulus came from the discovery of huge magnetic fields in astrophysical “laboratories”, viz. field strengths of order ~107–109 T in neutron stars and of order ~102–104 T in white dwarf stars. At these field strengths the magnetic forces acting on an atomic electron outweigh the Coulomb binding forces even in low-lying states, and thus atomic structure is completely changed. On the other hand, the rapid advancement of high-resolution laser spectroscopy has made it possible to produce atoms in highly excited states, with principal quantum numbers ranging up to n ≅ 520 (in Ba I) [1], and therefore Rydberg states can be used to investigate the effects of magnetic dominance on atomic structure also in terrestrial laboratories with magnetic fields of a few Tesla, or less.

A quantum model of collective motion in nuclei and its dequantization

Abstract Collective coherent states of Perelomov type are denned by acting with unitary operators from a representation of the symplectic group on the ground state of closed-shell nuclei. A dequantization scheme associates with quantum observables classical ones, and with the state space a phase space and a generalized classical dynamics. Applications to the nuclei 4 He, 16 O and 40 Ca are derived from microscopic interactions.

Fremde Welten auf dem Graphikschirm : die Bedeutung der Visualisierung für die Astrophysik

Unsere Vorstellung von der uns umgebenden Welt ist im wesentlichen durch optische Eindrucke gepragt. Durch die Beschrankungen des menschlichen Auges konnen wir viele Bereiche nicht direkt visuell wahrnehmen, wie z. B. atomare und kosmische Objekte, mit Lichtgeschwindigkeit ablaufende Vorgange und elektromagnetische Strahlung auserhalb des sichtbaren Bereichs. Die Menschen versuchen aus diesem Grund seit Jahrhunderten durch kunstvolle Instrumente wie Mikroskope, Fernrohre sowie schnelle und multispektrale Detektoren die Grenzen ihrer Wahrnehmung zu erweitern . Dies ist jedoch aufgrund physikalischer Gesetze nicht im beliebigen Mase moglich. Obwohl auch die Computer selbst diesen grundsatzlichen physikalischen Beschrankungen unterliegen, sind sie doch ein Instrument, um mit Simulationsrechnungen im Rahmen der gultigen physikalischen Gesetze und durch Visualisierung der Ergebnisse diese fremden Welten sichtbar zu machen. Dies soll an einigen Beispielen, bei denen der Graphikschirm als Supermikroskop, als Riesenfernrohr und als Fenster zur Welt von Einstein dient, demonstriert werden. Our picture of the world around us is determined essentially by optical impressions. Due to the limitations of the human eye, we cannot directly perceive many fjelds visualIy, e .g. atomic and cosmic objects, processes occurring with the velocity of light, and electromagnetic radiation outside the visual range. For this reason, humans have tried for centuries to expand the limits of their visual perception with the help of imaginative instruments such as microscopes, telescopes, and fast und multispectral detectors. Because of the laws of physics, this is not possible to an arbitrary extent. Although the computer itself is restricted to these fundamental physical constraints, it is an instrument with which we, using simulation calculations within the framework of the physical laws and through visualization of the results, can make these strange worlds visible. This will be demonstrated by several examples in which the graphics display serves as super microscope, giant telescope and window to the world of Einstein.

Simulation mit Supercomputern: Ein neues Werkzeug der Physik

Unser Wissen uber die Struktur des Kosmos und die darin enthaltenen Objekte stammt aus der sorgfaltigen Analyse der auf der Erde einfallenden elektromagnetischen Strahlung, verbunden mit einer theoretischen Modellierung im Rahmen der von uns erforschten Naturgesetze. Die astronomischen Beobachtungen erstrecken sich dabei heute vom Radiowellenbereich uber den Infrarot-, den optischen, den Rontgenbereich bis hin zum Hochstenergie-Gamma-Bereich, also uber mehr als 20 Dekaden des elektromagnetischen Spektrums.

Strongly Magnetized Atoms — in the Laboratory and in the Cosmos

Recent years have seen tremendous progress in studies of the properties of atoms in strong magnetic fields. Decisive stimulus came from the discovery of huge magnetic fields in astrophysical “laboratories,” viz. field strengths of order ~107 – 109T in neutron stars and of order ~ 102 – 104T in white dwarf stars. At these field strengths the magnetic forces acting on an atomic electron outweigh the Coulomb binding forces even in low-lying states, and thus atomic structure is completely changed. On the other hand, the rapid advancement of high-resolution laser spectroscopy has made it possible to produce atoms in highly excited states, with principal quantum numbers ranging, presently,1up to n ≅ 520, and therefore Rydberg atoms can be used to investigate the effects of magnetic dominance on atomic structure also in terrestrial laboratories with magnetic fields of a few Tesla, or less.

Liapunov Exponents for the Diamagnetic Kepler Problem and the Transition from Regular to Irregular Motion

For the diamagnetic Kepler problem the transition from regular to irregular motion is observed by calculating Liapunov exponents of periodic orbits over a large energy scale.