Graphen, Knotenfarbklassen und 0-1-Matrizen

Einen guten Überblick über Anzahlen von Knotenfärbungen eines Graphen findet der Leser in der grundlegenden Monografie von Norman Biggs(1). Bei der Untersuchung von Knotenfärbungen ausgewählter Graphen und deren Anzahlen ergaben sich verschiedene 0-1-Matrizen mit interessanten Eigenschaften. Diese sollen, nach einfachen Untersuchungen, hier beschrieben werden. Über Matrizen und ihre Polynome findet man unter den Publikationen ausreichend Literatur. Erwähnt seien die Standardwerke von M. Marcus and H. Minc(), F. R. Gantmacher() und D. M. Cvetkovic’, M. Doob and H. Sachs(). Nach einer Einführung in die Begriffswelt werden Zellengraphen , abgeleitet von einem Vierkreis (das Quadrat) ohne und mit Diagonalen, sowie mir deren Anzahl von Farbklassen der Knotenpunkte untersucht

Commissioning of the HITRAP Cooling Trap with Offline Ions

Highly charged heavy ions at rest offer a wide spectrum of precision measurements. The GSI Helmholtzzentrum für Schwerionenforschung GmbH is able to deliver ions up to U92+. As the production of these heavy, highly charged ions requires high kinetic energies, it is necessary to decelerate these ions for ultimate precision. The broad energy distribution, which results from the deceleration in the HITRAP linear decelerator, needs to be reduced to allow for further transportation and experiments. The HITRAP cooling trap is designed to cool, i.e., reduce, this energy spread by utilizing electron cooling. The commissioning of this trap is done with Ar16+-ions from a local EBIT ion source. By analyzing the signal of stored ions after ejection, properties such as ion lifetime, charge exchange, and ion motions can be observed. Here, we provide an overview of the recent results of the commissioning process and discuss future experiments

Collinear Laser Spectroscopy of Helium-like ¹¹B³⁺

Collinear laser spectroscopy in the 1s2s³S₁→1s2p³P₀,₂ transitions of helium-like ¹¹B³⁺ was performed using the HITRAP beamline at the GSI Helmholtz Centre. The ions were produced in an electron beam ion source, extracted, and accelerated to a beam energy of 4 keV/q. Results agree with previous measurements within uncertainty. Thus, it was demonstrated that the metastable state in He-like ions is sufficiently populated to carry out collinear laser spectroscopy. The measurement is a pilot experiment for a series of measurements that will be performed at a dedicated collinear laser spectroscopy setup at TU Darmstadt with light helium-like ions

Commissioning of the HITRAP Cooling Trap with Offline Ions

Highly charged heavy ions at rest offer a wide spectrum of precision measurements. The GSI Helmholtzzentrum für Schwerionenforschung GmbH is able to deliver ions up to U92+. As the production of these heavy, highly charged ions requires high kinetic energies, it is necessary to decelerate these ions for ultimate precision. The broad energy distribution, which results from the deceleration in the HITRAP linear decelerator, needs to be reduced to allow for further transportation and experiments. The HITRAP cooling trap is designed to cool, i.e., reduce, this energy spread by utilizing electron cooling. The commissioning of this trap is done with Ar16+-ions from a local EBIT ion source. By analyzing the signal of stored ions after ejection, properties such as ion lifetime, charge exchange, and ion motions can be observed. Here, we provide an overview of the recent results of the commissioning process and discuss future experiments

Collinear Laser Spectroscopy of Helium-like ¹¹B³⁺

Collinear laser spectroscopy in the 1s2s³S₁→1s2p³P₀,₂ transitions of helium-like ¹¹B³⁺ was performed using the HITRAP beamline at the GSI Helmholtz Centre. The ions were produced in an electron beam ion source, extracted, and accelerated to a beam energy of 4 keV/q. Results agree with previous measurements within uncertainty. Thus, it was demonstrated that the metastable state in He-like ions is sufficiently populated to carry out collinear laser spectroscopy. The measurement is a pilot experiment for a series of measurements that will be performed at a dedicated collinear laser spectroscopy setup at TU Darmstadt with light helium-like ions

Collinear Laser Spectroscopy of Helium-like ¹¹B³⁺

Collinear laser spectroscopy in the 1s2s3S1→1s2p3P0,2 transitions of helium-like 11B3+ was performed using the HITRAP beamline at the GSI Helmholtz Centre. The ions were produced in an electron beam ion source, extracted, and accelerated to a beam energy of 4 keV/q. Results agree with previous measurements within uncertainty. Thus, it was demonstrated that the metastable state in He-like ions is sufficiently populated to carry out collinear laser spectroscopy. The measurement is a pilot experiment for a series of measurements that will be performed at a dedicated collinear laser spectroscopy setup at TU Darmstadt with light helium-like ions