0000000000004504
AUTHOR
Stefan E. Schmidt
On Meet-Complements in Cohn Geometries
Within the frame of projective lattice geometry, the present paper investigates classes of meet-complements in Cohn geometries and especially in Ore and Bezout geometries. The algebraic background of these geometries is given by torsion free modules over domains — in particular Ore and Bezout domains. 1
A Lattice-Geometric Proof of Wedderburn’s Theorem
This note presents a proof of Wedderburn’s theorem concerning the classification of semisimple rings within the conceptual frame of projective lattice geometry.
Modulinduzierte affine Räume
Ausgehend von einem Liniensystem S:= (P, G) bezeichnen wir fur jede Abbildung α: P → P eine Linie l aus S als α-invariant, falls α(l) \( \alpha (l) \subseteq l \) gilt; die Menge aller α-invarianten Linien von S nennen wir die Spur von α bzgl. <S, d.h.
Laser spectroscopy of the ground-state hyperfine structure in H-like and Li-like bismuth
The LIBELLE experiment performed at the experimental storage ring (ESR) at the GSI Helmholtz Center in Darmstadt aims for the determination of the ground state hyperfine (HFS) transitions and lifetimes in hydrogen-like (209Bi82+) and lithium-like (209Bi80+) bismuth. The study of HFS transitions in highly charged ions enables precision tests of QED in extreme electric and magnetic fields otherwise not attainable in laboratory experiments. While the HFS transition in H-like bismuth was already observed in earlier experiments at the ESR, the LIBELLE experiment succeeded for the first time to measure the HFS transition in Li-like bismuth in a laser spectroscopy experiment.
On the algebraic representation of projectively embeddable affine geometries
The main result of this article is an application of [1] and [2] which yields that an at least 2-dimensional affine geometry is module-induced if and only if it is projectively embeddable into an Arguesian projective lattice geometry.
Lifetimes and g-factors of the HFS states in H-like and Li-like bismuth
The LIBELLE experiment performed at the experimental storage ring (ESR) at the GSI Helmholtz Center for Heavy Ion Research in Darmstadt, Germany, has successfully determined the ground state hyperfine (HFS) splittings in hydrogen-like ($^{209}\rm{Bi}^{82+}$) and lithium-like ($^{209}\rm{Bi}^{80+}$) bismuth. The study of HFS transitions in highly charged ions enables precision tests of QED in extreme electric and magnetic fields otherwise not attainable in laboratory experiments. Besides the transition wavelengths the time resolved detection of fluorescence photons following the excitation of the ions by a pulsed laser system also allows to extract lifetimes of the upper HFS levels and g-fac…
New Nuclear Magnetic Moment of Bi209 : Resolving the Bismuth Hyperfine Puzzle
A recent measurement of the hyperfine splitting in the ground state of Li-like ${^{208}\mathrm{Bi}}^{80+}$ has established a ``hyperfine puzzle''---the experimental result exhibits a $7\ensuremath{\sigma}$ deviation from the theoretical prediction [J. Ullmann et al., Nat. Commun. 8, 15484 (2017); J. P. Karr, Nat. Phys. 13, 533 (2017)]. We provide evidence that the discrepancy is caused by an inaccurate value of the tabulated nuclear magnetic moment (${\ensuremath{\mu}}_{I}$) of $^{209}\mathrm{Bi}$. We perform relativistic density functional theory and relativistic coupled cluster calculations of the shielding constant that should be used to extract the value of ${\ensuremath{\mu}}_{I}(^{209…
An improved value for the hyperfine splitting of hydrogen-like209Bi82+
We report an improved measurement of the hyperfine splitting in hydrogen-like bismuth (209Bi82+) at the experimental storage ring ESR at GSI by laser spectroscopy on a coasting beam. Accuracy was improved by about an order of magnitude compared to the first observation in 1994. The most important improvement is an in situ high voltage measurement at the electron cooler (EC) platform with an accuracy at the 10 ppm level. Furthermore, the space charge effect of the EC current on the ion velocity was determined with two independent techniques that provided consistent results. The result of nm provides an important reference value for experiments testing bound-state quantum electrodynamics in t…
Hyperfine transition in209Bi80+—one step forward
The hyperfine transitions in lithium-like and hydrogen-like bismuth were remeasured by direct laser spectroscopy at the experimental storage ring. For this we have now employed a voltage divider which enabled us to monitor the electron cooler voltage in situ. This will improve the experimental accuracy by about one order of magnitude with respect to our previous measurement using the same technique.
Simple Nuclear Structure inCd111–129from Atomic Isomer Shifts
Isomer shifts have been determined in ^{111-129}Cd by high-resolution laser spectroscopy at CERN-ISOLDE. The corresponding mean square charge-radii changes, from the 1/2^{+} and the 3/2^{+} ground states to the 11/2^{-} isomers, have been found to follow a distinct parabolic dependence as a function of the atomic mass number. Since the isomers have been previously associated with simplicity due to the linear mass dependence of their quadrupole moments, the regularity of the isomer shifts suggests a higher order of symmetry affecting the ground states in addition. A comprehensive description assuming nuclear deformation is found to accurately reproduce the radii differences in conjunction wi…
The decay energy of the pure s-process nuclide ¹²³ Te
Physics letters / B 758, 407 - 411 (2016). doi:10.1016/j.physletb.2016.04.059
Darstellung von Hyperebenen in verallgemeinerten affinen Räumen durch Moduln
The starting point of this article is a generalized concept of affine space which includes all affine spaces over unitary modules. Our main result is a representation theorem for hyperplanes of affine spaces: Every hyperplane which satisfies a weak richness condition is induced by a module. 1
The coordinatization of affine planes by rings
With every unitary free module of rank 2 there is naturally associated a generalized affine plane (e.g. the lines are just the cosets of all nonzero 1-generated submodules). Here we solve the converse problem by coordinatizing a given generalized affine plane which satisfies certain versions of Desargues' postulate.
Spaces of typen on partially ordered sets
This paper contains a generalized approach to incidence geometry on partially ordered sets. A difference to the usual geometrical concepts is that points may have different size. Our main result states that a large class of spaces allows lattice theoretic characterizations. Especially, a generalized version of the Veblen-Young axiom of projective geometry has a lattice theoretic equivalent, called then-generation property (which is a generalization of the ‘Verbindungssatz’). Modularity and distributivity of a lattice of subspaces are reflected in the underlying space. Finally we give specializations and examples.
Non-destructive single-pass low-noise detection of ions in a beamline.
We have conceived, built, and operated a device for the non-destructive single-pass detection of charged particles in a beamline. The detector is based on the non-resonant pick-up and subsequent low-noise amplification of the image charges induced in a cylindrical electrode surrounding the particles' beam path. The first stage of the amplification electronics is designed to be operated from room temperature down to liquid helium temperature. The device represents a non-destructive charge counter as well as a sensitive timing circuit. We present the concept and design details of the device. We have characterized its performance and show measurements with low-energy highly charged ions (such …
SpecTrap: precision spectroscopy of highly charged ions—status and prospects
We present the status of the SpecTrap experiment currently being commissioned in the framework of the HITRAP project at GSI, Darmstadt, Germany. SpecTrap is a cryogenic Penning trap experiment dedicated to high-accuracy laser spectroscopy of highly charged ions (HCI) near rest. Determination of fine structure and hyperfine structure splittings in HCI with an expected relative spectral resolution of 10−7 will offer the possibility to test quantum electrodynamics in strong fields with unprecedented accuracy. Recently, we have demonstrated trapping and laser Doppler cooling of singly charged magnesium ions in SpecTrap. We report on the status of the experimental apparatus, measurements and pre…
On stable geometries
Within the concept of projective lattice geometry we are considering the class of stable geometries which have also been introduced in [14]. The investigation of their basic properties will result in fundamental structure theorems which especially give a lattice-geometric characterization of free left modules of rank ≥6 over proper right Bezout rings of stable rank 2. This yields a proper generalization of previous results of ours.
Posets That Locally Resemble Distributive Lattices
Abstract Let P be a graded poset with 0 and 1 and rank at least 3. Assume that every rank 3 interval is a distributive lattice and that, for every interval of rank at least 4, the interval minus its endpoints is connected. It is shown that P is a distributive lattice, thus resolving an issue raised by Stanley. Similar theorems are proven for semimodular, modular, and complemented modular lattices. As a corollary, a theorem of Stanley for Boolean lattices is obtained, as well as a theorem of Grabiner (conjectured by Stanley) for products of chains. Applications to incidence geometry and connections with the theory of buildings are discussed.
Projective spaces on partially ordered sets and Desargues' postulate
We introduce a generalized concept of projective and Desarguean space where points (and lines) may be of different size. Every unitary module yields an example when we take the 1-and 2-generated submodules as points and lines. In this paper we develop a method of constructing a wide range of projective and Desarguean spaces by means of lattices.
On Barbilian spaces in projective lattice geometries
We introduce the notion of a Barbilian space of a projective lattice geometry in order to investigate the relationship between lattice-geometric properties and the properties of point-hyperplane structures associated with. We obtain a characterization of those projective lattice geometries, the Barbilian space of which is a Veldkamp space.
Laser Spectroscopy of Neutron-Rich Tin Isotopes: A Discontinuity in Charge Radii across the N=82 Shell Closure
Physical review letters 122(19), 192502 (2019). doi:10.1103/PhysRevLett.122.192502
From Calcium to Cadmium: Testing the Pairing Functional through Charge Radii Measurements of Cd100−130
Differences in mean-square nuclear charge radii of $^{100--130}\mathrm{Cd}$ are extracted from high-resolution collinear laser spectroscopy of the $5s\text{ }{^{2}S}_{1/2}\ensuremath{\rightarrow}5p\text{ }{^{2}P}_{3/2}$ transition of the ion and from the $5s5p\text{ }{^{3}P}_{2}\ensuremath{\rightarrow}5s6s\text{ }{^{3}S}_{1}$ transition in atomic Cd. The radii show a smooth parabolic behavior on top of a linear trend and a regular odd-even staggering across the almost complete $sdgh$ shell. They serve as a first test for a recently established new Fayans functional and show a remarkably good agreement in the trend as well as in the total nuclear charge radius.
Affine Hüllensysteme und affine Liniensysteme
Im folgenden werden wir auf den Zusammenhang affiner Hullensysteme und affiner Liniensysteme eingehen.
n-arguesische affine Räume
Unter Verwendung gewisser Reichhaltigkeitsbedingungen und Schlieβungssatze werden wir in diesem Paragraphen punkttransitive Translationsmengen und maximal transitive Mengen von o-Streckungen konstruieren, um dann im Ruckgriff auf Satz 10 einen algebraischen Darstellungssatz fur bestimmte n-arguesische affine Raume zu erzielen.
The TRAPSENSOR facility: an open-ring 7 tesla Penning trap for laserbased precision experiments
APenning-trap facility for high-precision mass spectrometry based on a novel detection method has been built. This method consists in measuring motional frequencies of singly-charged ions trapped in strong magnetic fields through the fluorescence photons from laser-cooled 40Ca+ ions, to overcome limitations faced in electronic single-ion detection techniques. The key element of this facility is an open-ring Penning trap coupled upstream to a preparation Penning trap similar to those used at Radioactive Ion Beam facilities. Here we present a full characterization of the trap and demonstrate motional frequency measurements of trapped ions stored by applying external radiofrequency fields in r…
On point-irreducible projective lattice geometries
Within the conceptual frame of projective lattice geometry (as introduced in [5]) we are considering the class of all point-irreducible geometries. In the algebraic context these geometries are closely connected with unitary modules over local rings. Besides several synthetic investigations we obtain a lattice-geometric characterization of free left modules over right chain rings which allows a purely lattice-theoretic version in the Artinian case.
The nuclear magnetic moment of 208Bi and its relevance for a test of bound-state strong-field QED
Physics letters / B 779, 324 - 330 (2018). doi:10.1016/j.physletb.2018.02.024
A note on projective coordinate systems of modular lattices
This note clarifies the combinatorial nature of projective coordinate systems of modular upper continuous lattices. It generalizes the classical relationship between 3-dimensional Desarguesian configurations and coordinate systems of projective 3-spaces.
Zum Aufbau des Buches
Die vorliegende Abhandlung gliedert sich in zwei Hauptteile, wobei Teil II um einen Anhang erweitert ist.
High precision hyperfine measurements in Bismuth challenge bound-state strong-field QED
Electrons bound in highly charged heavy ions such as hydrogen-like bismuth 209Bi82+ experience electromagnetic fields that are a million times stronger than in light atoms. Measuring the wavelength of light emitted and absorbed by these ions is therefore a sensitive testing ground for quantum electrodynamical (QED) effects and especially the electron–nucleus interaction under such extreme conditions. However, insufficient knowledge of the nuclear structure has prevented a rigorous test of strong-field QED. Here we present a measurement of the so-called specific difference between the hyperfine splittings in hydrogen-like and lithium-like bismuth 209Bi82+,80+ with a precision that is improve…
Projective mappings between projective lattice geometries
The concept of projective lattice geometry generalizes the classical synthetic concept of projective geometry, including projective geometry of modules.
The next generation of laser spectroscopy experiments using light muonic atoms
Precision spectroscopy of light muonic atoms provides unique information about the atomic and nuclear structure of these systems and thus represents a way to access fundamental interactions, properties and constants. One application comprises the determination of absolute nuclear charge radii with unprecedented accuracy from measurements of the 2S - 2P Lamb shift. Here, we review recent results of nuclear charge radii extracted from muonic hydrogen and helium spectroscopy and present experiment proposals to access light muonic atoms with Z ≥ 3. In addition, our approaches towards a precise measurement of the Zemach radii in muonic hydrogen (μp) and helium (μ 3He+) are discussed. These resul…
Hinreichende Kriterien für die Darstellbarkeit affiner Räume durch Moduln
Wir wollen uns zunachst mit elementaren Eigenschaften affiner Raume beschaftigen; spater werden wir darauf aufbauend als Anwendung von Korollar 1 einen algebraischen Darstellungssatz fur affine Raume beweisen.
Projective Geometry on Modular Lattices
Publisher Summary This chapter focuses on projective geometry on modular lattices. Incidence and Order are basic concepts for a foundation of modern synthetic geometry. These concepts describe the relative location or containment of geometric objects and have led to different lines of geometry, an incidence-geometric and a lattice-theoretic one. Modularity is one of the fundamental properties of classical projective geometry. It makes projections into join-preserving mappings and yields perspectivities to be (interval) isomorphisms. It is therefore natural that order-theoretic generalizations of projective geometry are based on modular lattices and even more, the theory of modular lattices …
A unified approach to projective lattice geometries
The interest in pursuing projective geometry on modules has led to several lattice theoretic generalizations of the classical synthetic concept of projective geometry on vector spaces.
Beamline for low-energy transport of highly charged ions at HITRAP
Abstract A beamline for transport of highly charged ions with energies as low as a few keV/charge has been constructed and commissioned at GSI. Complementary to the existing infrastructure of the HITRAP facility for deceleration of highly charged ions from the GSI accelerator, the new beamline connects the HITRAP ion decelerator and an EBIT with the associated experimental setups. Therefore, the facility can now transport the decelerated heavy highly charged ions to the experiments or supply them offline with medium-heavy highly charged ions from the EBIT, both at energies as low as a few keV/charge. Here we present the design of the 20 m long beamline with the corresponding beam instrument…