Cyclische Bis(amino)-arsa-, -stiba-, -bismachloride und ein spezielles Tris-(amino)bismutan

In den Trichloriden von Arsen, Antimon und Bismut lassen sich jeweils zwei Chloratome durch den Liganden -N(tBu)SiMe2N(tBu)- austauschen, wodurch viergliedrige Ringe (SiN2El) entstehen. Sowohl in Lösung (temperatur- und konzentrationsabhängige 1H-NMR-Spektren) als auch im Festkörper (Röntgenstrukturanalysen) besitzen die Verbindungen 3 (El = As), 4 (El = Sb) bzw. 5 (El = Bi) unterschiedliche Assoziationsgrade bzw. Strukturen. Das Arsenderivat 3 kristallisiert monoklin, in der Raumgruppe P21/c mit 4 Formeleinheiten pro Elementarzelle (a = 920,0(6), b = 1 462,9(9), c = 1240,8(7) pm, = 105,8(1)°), das Antimon- und Bismutderivat 4 und 5 sind isotyp und isostrukturell und kristallisieren ortho-rhombisch (Raumgruppe Pnma, Z = 4; Gitterkonstanten für 4: a = 1140,2(8), b = 1095,7(7), c = 1328,7(9) pm; für 5: a = 1105,1(5), b = 1123,3(5), c = 1340,0(8) pm). Während die Kristallstruktur von 3 im wesentlichen aus isolierten Molekülen besteht, die eine schwache Tendenz zu paarweiser Assoziation besitzen (AsClAs Brücken, AsCl = 234,5(1), ClAs = 442,3(1) pm), sind die Moleküle in den Kristallen von 4 und 5 eindimensional verkettet. Die zu den SbN2Si- bzw. BiN2Si-Ringen nahezu senkrecht stehenden Chlorsubstituenten treten mit Nachbarmolekülen derart in Wechselwirkung, daß jedes Sb- und Bi-Atom vierfach koordiniert wird und eine unendliche ElClElCl-Kette entsteht, die an den Chloratomen gewinkelt ist (4): 143,5°, (5): 145,7°. Die verbrückende Rolle des Chloratoms ist bei der Bi-Verbindung stärker ausgeprägt als bei der Sb-Verbindung (SbCl = 247,2(3), ClSb = 352,1(3) pm; BiCl = 274,8(4), ClBi = 304,7(4) pm). Als Nebenprodukt kann bei der Darstellung von 5, eine Verbindung 6 erhalten werden, die nur Stickstoffatome am Bismut gebunden hat: Me2Si(NtBu)2 BiN(tBu)SiMe2(tBu)NBi(NtBu)2SSiMe2. Diese Verbindung 6 kristallisiert monoklin (P21/c, a = 1474,2(3), b = 1477,6(3), c = 1997,7(6) pm, = 94,68(8)°). Die Abweichung von der C2-Symmetrie bei 6 (die zweizählige Achse verläuft durch die mittlere SiMe2-Gruppe) ist nur unbedeutend. Die BiN-Bindungslängen innerhalb der SiN2Bi-Ringe (BiN (Mittel) = 216,5(5) pm) sind kürzer als die außerhalb (BiN (Mittel) = 220,45(5) pm)

Fitting theories of nuclear binding energies

In developing theories of nuclear binding energy such as density-functional theory, the effort required to make a fit can be daunting due to the large number of parameters that may be in the theory and the large number of nuclei in the mass table. For theories based on the Skyrme interaction, the effort can be reduced considerably by using the singular value decomposition to reduce the size of the parameter space. We find that the sensitive parameters define a space of dimension four or so, and within this space a linear refit is adequate for a number of Skyrme parameters sets from the literature. We do not find marked differences in the quality of the fit between the SLy4, the Bky4 and SkP parameter sets. The r.m.s. residual error in even-even nuclei is about 1.5 MeV, half the value of the liquid drop model. We also discuss an alternative norm for evaluating mass fits, the Chebyshev norm. It focuses attention on the cases with the largest discrepancies between theory and experiment. We show how it works with the liquid drop model and make some applications to models based on Skyrme energy functionals. The Chebyshev norm seems to be more sensitive to new experimental data than the root-mean-square norm. The method also has the advantage that candidate improvements to the theories can be assessed with computations on smaller sets of nuclei.Comment: 17 pages and 4 figures--version encorporates referee's comment

Sequence of a putative Vitis vinifera PR-1

Research Note

Optical properties of the vibrations in charged C60_{60} molecules

The transition strengths for the four infrared-active vibrations of charged C$_{60}$ molecules are evaluated in self-consistent density functional theory using the local density approximation. The oscillator strengths for the second and fourth modes are strongly enhanced relative to the neutral C$_{60}$ molecule, in good agreement with the experimental observation of ``giant resonances'' for those two modes. Previous theory, based on a ``charged phonon'' model, predicted a quadratic dependence of the oscillator strength on doping, but this is not borne out in our calculations.Comment: 10 pages, RevTeX3.

Universal Pion Freeze-out Phase-Space Density

Results on the pion freeze-out phase-space density in sulphur-nucleus, Pb-Pb and pion-proton collisions at CERN-SPS are presented. All heavy-ion reactions are consistent with the thermal Bose-Einstein distrtibution f=1/(exp(E/T)-1) at T~120 MeV, modified for expansion. Pion-proton data are also consistent with f, but at T~180 MeV.Comment: 1 page, 1 figure; 98' report for GSI-Darmstad

Pygmy dipole resonance as a constraint on the neutron skin of heavy nuclei

The isotopic dependence of the isovector Pygmy dipole response in tin is studied within the framework of the relativistic random phase approximation. Regarded as an oscillation of the neutron skin against the isospin-symmetric core, the pygmy dipole resonance may place important constraints on the neutron skin of heavy nuclei and, as a result, on the equation of state of neutron-rich matter. The present study centers around two questions. First, is there a strong correlation between the development of a neutron skin and the emergence of low-energy isovector dipole strength? Second, could one use the recently measured Pygmy dipole resonance in 130Sn and 132Sn to discriminate among theoretical models? For the first question we found that while a strong correlation between the neutron skin and the Pygmy dipole resonance exists, a mild anti-correlation develops beyond 120Sn. The answer to the second question suggests that models with overly large neutron skins--and thus stiff symmetry energies--are in conflict with experiment.Comment: 16 pages with 6 figure

Source Dimensions in Ultrarelativistic Heavy Ion Collisions

Recent experiments on pion correlations, interpreted as interferometric measurements of the collision zone, are compared with models that distinguish a prehadronic phase and a hadronic phase. The models include prehadronic longitudinal expansion, conversion to hadrons in local kinetic equilibrium, and rescattering of the produced hadrons. We find that the longitudinal and outward radii are surprisingly sensitive to the algorithm used for two-body collisions. The longitudinal radius measured in collisions of 200 GeV/u sulfur nuclei on a heavy target requires the existence of a prehadronic phase which converts to the hadronic phase at densities around 0.8-1.0 GeV/fm$^3$. The transverse radii cannot be reproduced without introducing more complex dynamics into the transverse expansion.Comment: RevTeX 3.0, 28 pages, 6 figures, not included, revised version, major change is an additional discussion of the classical two-body collision algorithm, a (compressed) postscript file of the complete paper including figures can be obtained from Authors or via anonymous ftp at ftp://ftp_int.phys.washington.edu/pub/herrmann/pisource.ps.

Liquid-Drop Model and Quantum Resistance Against Noncompact Nuclear Geometries

The importance of quantum effects for exotic nuclear shapes is demonstrated. Based on the example of a sheet of nuclear matter of infinite lateral dimensions but finite thickness, it is shown that the quantization of states in momentum space, resulting from the confinement of the nucleonic motion in the conjugate geometrical space, generates a strong resistance against such a confinement and generates restoring forces driving the system towards compact geometries. In the liquid-drop model, these quantum effects are implicitly included in the surface energy term, via a choice of interaction parameters, an approximation that has been found valid for compact shapes, but has not yet been scrutinized for exotic shapes.Comment: 9 pages with 3 figure

Absorption of Energy at a Metallic Surface due to a Normal Electric Field

The effect of an oscillating electric field normal to a metallic surface may be described by an effective potential. This induced potential is calculated using semiclassical variants of the random phase approximation (RPA). Results are obtained for both ballistic and diffusive electron motion, and for two and three dimensional systems. The potential induced within the surface causes absorption of energy. The results are applied to the absorption of radiation by small metal spheres and discs. They improve upon an earlier treatment which used the Thomas-Fermi approximation for the effective potential.Comment: 19 pages (Plain TeX), 2 figures, 1 table (Postscript