Experimental and theoretical studies of the Bi-excited collision systems He*(23 S) + He*(23 S, 21 S) at thermal and subthermal kinetic energies

We have carried out a comprehensive experimental and theoretical investigation of the autoionizing collision systems He*(2³ S, 2¹ S) + He*(2³ S). We present high resolution electron energy spectra, obtained with a single He* beam (average relative collision energy 〈E _rel〉=1.6 meV) and with crossed He* beams (〈E _rel〉> =61 meV). The spectra show substantial structure, and under single beam conditions fast oscillations due to the interference of incoming and outgoing heavy particle waves in the entrance channels are observed. Accurate ab initio potential curves for the seven lowest He*—He*(Σ) molecular states have been obtained from a Feshbach projection scheme, and width functions for He*(2³ S) + He*(2³ S) have been derived by Stieltjes imaging. Based on these ab initio data, detailed quantum mechanical calculations of the electron spectra have been carried out and provide a thorough understanding of the experimentally observed spectral features. Good overall agreement of the calculated spectra with the experimental data is observed. The close coincidence in the positions of the experimental and theoretical peaks, especially for He*(2³ S) + He*(2³ S), underlines the reliability of the ab initio potentials. In the He*(2¹ S) + He*(2³ S) electron spectrum, the dominant peak is traced to be due to autoionization from the 2³Σ⁺ _g molecular state accessed via an avoided crossing. We also present a detailed discussion of the total ionization cross sections σ_tot and of the fraction σ_AI/σ_tot for associative ionization together with a critical comparison with previous work. The ionization probabilities for close collisions in entrance channels, from which autoionization is spin-allowed, are near unity, and therefore the absolute values and the collision energy dependence of the total cross sections simply reflect the long-range behaviour of the excited state potentials.     

Excision of uranium oxide chains and ribbons in the novel one-dimensional uranyl iodates K(2)[(UO(2))3(IO(3))(4)O(2)] and Ba[(UO(2)2(IO(3))(2)O(2)](H(2)O)

The alkali metal and alkaline-earth metal uranyl iodates K(2)[(UO(2))(3)(IO(3))(4)O(2)] and Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O) have been prepared from the hydrothermal reactions of KCl or BaCl(2) with UO(3) and I(2)O(5) at 425 and 180 degrees C, respectively. While K(2)[(UO(2))(3)(IO(3))(4)O(2)] can be synthesized under both mild and supercritical conditions, the yield increases from <5% to 73% as the temperature is raised from 180 to 425 degrees C. Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O), however, has only been isolated from reactions performed in the mild temperature regime. Thermal measurements (DSC) indicate that K(2)[(UO(2))(3)(IO(3))(4)O(2)] is more stable than Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O) and that both compounds decompose through thermal disproportionation at 579 and 575 degrees C, respectively. The difference in the thermal behavior of these compounds provides a basis for the divergence of their preparation temperatures. The structure of K(2)[(UO(2))(3)(IO(3))(4)O(2)] is composed of [(UO(2))(3)(IO(3))(4)O(2)](2)(-) chains built from the edge-sharing UO(7) pentagonal bipyramids and UO(6) octahedra. Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O) consists of one-dimensional [(UO(2))(2)(IO(3))(2)O(2)](2)(-) ribbons formed from the edge sharing of distorted UO(7) pentagonal bipyramids. In both compounds the iodate groups occur in both bridging and monodentate binding modes and further serve to terminate the edges of the uranium oxide chains. The K(+) or Ba(2+) cations separate the chains or ribbons in these compounds forming bonds with terminal oxygen atoms from the iodate ligands. Crystallographic data: K(2)[(UO(2))(3)(IO(3))(4)O(2)], triclinic, space group P_1, a = 7.0372(5) A, b = 7.7727(5) A, c = 8.9851(6) A, alpha = 93.386(1) degrees, beta = 105.668(1) degrees, gamma = 91.339(1) degrees, Z = 1; Ba[(UO(2))(2)(IO(3))(2)O(2)](H(2)O), monoclinic, space group P2(1)/c, a = 8.062(4) A, b = 6.940(3) A, c = 21.67(1), beta= 98.05(1) degrees, Z = 4.     

Formation of negatively-charged cluster ions in thermal energy collisions with state-selected rydberg atoms

Using crossed atomic, molecular cluster, and cw laser beams in conjunction with mass spectrometric ion detection, we have obtained for the first time results for electron transfer fromstate-selected Rydberg atoms to molecular clusters. We report negative ion mass spectra for (CO₂) _k ^? (4≦k≦25) and (O₂) _k ^? (1≦k≦13) cluster ions, resulting from collisions of Ar** (nd) Rydberg atoms (12≦n≦40) with (CO₂) _m and (O₂) _m clusters at relative velocities around 830 m/s, and, for comparison, positive ion mass spectra due to Ne(3s ³ P _{2, 0}) Penning ionization. For both CO ₂ ^? and O₂-clusters, the negative and the positive ion mass spectra are very different. For (CO₂) _k ^Emphasis>/? cluster ions, the mass spectra show distinct variations with principal quantum number of the Rydberg atom, corresponding to differentn-dependences of the effective rate constant for selected cluster ions, as measured relative to the knownn-dependence for SF ₆ ^? formation in collisions with SF₆. For (O₂) _k ^? cluster ions, on the other hand, the mass spectra are almost independent ofn with ion intensities, which clearly reflect their thermochemical stabilities (O ₄ ^? as dominant species).     

Penning ionization electron spectrometry of hydrogen chloride

An electron spectrometric study has been performed on HCl using metastable helium and neon atoms as well as neon resonance photons. High resolution electron spectra were obtained with two different beam apparatuses for a mixed He(2¹ S, 2³ S) beam, a pure He(2³ S) beam, and, for the first time, state-selected pure Ne(3s ³ P ₂) and pure Ne(3s ³ P ₀) beams, and for NeI resonance photons. For the system He(2³ S)+HCl the vibrational populationsP(υ′) of the formed HCl⁺ (X ²∏ _i , υ′) and HCl⁺ (A ²Ω⁺, υ′) ions are found to differ from the Franck-Condon factors for unperturbed potentials, indicating slight bond stretching in HCl upon He(2³ S) approach. For He(2¹ S)+HCl the vibrational peak shapes and vibrational populations are substantially different from the He(2³ S) case, pointing to an additional, charge exchanged interaction (He⁺+HCl^?) in the entrance channel of the former system. For the first time, we have detected the electrons in both the He(2¹ S)+HCl and He(2³ S)+HCl spectra associated with the major mechanism for the formation of Cl⁺ ions: energy transfer to repulsive HCl** Rydberg states, dissociating toH(1s) and autoionizing Cl**(¹ D ₂ nl) atoms. For both Ne(³ P ₂)+HCl and Ne(³ P ₀)+HCl, the populationsP(υ′) of both final molecular states HCl⁺ (X, A) agree closely with the Franck-Condon factors at the average relative collision energyē _coll=55 meV and, for HCl⁺ (A ²Ω⁺), also atē _coll=130 meV.     

Existence,Non-existence,and Uniqueness for a Heat Equation with Exponential Nonlinearity in ℝ2

We consider a semilinear heat equation with exponential nonlinearity in ?². We prove that local solutions do not exist for certain data in the Orlicz space exp L ²(?²), even though a small data global existence result holds in the same space exp L ²(?²). Moreover, some suitable subclass of exp L ²(?²) for local existence and uniqueness is proposed.

     

A novel electron scattering apparatus combining a laser photoelectron source and a triply differentially pumped supersonic beam target: characterization and results for the resonance

A novel electron scattering apparatus for high resolution studies of angle-differential elastic and inelastic electron scattering from atoms and molecules in the gas phase is described and its performance characterized. It combines a laser photoelectron source, a triply differentially pumped collimated supersonic beam target (half angle 0.015 rad, background to beam density ratio < 0.01), and several electron multipliers for simultaneous detection of elastically scattered electrons and metastable atoms (or molecules) due to inelastic scattering. In detailed test measurements of the yield for the production of metastable He^*(2³S₁) atoms around its threshold, the dependence of the overall energy width on various experimental parameters has been investigated. So far a resolution down to 7 meV (FWHM) has been obtained. Under such conditions we have investigated the profile of the He^- (1 s 2 s ^{2 2} S _1/2 ) resonance at the scattering angles 22 ^° , 45 ^° , and 90 ^° . From a consistent fit of the measured profiles by resonant scattering theory we determine a new value for the resonance energy ( E _r = 19.365(1) eV) and an accurate resonance width ( Γ = 11.2(5) meV). These results are consistent with the previously recommended values. Received 23 July 2002 Published online 29 October 2002 RID="a" ID="a"e-mail: hotop@physik.uni-kl.de RID="b" ID="b"Permanent address: Department of Physics and Astronomy, Drake University, Des Moines, IA 50311, USA.     

On an inequality by N. Trudinger and J. Moser and related elliptic equations

It has been shown by Trudinger and Moser that for normalized functions u of the Sobolev space ??^{1, N} (Ω), where Ω is a bounded domain in ?^N, one has ∫_Ω exp(α_N|u|^{N/(N ? 1)})dx ≤ C_N, where α_N is an explicit constant depending only on N, and C_N is a constant depending only on N and Ω. Carleson and Chang proved that there exists a corresponding extremal function in the case that Ω is the unit ball in ?^N. In this paper we give a new proof, a generalization, and a new interpretation of this result. In particular, we give an explicit sequence that is maximizing for the above integral among all normalized “concentrating sequences.” As an application, the existence of a nontrivial solution for a related elliptic equation with “Trudinger‐Moser” growth is proved. © 2002 John Wiley & Sons, Inc.