Optimal Hylleraas wave functions

Hylleraas wave functions composed of the optimally combinedN terms (2 N 20) are presented for two-electron atoms with nuclear chargesZ = 1 (H^–), 2(He), 3(Li⁺), 5(B³⁺), and 10(Ne⁸⁺). The spherically-averaged electron density (r) and electron-pair densityh(r ₁₂) are constructed in a simple and analytical functional form from the 20-term functions. Comparison of several one- and two-electron moments r ^k and r ₁₂ ^k shows that the present density functions have near-exact accuracy.     

Reactive scattering of sodium clusters with molecular oxygen

The first reactive differential scattering study for atomic clusters is reported. Oxidation of Na _x (x8) with O₂ is investigated in a crossed beam apparatus. Sodium oxide (Na _n O,n4) and sodium dioxide (Na _n O₂,n6) are produced with a total reactive cross section from 50 to 80 Ų, depending on the cluster size. The excess energies for these reactions are estimated by an SCF type ab initio calculation and range from 0.5 to 5 eV. The large cross section may then be understood quantitatively in terms of a harpooning mechanism as a first step in the reaction path. Angular distributions have been determined for the most abundant products, showing strong forward scattering. Two different schemes are discussed for the reaction: while the dioxides Na _n O₂ may be formed by an evaporative cooling process from a highly excited collision complex, formation of Na _n O appears to originate from a direct process. In both cases the experimental data suggest that most of the exothermicity remains in the reaction products.     

Laser induced fission of C60 with kinetic energy release

A neutral C₆₀ fullerene beam is ionised by 308 nm laser pulses. For each cluster sizeC _n ⁺ , 0n60 of the typical bimodal mass distributions known from the literature [1] velocity distributions have been determined by a time of flight method. A consistent interpretation of the measured mean velocities is obtained when binary fission of the parent molecule is assumed to be responsible for the fragmentation patterns, the total kinetic energy release being 0.45±0.1 eV independent of fragment mass and of laser fluence.     

Electron bombardment induced fragmentation of size selected neutral (D2O) n clusters

The fragmentation behaviour of size selected neutral (D₂O) _n clusters withn4 after ionization with 70 eV electrons is subject of this work. Size selection by scattering the cluster beam from a He target beam in combination with a quadrupole mass filter and time resolved measurements at specific laboratory angles enables us to determine the neutral precursor masses of the detected ions. The measured fragment pattern is dominated by deuterated ions of the form (D₂O) _n–x D⁺ withx1. The dimer fragmentation which leads with a probability of 62.5% to the D₃O⁺ ion and with 37.5% to D₂O⁺ can be explained by fast intracluster ion-molecule reactions of charged monomer fragments reacting with the partner molecule. For larger clusters the fragmentation process can be rationalised by the creation of an initially highly excited D₃O⁺ (D₂O) _x complex which is stabilized by evaporating additional monomer units with the main fragment channel (D₂O)D⁺ forn=3 and (D₂O)₂D⁺ forn=4. With increasing cluster size an increasing tendency of evaporation of more than one water monomer unit has been observed.     

Characterization of the fluxes of neutral and positively charged clusters (Agn and Agn+; n≤4) produced by argon ion sputtering of silver

The emission of neutral and positively charged silver clusters during sputtering of a polycrystalline silver target by 5 keV Ar⁺ ion bombardment has been studied and the sputter ejected silver flux has been characterized. As a result, the silver flux is found to be strongly dominated byneutral clusters rather than cluster ions. The contribution of neutral clusters in the overall silver flux decreases rapidly and monotonically with increasing cluster size n and decreases, in addition, with decreasing bombarding energy. The well known alternation of the secondary ion intensities of Ag _n ⁺ as a function of cluster size (higher intensities for odd n) is found to be correlated with the effective ionization potentials of the corresponding sputtered neutral clusters.     

Structural properties of VP1−x As x ; 0.00≦x≦1.00

The VP-VAs system has been studied by powder diffraction and magnetic susceptibility measurements. Three regions of solid solubility, separated by two phase regions, are found for VP_1–x As _x as function of composition (x). An NiAs type phase prevails for 0.00x0.07±0.02, a hexagonal phase of unknown crystal structure for 0.17±0.02x0.63±0.02 and an MnP type phase for 0.83±0.02x1.00. No phase transition is observed between 10 and 1 300 K. The various VP_1–x As _x phases exhibitPauli paramagnetism.Dedicated to Professor Dr.Kurt L. Komarek on his 60th birthday June 23, 1986.     

Charge monotonicity of atomic systems and radial expectation values

A functionf(r) is monotone of orderp if itspth-derivativef ^(p)(r) fulfils that (–1) ^p f ^(p)(r)0. So, e.g. the monotonicity properties of orderp=0, 1, 2 describe the non-negativity (p=0), the monotonic decreasing from the origin (p=1) and the convexity (p=2) of the function, respectively. Here, the monotonicity properties of the electron functiong _n (r; )=(–1) ^{n (n)} (r)r ^– , 0, of the ground state of atomic systems are analysed both analytically and numerically. The symbol (r) denotes the spherically averaged electron density. First of all, the condition which specifies, if exists, a value _np such thatg _n (r; _np ) be monotone of orderp is obtained. In particular, it is found that ₀₁=max {r(r)/(r)}, ₀₂=max {q ₀(r)}, ₁₁=max {r(r)/(r)} and ₁₂=max {q ₁(r)}, whereq ₀(r) andq ₁(r) are simple combinations of the first few derivatives of (r). Secondly, numerical calculations of the first few values _np in a Hartree-Fock framework for all ground-state atoms with nuclear chargeZ54 are performed. In doing so, the pioneering work of Weinstein, Politzer and Srebrenik about the monotonically decreasing behavior of (r) is considerably extended. Also, it is found that Hydrogen and Helium are the only two atoms having the functions (r), –(r) and (r) with the property of convexity. Thirdly, it is analytically shown that the charge functionr ^– (r) with [(1+4Z ²/I)^1/2–1]/2, I being the first ionization potential, is convex everywhere. Finally, the above mentioned monotonicity properties are used to obtain rigorous, simple and universal inequalities involving three radial expectation values which generalize all the similar ones known up to now. These inequalities allow to correlate various statical and dynamical quantities of the atomic system under study, due to the physical meaning of the radial expectation values. It is worth to remember that some of these expectation values may be experimentally measured in experiments of (e, 2e)-type.     

Sodium doped binary clusters I: Ionization potentials of SinNam clusters

Sodium doped silicon clusters (Si_nNa_m, 3n11, 1m4) were produced by two independent laser vaporization methods and their ionization potentials were measured by scanning the wavelength of the UV dye laser. The IPs of most Si_nNa_m clusters decrease monotonously with the number of Na atoms, but IPs of Si₇Na_m and Si₁₀Na_m clusters show an apparent even-odd alternation; odd numbers of Na atoms efficiently decrease the IP but even numbers of Na atoms never significantly decrease the IPs. In addition, the reactivity of Si_nNa_m clusters for NO molecules was investigated with a fast flow reactor, and an anti-correlation between IP and the reactivity was clearly observed; clusters having high IP show low reactivity andvice versa.     

Mechanisms of anion formation in O2, O2/Ar and O2/Ne clusters; the role of inelastic electron scattering

Measurements are reported on the formation of negative ions in O₂, O₂/Ar and O₂/Ne clusters aimed at establishing the mechanisms of anion formation and the role of inelastic electron scattering by the cluster constituents on negative ion formation in clusters. In the case of pure O₂ clusters the main anions we detected are of two types: O^–(O₂) _n0 and (O₂) _n ^1– . The yields of O^–(O₂) _n showed maxima at 6.3, 8.0 and 14.0 eV and the data suggest O^– as their precursor; the maxima at 8 and 14 eV are due to the production of O^– via symmetry forbidden dissociative attachment processes in O₂ at these energies which become allowed in clusters. The yields of (O₂) _n ^– showed a strong maximum at near-zero energy (0.5 eV) and also at 6.3, 8 and 14 eV. With the exception of the near-zero energy resonance, the (O₂) _n ^– anions at 6.3, 8 and 14 eV are attributed to nondissociative attachment of near-zero energy secondary electrons to O₂ clusters. The slow secondary electrons result predominantly from scattering via the O ₂ ^– negative ion states of incident electrons with energies in their respective regions. Similar results were obtained for the mixed O₂/rare gas clusters except that now a feeble and distinctly structured contribution in the yields of O^–(O₂) _n , (O₂) _n ^– (and Ar(O₂) _n ^– ) was observed at energies >10 eV. These anions are believed to have the lowest negative ion states of Ar*^– (Ne*^–) as their precursors.     

Donorstärken von Halogenid- und Pseudohalogenidionen

Zusammenfassung Die Komplexbildung von Vanadyl(IV)-acetylacetonat wird mit Neutraldonatoren sowie mit Halogenid- und Pseudohalogenidionen in CH₂Cl₂ und CH₃CN als Lösungsmittel spektrophotometrisch untersucht. Daraus ergibt sich folgende Reihung der Donorstärken: J^––<TMP<DMFCl^–<DMSO< <Ph ₃PO<HMPAP _y–3 ^–.

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Complex formation of vanadyl(IV) acetylacetonate with neutral donors, halide and pseudohalide ions was measured spectrophotometrically in acetonitrile and methylene chloride solutions. The following order of donor strengths was found: J^––<TMP<DMFCl^–<DMSO<Ph ₃PO< <HMPAPy–3 ^–.

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Mit 2 Abbildungen     

Levels of artificial radionuclides and uranium in rain water collected from Ibaraki (Japan) following the Tomsk-7 accident in Russia

Measurements of some selected radionuclides were carried out in rain waters collected from Ibaraki Prefecture, Japan, following the nuclear accident at Tomsk-7, Russian Federation, in April 1993. The concentrations obtained for artificial radionuclides were⁹⁰Sr1.8 mBq l^–1,¹³⁷Cs0.1 Bq l^–1,¹³¹I0.1 Bq l^–1 and¹²⁹I4 Bq l^–1. Uranium (²³⁸U) concentrations in rainfalls in April 1993 were 6.3–39 ng l^–1. These data were compared to control values obtained previously and there was no appreciable influence on the radioactivity levels in Japan after the Tomsk-7 accident. Since only limited data on the concentrations of¹²⁹I and uranium in rain water are available, these new analytical results contribute to understanding the background levels for these nuclides.     

Structure of nm-sized InSb clusters formed by spontaneous alloying

The negative ion photoelectron spectrum of⁷Li ₂ ^– is reported at 488 nm (2.540 eV). Three electronic bands are observed in this spectrum and are assigned to the following photodetachment transitions:⁷Li₂,X ¹ _g ⁺ +e ^{– 7}Li ₂ ^– ,X ² _u ⁺ ;⁷Li₂,a ³ _u ⁺ +e ^{– 7}Li ₂ ^– ,X ² _u ⁺ ; and⁷Li₂,A ¹ _u ⁺ +e ^{– 7}Li ₂ ^– ,X ² _u ⁺ . The electron affinity of⁷Li₂ is determined to be 0.437±0.009 eV, leading to an anion dissociation energy,D ₀, of 0.865±0.022 eV for the ground state of⁷Li ₂ ^– . A Franck-Condon analysis of the⁷Li₂,X ¹ _g ⁺ +e ^{– 7}Li ₂ ^– ,X ² _u ⁺ band yields the following spectroscopic constants for the ground state of⁷Li ₂ ^– :B _e =0.502±0.005 cm^–1,r _e =3.094±0.015 Å, and _e =232±35 cm^–1.     

Adsorption kinetics of surface-active substances from micellar solutions on solid phase

Summary The adsorption kinetics was studied of anion- and cation-active tensides on mineral surface from solutionsc _eq < CMC andc _eq CMC, and the adsorption mechanisms of ion exchange and ion pairing were discussed.In the range ofc _eq c _eb mono, the adsorption mechanism can be described using the Elovi-Zeldovi kinetic equations.In the rangec _eq CMC, the adsorption kinetics is more complicated. For very small values oft that lie beyond the possibility of measurements, the tenside molecules adsorb spontaneously, most probably as micelles, and then they desorb.As the measurements of _t (t) for the adsorption of H⁺ or OH^– have shown, the adsorption of tenside molecules in aqueous solutions occur in the presence of H⁺ or OH_– in the electric bilayer.The parallel course of both kinetics explains the anomalous behaviour in the range of the maximum, before the kinetic equilibrium is reached.

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Zusammenfassung Die Kinetik der Adsorption der anion- und kationaktiven Tenside auf der Mineraloberfläche aus LösungenC _eq < CM undC _eq CMC wurde untersucht und der Adsorptionsmechanismus des Ionenaustausches oder ion pairing diskutiert.Im BereichC _eq C _eq mono läßt sich der Adsorptionsmechanismus mit der kinetischen Gleichung nach Elovi-Zeldovi beschreiben.Im BereichC _eq CMC ist die Kinetik der Adsorption kompliziert. Für kleinet-Werte, die außerhalb der Meßmöglichkeiten liegen, kommt es zur spontanen Adsorption (wahrscheinlich in mizellarer Form) und danach folgender Desorption des Tensids.Wie die Messungen _t (t) für die Adsorption von H⁺ oder OH^– gezeigt haben, ist die Adsorption der Tensidmoleküle durch die Anwesenheit von H⁺ oder OH^– in der elektrischen Doppelschicht bedingt.Der parallele Verlauf beider Kinetiken erklärt das anomale Verhalten im Bereich des Maximums vor Erreichen des kinetischen Gleichgewichts.

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With 11 figures     

Studies of the energy spectrum of α, ω- substituted polymethine chains. II. Polymethine chains with odd number of methine groups

The analysis of the experimental data for the energy of the longest wavelength optical transitions _n,opt of substituted polymethines X (CH)_2n+1 X shows that in the asymptotic case (n) _,opt does not tend to zero, as it follows from the empirically established correlations, but has a finite, non-zero value. It is shown that the energy gap of odd polymethines is the same as that of the even polymethines - the polyenes (E 2 eV). The substituents (X N, O, B) are responsible for the appearance of levels in the gap. These, depending on the substituent character, are vacant (X B) or occupied (X N, O). The transition from or to such a level determines the longest wavelength optical transition energy of polymethines.     

Effect of thick fixed-charge layers on electrostatic interaction — a theoretical approach

The electrostatic interaction pressure of charged surface layers is considered qualitatively and quantitatively. In the case of mutual penetration of the surface layers in addition to Maxwell stress and osmotic resp. hydrostatic pressure an isotropic stress on the fixed charges carrying molecules of the surface layers has to be taken into account. The derivation of the pressure-distance equations is given starting from both thermodynamic/electrostatic and hydrostatic/electrostatic principles. A possible biological significance of the additional stress is discussed emphasizing its role in modifying the structure of surface layer molecules.List of symbols e ₀ elementary charge - k Boltzmann constant - n _i concentration of theith ionic species in the bulk solution - P hydrostatic pressure - P hydrostatic pressure in the bulk volume (× ) - P ^h integration constant, independent on ×:P ^h =P(h) - T absolute temperature - Z _i electrovalence of theith ionic species - thickness of the surface layer - , ₀ relative and absolute permittivities - II(×) osmotic pressure at position × - II osmotic pressure in the bulk solution (× ) - osmotic pressure in the symmetry plane of interacting identical surface layers (electric field strength equals zero) - integration constant, independent on ×: - _e ^h electrostatic component of the disjoining pressure _e ^h = _e (h) - (×) mobile charge density profile (cations and anions of the electrolyte) - (×) fixed charge density profile - ^t(x) total charge density profile ( ^t = +) - ¹(x) fixed charge density profile of one of the two surface layers ( ¹(×) 0 for 0×) - (×) electric potential profile     

Photoionization of Xe2, Xe3 and Xe4 in the 1024–1113 Å region

The mass spectra of Xe _n ⁺ clusters (n=2–13) were recorded using a supersonic beam and an ion time-of-flight mass analyser. The yield of Xe ₂ ⁺ , Xe ₃ ⁺ and Xe ₄ ⁺ cluster ions was measured with a resolution of 0.1 Å (1 meV) in the 1024–1113 Å (11.1–12.1 eV) region. Autoionizing Rydberg series of Xe₂ converging to theC ²_3/2u state of Xe ₂ ⁺ were observed in the spectrum of Xe ₂ ⁺ . The photoionization yield of Xe ₃ ⁺ and Xe ₄ ⁺ ions each displayed similar broad features that contained no fine structure corresponding to vibrational states. The broad features were assigned to autoionizing Rydberg series by analogy with the dimer ion spectrum.     

Collisional process involving atomic cluster ions

Collision of Ar cluster ions, Ar _n ⁺ (n=3–16), with He and Ne atoms was investigated by use of mass spectroscopic techniques. The cross sections for the production of Ar _n ⁺ (nn) were measured as functions of the size of the parent cluster ion and the collision energy (0.1–10 eV in the center-of-mass frame). These results were analyzed in the scheme of hard-sphere spectator collision with RRK theory. It was concluded that the reaction proceeds via collisional excitation of the parent cluster ion and following sequential loss of the constituent Ar atoms.This paper was originally submitted in connection with the 2nd. Int. Conference on Atomic and Nuclear Clusters held in Santorini from 28. June-2. July 1993 and is published here as a regular article after an independent refereeing procedure according to the standards of Z. Phys. D     

Photoionization of oriented molecules in a gas phase

Use of a coincidence technique for registration of fragment ions and photoelectroms from dissociative ionization of molecules opens the possibility of studying the photoionization of oriented molecules in a gas phase. The first results obtained by this technique for O₂ molecules are presented. The angular distribution of photoelectrons as a function of an angle between molecular axis and a photoelectron momentum is measured for theB ² _g ^– final ionic state using the HeI resonance radiation. From measured data it follows that the ratio of channel cross sections is /=0.67±0.08.     

The influence of “communicating states” on the dissociation yield in theS 1 of benzene

Non-radiative communicating states rate calculations forS ₁ S ₀ transitions in benzene are presented. The contribution ofC ₆ H ₅+H predissociation to the non-radiative rates with varying excess energy is investigated. Local modes with Morse oscillators for CH-stretch vibrations are introduced. In the channel-three region one finds that much less than 1% of the initial excited energy is found to be of discrete continuum character.C ₆ H ₅+H vibrational predissociation does not conform to the strong increase of pure internal conversion for high excess energies. The steep decrease of the dissociation yield at still higher excess energies is found to be closely related to the energy acceptor behaviour of the (harmonic) out-of-plane modes.