Density functional theory study of the carbon chains C<Subscript>n</Subscript>X,C<Subscript>n</Subscript>X<Superscript>+</Superscript> and C<Subscript>n</Subscript>X<Superscript>-</Superscript> (X = O and Se; n = 1–10)

A theoretical study of C_nX, C_nX⁺ and C_nX^- (X = O and Se; n = 1-10) clusters is carried out employing the density functional theory and the B3LYP functional. All species are fully optimized using the basis set 6-31G(d) for all atoms and further, single-point computations are done using the B3LYP/aug-cc-pVTZ level. Molecular properties such as equilibrium parameters, dipole moment, infrared vibrational frequencies, Raman activities and rotational constant are predicted. The computations indicate that the equilibrium structures are either linear or quasi-linear. We report the different forms of electron affinities, ionization energy, atomization energy and binding energy of the C_nO and C_nSe chains. The results indicate parity effect is very apparent for electron affinity, ionization energy, and binding energy but the effect is less pronounced for atomization energy. The n-even linear chains have larger ionization energy and atomization energy than the n-odd ones but this effect is reversed for electron affinity. The findings from this work are critically discussed and they are very similar to those obtained previously for the hetero-atom doped carbon chains. This research indicates that n-odd carbon chains are more stable than n-even and this is the trend for the chalcogens carbon chains.     

Decays of baryon resonances into ΛK<Superscript>+</Superscript>, ΣK<Superscript>+</Superscript> and Σ<Superscript>+</Superscript>K<Superscript>0</Superscript>

Cross-sections, beam asymmetries, and recoil polarisations for the reactions γp → K ⁺Λ;γp → K ⁺Σ⁰, and γp → K ⁰Σ⁺ have been measured by the SAPHIR, CLAS, and LEPS Collaborations with high statistics and good angular coverage for centre-of-mass energies between 1.6 and 2.3 GeV. The combined analysis of these data with data from π and η photoproduction reveals evidence for new baryon resonances in this energy region. A new P₁₁ state with mass 1840 MeV and width 140 MeV was observed contributing to most of the fitted reactions. The data demand the presence of two D₁₃ states at 1875 and, optimistically, at 2170 MeV.     

Exclusive ωπ<Superscript>0</Superscript> production with muons<Superscript>⋆</Superscript>

Using 160GeV muon scattering data collected with the COMPASS experiment at CERN, the exclusive production of ωπ⁰ via virtual photons was studied. Selective population of a peak around 1250MeV is observed. Possible contributions from spin-parity 1^- are searched for, inspecting decay angular correlations. In particular, the orientation of the ω decay plane may allow a distinction from the 1⁺ b ₁(1235) state. Our observation is compared with indications of a (1250) in annihilation and in γp . Original article based on material presented at HADRON 2007.     

Processes e<Superscript>+</Superscript>e<Superscript>−</Superscript> → π<Superscript>0</Superscript>(π<Superscript>0</Superscript>′) γ in extended NJL model

The processes of electron-positron annihilation into π⁰γ and into π′(1300)γ are considered within an extended NJL model. The intermediate vector mesons ρ ⁰, ω ρ′(1450), and ω(1420) are taken into account. The latter two mesons are treated as the first radial excited states. They are incorporated into the NJL model by means of a polynomial form factor. Numerical predictions for the cross-sections of these processes are received for the center-of-mass energies below 2 GeV. Our results for the π⁰γ production are in agreement with experimental data obtained in the energy region 600–1020 MeV.     

Spin physics at e<Superscript>+</Superscript>e<Superscript>−</Superscript> colliders

A large number of measurement related to spin was performed during the last decade at the e ⁺ e ^? colliders LEP and SLC providing important information on the dynamics of high energy interactions. In this paper three main topics will be covered: the measurements of the electroweak couplings, the study of fragmentation dynamics and the search for physics beyond the Standard Model.     

<Emphasis Type="Italic">J</Emphasis><Superscript>π</Superscript>0<Superscript>−</Superscript> levels in <Superscript>156</Superscript>Gd and <Superscript>158</Superscript>Gd

The 0^? states in the ¹⁵⁶Gd nucleus at E = 1952.38 keV and in the ¹⁵⁸Gd nucleus at E = 2269.16 keV are established on the basis of an analysis of available data on even-even deformed nuclei. From data on the deexcitation of the levels and on the probability of their population by beta transitions, it is found that these states have a two-particle proton structure. A comparison of our data with information about the 0^? levels in the ¹⁷⁰Yb and ¹⁷⁶Hf nuclei makes it possible to conclude that J^π0^? two-particle states exist at an excitation energy of about 2 MeV and higher.     

A new determination of the γπ → ππ anomalous amplitude via πe<Superscript>-</Superscript> → π<Superscript>-</Superscript>e<Superscript>-</Superscript>π<Superscript>0</Superscript> data

We discuss the reaction π^-e^- → π^-e^-π⁰ with the purpose of obtaining information on the γπ → ππ anomalous amplitude _3π. We compare a full calculation at (p⁶) in chiral perturbation theory and various phenomenological predictions with the existing data of Amendolia et al. By integrating our theory results using Monte Carlo techniques, we obtain σ = 2.05 nb at (p⁶) and σ = 2.17 nb after including the dominant electromagnetic correction. Both results are in good agreement with the experimental cross-section of σ = (2.11±0.47) nb. On the basis of the ChPT results one would extract from the experimental cross-section as amplitudes _3π^(0)extr = (9.9±1.1) GeV^-3 and _3π^(0)extr = (9.6±1.1) GeV^-3, respectively, which have to be compared with the low-energy theorem _3π = e/(4π²F_π³) = 9.72GeV^-3. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain _3π with smaller uncertainty.     

Two photons into π<Superscript>0</Superscript>π<Superscript>0</Superscript>

We perform a theoretical study based on dispersion relations of the reaction γγ → π ⁰ π ⁰ emphasizing the low-energy region. We discuss how the ƒ ⁰(980) signal emerges in γγ → ππ within the dispersive approach and how this fixes to a large extent the phase of the isoscalar S-wave γγ → ππ amplitude above the threshold. This allows us to make sharper predictions for the cross-section at lower energies and our results could then be used to distinguish between different ππ isoscalar S-wave parameterizations with the advent of new precise data on ππ → π ⁰ π ⁰. We compare our dispersive approach with an updated calculation employing the unitary chiral perturbation theory (U _gC PT). We also pay special attention to the role played by the σ-resonance in γγ → ππ and calculate its coupling and width to γγ, for which we obtain Γ(σ → γγ) = (1.68 ± 0.15) keV.     

Emission spectroscopy of the A<Superscript>1</Superscript>Π–X<Superscript>1</Superscript>Σ<Superscript>+</Superscript> system of AlH

The high-resolution emission spectrum of the A¹ Π–X¹Σ⁺ transition of AlH was observed in the 18 000–25 000 cm^-1 spectral region using a conventional spectroscopic technique. The AlH molecules were excited in an Al hollow-cathode lamp filled with a mixture of Ne carried gas and a trace amount of NH₃. The emission from the discharge was observed with a plane grating spectrograph and recorded by a photomultiplier tube. In total 163 transition wave numbers belonging to six bands (0-0,1 and 1-0,1,2,3) were precisely measured and rotationally analysed. In the final fit the present data have been combined with available high-resolution measurements of the vibration-rotation bands by White et al. [J. Chem. Phys. 99, 8371 (1993)]. This procedure enabled extracting molecular constants for the A¹ Π and X¹ Σ⁺ states of AlH. A very slight local perturbation has been discovered in the v=1 vibration level of the A¹ Π state at J=5. This was probably caused by the interaction with the a³Π state.     

Potential energy of <Superscript>∞</Superscript>H<Stack><Subscript>2</Subscript><Superscript>-</Superscript></Stack>(<Superscript>2</Superscript>∑<Stack><Subscript>u</Subscript><Superscript>+</Superscript></Stack> in the bound-state region

An accurate calculation of the lowest negative electronic state of H ₂ ^- (fixed nuclei) is reported using the CCSD(T) method and doubly augmented cc-pv5z basis set. Comparison has been made with the reference data by Senekowitsch et al. [Chem. Phys. Lett. 111 (1984) 211]. Owing to larger size of the basisset and inclusion of triple excitations, no vertical shift in this work is necessary to reproduce the asymptotics of H + H ^-. In addition, the effect of basis-set truncation is estimated, based on the complete-basis-set extrapolation method. The contribution of correlated electron-proton motion to the electron-energy curve for H₂ ^– dynamics is pointed out.Dedicated to Prof. Jií Horáek on the occasion of his 60th birthday.     

Negative ions Ar<Superscript>−</Superscript>, Kr<Superscript>−</Superscript>, and Xe<Superscript>−</Superscript> in superfluid helium

The catalogue of negative ions in superfluid helium has been extended using the example of Ar⁻, Kr⁻, and Xe⁻. Such objects cannot exist in vacuum, since the polarization attraction of an electron to the inert A atom is insufficient for the formation of the bound state A⁻. However, these objects exist in helium as stable or metastable with a very long lifetime. The effect is due to the electron localization in liquid helium. If a mixture of excited A* atoms and electrons is prepared in the gas phase above liquid helium, the reaction A* + e = A*⁻ becomes possible for all atoms of the periodic table. Such charges can be immersed into liquid helium by the electric field. In this case, the radiative decay A*⁻ = A + e allowed in vacuum can be forbidden in liquid. This leads to the formation of the new unique objects A⁻, which can exist in liquid helium but are absent in nature. The size of such charged formations has been determined and is close the radius of a usual electron bubble in helium.     

Charge transfer in energetic Li<Superscript>2+</Superscript>–H and He<Superscript>+</Superscript>–He<Superscript>+</Superscript> collisions

The total cross sections for charge transfer in Li²⁺-H and He⁺-He⁺ collisions have been calculated, using the four body first Born approximation with correct boundary conditions (CB1-4B) and four body continuum distorted wave method (CDW-4B) in the energy range 10–5000 keV/amu. The role of dynamic electron correlations is examined as a function of the impact energy. The present results call for additional experimental data at higher impact energies than presently available.     

Inversion of the <Emphasis Type="Italic">K</Emphasis><Superscript>π</Superscript>=1<Superscript>−</Superscript> states in <Superscript>156</Superscript>Gd and <Superscript>170</Superscript>Yb

For the ¹⁵⁶Gd and ¹⁷⁰Yb nuclei, where the inversion of levels in the K^π=1^? bands is observed, the energies of rotational levels are calculated on the basis of the Coriolis interaction model for the states of two bands whose quantum numbers are K^π=1^?. New 0^? levels are introduced in ¹⁷⁰Yb, and the structure of ¹⁷⁰Er is refined. The interaction parameters calculated for six nuclei are considered within the structure predicted by the quasiparticle-phonon model.     

<Superscript>16</Superscript>O/<Superscript>18</Superscript>O oxygen isotope exchange kinetics in MnO<Stack><Subscript>4</Subscript><Superscript>−</Superscript></Stack> as probed by <Superscript>55</Superscript>Mn NMR

The effect of the ¹⁶O ? ¹⁸O substitution in the coordination sphere of permanganate anion MnO ₄ ^? on the chemical shift of ⁵⁵Mn nuclei have been studied by ¹⁷O and ⁵⁵Mn NMR. Time constants τ _n,k of oxygen exchange in the water–permanganate anion system have been estimated. In nearly neutral solutions (pH ≈ 6.8–7.2), the oxygen exchange time is on the order of tens of hours. Bubbling gaseous HCl through this solution for a few seconds leads to the equilibrium distribution of oxygen isotopes in the manganese coordination sphere. The observed temperature dependences of isotope-induced ⁵⁵Mn NMR shifts in Mn¹⁶ O _44-n ¹⁸ O _n ^– (n = 0–4) have been treated as a result of rovibrational averaging of Mn–O bond lengths. The change in the Mn—O bond length in caused by the ¹⁶O → ¹⁸O isotope substitution is on the order of 10^–4 Å.     

The evaluation of the branching ratios of the decays φ(1020)→2π<Superscript>+</Superscript>2π<Superscript>−</Superscript>π<Superscript>0</Superscript>, π<Superscript>+</Superscript>π<Superscript>−</Superscript>3π<Superscript>0</Superscript>

Combining the Okubo-Zweig-Iizuka rule in the decay φ→ρπ→π⁺π^?π⁰ with the ρ→4π decay amplitudes, we calculate the φ→2π⁺2π^?π⁰ and φ→π⁺π^?3π⁰ ones. The partial widths of the above φ decays are evaluated, and the excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the parameters characterizing the anomalous terms of the HLS Lagrangian. The evaluated branching ratios B_φ→π⁺_π^?_3π⁰ ≈ 2 × 10^?7 and B_φ→2π⁺_2π^?_π⁰ ≈ 7 × 10^?7 are such that, with the luminosity L=500 pb^?1 attained at DAΦNE φ factory, one may already possess about 1685 events of the decays φ→5π.     

Analysis of the vector form factors f<Superscript>+</Superscript><Subscript>Kπ</Subscript>(Q<Superscript>2</Superscript>) and f<Superscript>-</Superscript><Subscript>Kπ</Subscript>(Q<Superscript>2</Superscript>) with light-cone QCD sum rules

In this article, we calculate the vector form factors f⁺ _Kπ(Q²) and f^- _Kπ(Q²) within the framework of the light-cone QCD sum rule approach. The numerical values of f⁺ _Kπ(Q²) are compatible with existing theoretical calculations, and the central value of f⁺ _Kπ(0) (f⁺ _Kπ(0)=0.97) is in excellent agreement with the values from chiral perturbation theory and lattice QCD. The values of |f^- _Kπ(0)| are very large compared to the theoretical calculations and experimental data, and they cannot give any reliable prediction. At large momentum transfer with Q² > 5 GeV², the form factors f⁺ _Kπ(Q²) and |f^- _Kπ(Q²)| can either show the asymptotic behavior of or decrease more quickly than ; more experimental data are needed to select the ideal sum rules. PACS 12.38.Lg; 12.38.Bx; 12.15.Hh     

Odd autoionizing 2p<Subscript>1/2</Subscript><Superscript>5</Superscript>n(s<Superscript>′</Superscript>/d<Superscript>′</Superscript>) resonances of Ne excited from the 2p<Superscript>5</Superscript>3p[K]<Subscript>J</Subscript> states

Absolute photoionization cross sections for Ne atoms in the excited levels (Paschen notation ) were calculated at near threshold energies within the configuration interaction Pauli-Fock approach including core polarization. The computed spectra and the lineshape parameters of the odd parity 2p_1/2 ⁵ns^′/d^′ autoionizing resonances are found to be in good agreement with high resolution laser spectroscopic results. Guided by the theoretical results, improved analyses of the measured spectra by superimposed Fano-type profiles were achieved. Theoretical predictions are presented for resonances which have not yet been studied experimentally. In addition, we report the absolute partial photoionization cross sections for the ²P_3/2 and ²P_1/2 channel at photoelectron energies up to 7 eV. Except for the highest lying 2p₁(¹S₀) level, these cross sections monotonically decrease with energy (as reported earlier in single-electron calculations for the Ne(2p⁵3p) configuration) with branching ratios which essentially reflect the core composition of the 2p_x levels. For the 2p₁ level the resonance structure and the partial cross sections are strongly influenced by a Cooper-Seaton minimum in the d_3/2 ^′ channel,located just above the ²P_1/2 ionization limit.     

Hyperfine Interactions in Pb<Superscript>3+</Superscript>F<Stack><Subscript>8</Subscript><Superscript>−</Superscript></Stack>F<Stack><Subscript>a</Subscript><Superscript>−</Superscript></Stack> clusters in fluorite crystals

The parameters of hyperfine interactions in Pb³⁺F ₈ ^? F _a ^? tetragonal clusters of MeF₂ crystals (Me=Ca, Sr, Ba) are interpreted. The contributions of the spin polarization to the parameters of the proper hyperfine interaction and additional (ligand) hyperfine interactions are calculated in the approximation of weak binding between a charge-compensating ion F _a ^? and a cubic fragment in the tetragonal cluster. It is demonstrated that correct inclusion of the contributions from the spin polarization to the ligand isotropic hyperfine interaction for the F _a ^? ion leads to anomalously large parameters of this interaction for MeF₂ crystals. These results are in agreement with experimental data.     

Bose-Einstein Correlations in W<Superscript>+</Superscript> W<Superscript>–</Superscript> events at LEP2

Bose-Einstein correlations (BEC) between final state particles in the reaction have been studied. Data corresponding to a total integrated luminosity of 550 pb^-1, recorded by the DELPHI detector at centre-of-mass energies ranging from 189 to 209 GeV, were analysed. An indication for inter-W BEC between like-sign particles has been found at the level of 2.4 standard deviations of the combined statistical and systematic uncertainties. Received: 11 January 2005, Revised: 13 July 2005, Published online: 13 September 2005 This paper is dedicated to the late Frans Verbeure. Frans was a very active member of the DELPHI collaboration and its QCD and WW working groups. The loss of Frans touched us all deeply.