Exactly solvable models through the generalized empty interval method,for multi-species interactions

Multi-species reaction-diffusion systems, with nearest-neighbor interaction on a one-dimensional lattice are considered. Necessary and sufficient constraints on the interaction rates are obtained, that guarantee the closedness of the time evolution equation for E _n(t)'s, the expectation value of the product of certain linear combination of the number operators on n consecutive sites at time t. The constraints are solved for the single-species left-right-symmetric systems. Also, examples of multi-species system for which the evolution equations of E _n(t)'s are closed, are given. Received 25 September 2002 / Received in final form 3 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: mamwad@iasbs.ac.ir     

Solvable lattice models related to the vector representation of classical simple Lie algebras

A series of solvable lattice models with face interaction are introduced on the basis of the affine Lie algebraX _n ⁽¹⁾ =A _n ⁽¹⁾ ,B _n ⁽¹⁾ ,C _n ⁽¹⁾ ,D _n ⁽¹⁾ . The local states taken on by the fluctuation variables are the dominant integral weights ofX _n ⁽¹⁾ of a fixed level. Adjacent local states are subject to a condition related to the vector representation ofX _n . The Boltzmann weights are parametrized by elliptic theta functions and solve the star-triangle relation.     

Doppler-free two-photon absorption spectroscopy of trans-glyoxal under magnetic fields up to 6T

In order to measure the Doppler-free two-photon absorption (DFTPA) spectrum in the presence of a strong magnetic field, a sample cell placed in an optical resonator was installed at the centre of the bore of a superconducting magnet capable of generating a magnetic field of up to 6T. Changes in spectra of the A ¹A_u ← X ¹A_g transition of trans-glyoxal were measured as a function of magnetic field strength. Level crossings induced by Zeeman energy shifts were observed. The perturbing level, which shows hyperfine splitting, was identified as the ³A_u(nπ?) state, because the hyperfine splitting is small in the ³B_u(^ππ?) state and large in the ³A_u(nπ?) state. The perturbation between the A ¹A_u(nπ?) and ³A_u(nπ?) states was shown to take place by either vibronic interaction or Zeeman interaction between the ³A_u(nπ?) state and the ³B_u(ππ?) component mixed to the A ¹A_u(nπ?) state by spin-orbit interaction. The magnetic moment of the A ¹A_u state was determined to be approximately 0.0028μ_B, and the magnitude of the mixing coefficients 〈1 ³B_u|H _so|1 ¹A_u〉/[E(1 ¹A_u) ? E(1 ³B_u)] was evaluated to be 0.026.     

Single-ion approach to the interpretation of the x-ray photoelectron spectra of the valence bands of monoxides of 3d elements

The single-ion approach taking account of only the intra-atomic Coulomb interaction in free d ⁿ ions and in d ⁿ ions in an O _h crystal field is used to analyze the fine structure of the x-ray photoelectron spectra of the valence bands of monoxides of 3d elements. The x-ray photoelectron spectra were studied as a collection of d ⁿ⁻¹ and d ⁿ L multiplets representing the unscreened and screened parts, respectively, of the final state. The unscreened part of the final state can be described by the distribution of the line strengths of the photoelectronic transition d ⁿ → d ⁿ⁻¹ and the screened part can be described as a partially relaxed distribution of the statistical weights of the d ⁿ ions. Fiz. Tverd. Tela (St. Petersburg) 39, 1056–1063 (June 1997)     

Chemical origin of C–O blue shift and nature of Cu+…C bonding in non-classical copper carbonyl Cu+(CO)n (n = 1–8) complexes

Natural bond orbital (NBO) method and atoms-in-molecules (AIM) theory are used to study the chemical origin in the direction and ordering of C–O frequency shift, as well as Cu^+…C bond nature in copper carbonyl cations Cu⁺(CO)_n (n = 1–8). This study emphasises the role of π-back donation in explaining the ordering of C–O blue shift. NBO analyses show that the interplay of two competing factors, including π-back donation and rehybridization, is responsible for both the direction and the ordering of C–O stretching frequency shift in Cu⁺(CO)_n (n = 1–8) complexes. In addition, the Cu^+…C interaction is interesting because Cu⁺(CO)_n (n = 1–4) structure has one-sphere CO ligands but Cu⁺(CO)_n (n = 5–8) has two-sphere CO ligands. Topological analyses of electron density are applied to characterise the Cu^+…C interactions of first- and second-sphere CO with Cu⁺ and to explore the Cu^+…C interactions in the nature.     

Doubly Excited <Superscript>1,3</Superscript><Emphasis Type="Italic">P</Emphasis><Superscript>e</Superscript> Resonance States of the Positronium Negative Ion with Coulomb and Screened Coulomb Potentials

We have investigated the doubly excited ^1,3 P ^e resonance states of positronium negative ion with Coulomb and screened Coulomb potentials using highly accurate correlated exponential wavefunctions. For Coulomb interaction, the stabilization and the complex-rotation methods are employed to extract resonance parameters (resonance positions and widths). We have obtained two ¹ P ^e resonances and three ³ P ^e resonances below the n = 3 Ps threshold. In addition to Feshbach resonances lying below n = 3 Ps threshold, we have calculated one ³ P ^e shape resonances lying above the Ps (n = 2) threshold. For screened Coulomb (Yukawa) interaction, we employ the stabilization method to extract resonance parameters as functions screening parameter. The resonance energies and widths for ^1,3 P ^e resonance states of Ps⁻ below the n = 3 Ps threshold for different screening parameters ranging from infinity (Coulomb case) to small values are reported, along with the Ps(3S) and Ps(3P) threshold energies. The screened Coulomb results for the ^1,3 P ^e resonance states are reported for the first time in the literature.     

Single and double electron capture processes in slow Ne q+-He (q=10, 6) collisions

The cross sections for single and double electron capture to the states Ne⁹⁺ n) with n=3–6 and Ne⁸⁺(3l,n′l′), Ne⁸⁺(4l,n′l′) with n′⩾4 and also the cross sections for single electron capture to the states Ne⁵⁺(3) in collisions of Ne¹⁰⁺ and Ne⁶⁺ with He atoms are calculated for collision energies in the interval from 10 to 150 keV. The calculation is carried out in the multichannel Landau-Zener, Nikintin, and Landau-Zener-Chaplik models with allowance for the radial coupling of the channels at crossing points of the energies of the quasidiabatic twoelectron states of the quasimolecule. The energies of the two-electron states are calculated in the effective potential method to first order in perturbation theory in the residual electron-electron interaction. The energies of the adiabatic states in the neighborhoods of the crossings of quasidiabatic terms are determined by the configuration interaction method. It is found that in Ne¹⁰⁺-He collisions the electron is captured mainly to the n=5 state of the Ne⁹⁺ ion. The cross section for double electron capture to the 3lnl′ state (n⩾4) of the Ne⁸⁺ ion is an order of magnitude smaller than the cross section for single electron capture. The contribution to the total cross section for double electron charge transfer from the 4l4l′ 4l5l′, and 4l6l′ states is approximately 25%. The dependence of the cross sections for double electron charge transfer on the values of l and l′ is investigated. Zh. Tekh. Fiz. 69, 15–28 (January 1999)     

A theoretical investigation of the interaction between fluorinated dimethyl ethers and molecular chlorine

Halogen bonds have received a great deal of attention in recent years. In this work, the interaction between fluorinated dimethyl ethers (n_F = 0–4) and molecular chlorine has been investigated by the theoretical methods. The two molecules are bonded together by an O···Cl?Cl halogen bond and the interaction energies calculated at the MP2/aug-cc-pVDZ level range between ?15.5 (n_F = 0) and ?6.1 (n_F = 4) kJ mol^?1. The correlations between interaction energies and proton affinity or ionisation potential of the ethers are discussed. The interaction between the molecules results in a small contraction of the CH bond of ethers and an elongation of the Cl?Cl bond. The data are analysed by a natural bond orbital analysis carried out at the wB97XD/6-311++G(d,p) level. The charge transfer from the ethers to Cl₂ is weak, ranges between 0.044 and 0.008 e and occurs mainly to the external Cl atom. The elongation of the Cl?Cl bond is related to the occupation of the σ^*(Cl?Cl) orbital and to the intermolecular hyperconjugation interaction between LP(O) and σ^*(Cl?Cl) orbitals. The interaction between the ethers and chlorine induces an enhancement of the infrared intensity and Raman scattering activity of the ν(Cl?Cl) vibration.     

Combined Raman scattering and ab initio investigation of the interaction between pyrene and carbon SWNT

Raman spectra of HiPco SWNT and SWNT-pyrene films were measured in the 160–1800 cm^?1 range. Due to the non-covalent interaction between SWNT and pyrene the most intensive component of the SWNT G mode (1590 cm^?1) is downshifted by 2 cm^?1 and becomes narrower. Also the intensity of the low-frequency component of the G mode (1550 cm^?1) decreases by about 30%. Structures and interaction energies in the complexes of pyrene and zigzag (n, 0) SWNTs [6 ≤ n ≤ 20] were determined at the MP2 level of theory. The BSSE-free geometry optimization of the pyrene-zigzag (12,0) SWNT complex converged to a structure with a 1/2staggered conformation and with an intermolecular distance of 3.5 Å. The BSSE-free interaction energy in the complex is ?30.8 kj mol^?1. Increasing of the nanotube diameter leads to a higher interaction energy. This energy becomes equal to ?37.2 kJ mol^?1 in the case of a planar carbon surface.     

Density expansion of the energy of N close-to-boson excitons

Pauli exclusion between the carriers of N excitons induces novel many-body effects, quite different from the ones generated by Coulomb interaction. Using our commutation technique for interacting close-to-boson particles, we here calculate the Hamiltonian expectation value in the N-ground-state-exciton state. Coulomb interaction enters this quantity at first order only by construction; nevertheless, due to Pauli exclusion, subtle many-body effects take place, which give rise to terms in (Na _x ³/)ⁿ with n ≥ 2. An exact procedure to get these density dependent terms is given. Received 11 February 2002 / Received in final form 30 May 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: combescot@gps.jussieu.fr     

Temperature dependence of the dual phosphorescence from xanthone in n-hexane matrices

The phosphoresence spectrum and lifetime of xanthone embedded in an n-hexane matrix has been investigated as a function of temperature (1·6-100 K). Vibrational analyses of the spectra reveal that emission occurs from three sites, two of which are dominant. Emission from one site (B) occurs from the ³ nπ* state of a planar xanthone molecule and is characterized by strong totally symmetric carbonyl stretching vibrations and a short lifetime (2·4 ms). Emission from the other site (C) is shown to arise from the ³ππ* state of an out-of-plane distorted xanthone molecule. It displays a vibrational structure rich in modes of a ₁, b ₁, and b ₂ (C _2v notation) symmetry and a long lifetime (115 ms). Both direct spin orbit coupling via configurational mixing of the nπ* and ππ* states due to the non-planarity of the molecule in its ³ππ* state and spin-orbit vibronic interaction involving ³ A ₁(ππ*)-¹ A ₂(nπ*) spin-orbit and ¹ A ₂(nπ*)-¹ B ₂(ππ*) vibronic interaction via out-of-plane b ₁ vibrations are shown to be responsible for the C site emission intensity. Vibronic mixing between the ³ππ* and ³ nπ* states is not important. With increasing temperature, the phosphorescence intensity from the B site (³ nπ*) emitters increases at first, reaches a maximum at ～20 K and then decreases. The C site (³ππ*) intensity simply decreases with rising temperature. At a given temperature, the phosphorescence lifetimes are identical and exponential for all emission bands regardless of site origin. These observations indicate an equilibrium between emitters in the two sites throughout the lattice. A phonon-assisted energy transfer mechanism is proposed to account for these observations.     

A Comparative Study of Proton-Emulsion and Heavy-Ion-Emulsion Interactions at 4.5 GeV/c per Nucleon

This paper presents a comparative study of inelastic interactions of proton-Emulsion, ¹²C-Emulsion and ²⁴Mg-Emulsion at 4.5 GeV/c per nucleon. The multiplicity distribution and their correlations have been studied. A strong correlation between 〈n_s〉 and n_h in case of ²⁴Mg-Emulsion and ¹²C-Emulsion is observed which is not so in the case of proton-Emulsion interaction. It is also observed that 〈n_s〉 increases with the increase of the projectile mass. The angular distribution of the target fragments in ²⁴Mg-Emulsion and ¹²C-Emulsion interactions show massive forward collimations. Comparison is also made in the pseudorapidity distributions of ²⁴Mg-Emulsion, ¹²C-Emulsion and proton-Emulsion interactions. The result shows many interesting features.     

Three-Body Spectrum of 18C and its Relevance to r-Process Nucleosynthesis

The ¹⁸C spectrum has been studied in a three body n + n +¹⁶C model that includes deformation and the 2⁺ excitation of the ¹⁶C core as well as Pauli projection of forbidden states. The ¹⁶C – n interaction employed in this study has been fitted to reproduce the experimental spectrum of ¹⁷C. The calculations show that two neutron separation energy in ¹⁸C in consistent with three-body structure of this nucleus and predict more states bound with respect to three-body decay. The comparison of their position to known excited states in ¹⁸C is discussed. These calculations suggest also that a few states may exist in astrophysically relevant region between the ¹⁷C+n and ¹⁶C + 2n decay thresholds. The most important of them is 1⁻ as it can give a large E1 resonant contribution to ¹⁷C(n, γ)¹⁸C neutron capture. The calculations also suggest that a virtual s-wave state may exist above the ¹⁷C + n threshold that can give rise to non-negligible M1 contributions to the ¹⁷C(n, γ)¹⁸C reaction rate. The presence of these states in the ¹⁸C spectrum can lead to an increased ¹⁷C(n, γ)¹⁸C reaction rate, which can significantly influence the abundances of uranium and thorium synthesized in the r-process in the supernovae explosions.     

Ab Initio Investigation of the Microspecies and Energy in Hydrated Strontium Ion Clusters

Quantum chemistry calculations were used to study the structure and energy of strontium (Sr) ion hydrated clusters [Sr(H₂O)_1?25]²⁺. The saturated hydration number of the first hydration layer of Sr²⁺ was 8, and the hydration distance was 2.58 Å. The second hydration layer had 1–9 hydration numbers, and the hydration distance was in the range of 4.4–4.6 Å. This work also developed the relationship between the thermodynamic data (average water binding energy E_n and successive water binding energy ΔE_n,n?1, etc.) of the aforementioned low-energy structure and the hydration structures. The first hydration layer was formed by the strong electrostatic interaction between Sr²⁺ and water molecules, and the decrease in ΔE_n,n?1 was relatively large. Hydrogen bonds were formed between water molecules of the second hydration layer and water molecules of the inner layer, and the decrease in ΔE_n,n?1 was relatively small. When one water molecule was added beyond the second hydration layer, ΔE_n,n?1 was close to the hydrogen bond energy 8.88 kcal/mol (37.1 kJ/mol) of dimer water molecule, indicating that there was very weak interaction between Sr²⁺ and the water molecules beyond the second hydration layer.     

Dispersion of the Voigt effect in the magnetic semiconductors Cd1−x MnxTe

Spectral measurements of the Voigt birefringence Δn were performed for the cubic magnetic semiconductor Cd_1−x Mn _x Te (0≤x≤0.52) in order to investigate how the exchange interaction of Mn²⁺ ions with itinerant electrons depends on the electron wave vector. It was determined that Δn/x ² is independent of x and the magnetic field direction, i.e., the effect is due to the Mn²⁺ ions and is isotropic. Below the band gap edge the dispersion of the birefringence Δn can be described well in all samples by the unusual dependence Δn∼(E _g −ℏω) ^−3.5. This can be explained by a decrease of the exchange interaction of Mn²⁺ ions with itinerant electrons with increasing distance from the center of the Brillouin zone. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 8, 569–573 (25 April 1998)     

The Peierls phase transition in <Emphasis Type="Italic">n</Emphasis>-Ge caused by impurity interaction

The study of the electron paramagnetic resonance in Ge:As has revealed that the insulating state in uncompensated semiconductors is preserved near the insulator-metal phase transition because of the appearance of lattice distortions. The latter are caused by the interaction of the spins localized on impurity atoms due to the spin-Peierls transition. In Ge:As, this effect manifests itself in the concentration range n = n = 3 × 10¹⁷–3.7 × 10¹⁷ cm⁻³.     

TDPAC studies of the intercalation compound Li x TiS2 in the region 0≤x≤1

The electrochemical intercalation of Li⁺ into hafnium-doped TiS₂ was studied using time-differential perturbed angular correlations (TDPAC). The¹⁸¹Ta nuclear quadrupole interaction was monitored as a function of the charge transfer,n _F. For low uptakes, 0≤n _F≤0.03, a two-phase region was found with an empty host interaction, characterized byV _q=458(4) MHz, η=0.19(3) and δ-0.083(5), and a second interaction corresponding to lithiated material withv _q=597(5) MHz, η=0.13(4) and δ=0.061(5). No evidence was found for intermediate phases.     

Quartet states of He+ 2

The low lying quartet spectrum of the molecular helium cation is investigated by configuration interaction calculations. Using large Gaussian basis sets, potential energy curves for n ⁴Σ⁺ _u,g and n ⁴Π_u,g are computed for the states n = 1,…, 5. Several of these states lead to equilibrium configurations having rather extended bond lengths and some of them also a relatively large dissociation energy. The spectroscopic properties of these equilibrium configurations are studied. Quartet He⁺ ₂ is most strongly bound in its lowest state 1 ⁴Σ_u with R _e = 3.424 Å and D _e = 1.348 eV.     

Gauge invariance and average excitation energy approximation in the theory of nuclear magnetic shielding

The effects of three-body non-additivities on the most stable structures of Ar⁺ _n (3 ≤ n ≤ 27) clusters have been investigated in an extended diatomics-in-molecules (DIM) approach. Non-additive interaction terms for both the neutral and the ionic trimer have been included explicitly in the DIM Hamiltonian. Structural rearrangement is observed for a number of cluster sizes due to induced dipole—induced dipole interactions.     

Long range scattering for non-linear Schrödinger and Hartree equations in space dimensionn≥2

We consider the scattering problem for the non-linear Schrödinger (NLS) equation with a power interaction with critical powerp=1+2/n in space dimensionsn=2 and 3 and for the Hartree equation with potential |x|^–1 in space dimensionn2. We prove the existence of modified wave operators in theL ² sense on a dense set of small and sufficiently regular asymptotic states.Laboratoire associé au Centre National de la Recherche Scientifique