ΛN and ΣN Interactions from Lattice QCD

We present our recent study on ΛN and ΣN (isospin I = 3/2) interactions by measuring Nambu–Bethe–Salpeter wave functions on the Lattice QCD. The lattice QCD calculation is performed by using the N _f  = 2 + 1 gauge configurations generated by PACS-CS collaboration together with employing an improved method to obtain potentials in lattice QCD simulations. For the ¹ S ₀ channel, the central ΣN (I = 3/2) potential and the central ΛN (¹ S ₀) potential are found to be very similar. For the spin triplet (³ S ₁?³ D ₁) channels, the central ΛN(³ S ₁?³ D ₁) potential is attractive while the central ΣN(I = 3/2, ³ S ₁?³ D ₁) potentials is repulsive. Tensor potentials, on the other hand, are rather weak in both ΛN and ΣN(I = 3/2) systems.     

Crossover behavior of anisotropic cubic system with ionic anisotropy

Crossover behavior of anisotropic cubic N-component spin system with ionic anisotropies of different magnitude is studied in terms of the renormalization-group (RG) approach in momentum space. As a fundamental case, we choose a system with two kinds of strength of ionic anisotropies (i.e. m²₁ for the M-component spin and m²₂ for the other (N–M)-one), which has a bicritical point. We discuss the critical behavior and crossover behavior between the M- component system and the N-component system on the critical exponents [i.e., coefficient functions appearing in the RG equation of γS for the spin field S, γS² for the S²-field and γδS² for the δS² (≡[(N-M)S²₂-MS²₂]/N)-field] and on the temperature-dependent crossover exponent γeff.     

Fit values of N subshell fluorescence yields and Coster-Kronig yields for elements with 38?Z?103

Most probable values of Coster-Kronig (CK) transition probabilities (S₁₂, S₁₃, S₁₄, S₁₅, S_1,67, S₂₃, S₂₄, S_2,67, S₃₄, S₃₅, S₃₅, S_3,67, S₄₅ and S_4,67) and N_i subshell fluorescence yields (N₁, N₂, N₃, N₄, N₅ and N₆₇) have been determined by using least-squares fitted to obtain the polynomials, which is plotted by using the McGuire's values (Phys Rev A 9(5) (1974) 1840), representing them as a function of atomic number. The S_ij represents the N subshell vacancy transitions from ith subshell to jth subshell. The obtained values of N_i subshell fluorescence yields—N₁, N₂, N₃, N₄, N₅, N₆₇, and CK transition probabilities—S₁₂, S₁₃, S₁₄, S₁₅, S_1,67, S₂₃, S₂₄, S_2,67, S₃₄, S₃₅, S₃₅, S_3,67, S₄₅ and S₄₆ are presented.     

N-point functions and low-energy scattering by N centres

The scattering of a low-energy particle by a potential of a small range is known to be described satisfactorily by the s-wave alone. In the present paper we give a method of describing low-energy scattering by N potentials with the aid of N waves. For this purpose, a special system of Laplacian eigenfunctions is suggested. The scattering amplitude depends on only N parameters, irrespective of overlapping of potentials. The physical significance of these parameters δ_λ, λ=1,2,…N, is shown by exp (2iδ_λ)=S_λ where S_λ is the eigenvalue of the S matrix. The parameters δ_λ may be obtained by direct methods and perturbation theory.The low-energy scattering by an arbitrary configuration of N centres is discussed. The differential cross-section is averaged over all orientations of the configuration and radially about the direct beam, giving it as a function of the scattering angle. This formula may be used for the phase shift analysis.     

Density correlations of hadron gas and the origin of early multiplicity scaling

We will define a sequence of functions called density correlations which measure statistical correlations between momentum space densities of particles in the ensemble of inelastic final states produced by scattering a pair of hadrons. Then we will show that early multiplicity scaling of the distribution of charged particles produced by pp collisions can primarly be explained by the assumption that fluctuations of the density of charged particles are quite random and therefore higher correlation functions are small in an appropriate sense, combined with the assumption that the first three density correlations fulfill an approximate form of Feyman scaling at small values of x. These assumptions will aslo be used to derive an expression for the scaling function Ψ(η) which is completely determined by <N²>_S/<N>_S² and <N³>_S/<N>_S³, and recursion relation to calculate <N^m>_S/<N>_S^m, m ? 4, from <N²>_S/<N>_S² and <N³>_S/<N>_S³. The prediction for Ψ(η) accurately reproduces data in the interval 0.2 ? η ? 3.1, 50 GeV/c ? p_L ? 303 GeV/c, and the predictions for <N_S>^m/<N>_S^m, 4 ? m ? 10, agree with observed values in the interval 50 GeV/c ? p_L ? 303 GeV/c.     

The mass of the scalar boson beyond the large- N c limit

Within the framework of the 1/N_c expansion of four-fermion interaction models, we analyse the next to leading 1/N_c corrections to the well known large-N _c result M _S = 2M _Q where M _S is the mass of the scalar boson and M _Q is the constituent quark mass. The calculation is performed in the Extended Nambu-Jona Lasinio (ENJL) model which is suitable for describing low energy hadron properties. We treat the model as fully non renormalizable and discuss the comparison with approaches based on the equivalence with renormalizable Yukawa type models. We consider both the G _V = 0 and the G _V ≠ 0 cases with n _f = 2 flavours and study the dependence upon the regularization scheme. We find that pure next-to-leading 1/N _c corrections are large and negative, while a partially resummed treatment can induce positive and smaller corrections. A triplet-singlet states’ splitting is observed.     

Effect of the pump absorption on generation of infrared stimulated electronic Raman scattering in alkali-metal vapors

The main properties of infrared stimulated electronic Raman scattering (SERS) at the 6² S _1/2-7² S _{1/2, 3/2} transitions in cesium atoms are studied theoretically and experimentally as functions of the atomic concentration, which was varied from 10¹¹ to 10¹⁶ cm^?3. It is found that the efficiency of generation of Stokes radiation strongly depends on one-photon absorption of the pump radiation tuned near frequencies of the 6² S _1/2-7² P _{1/2, 3/2} transitions. By using the equation for the density matrix, which describes the evolution of a three-level system, the theory of resonance excitation of IR radiation upon one-photon absorption at an adjacent transition is developed. The theory describes well the main features of IR SERS in alkali-metal vapors.     

Interaction of Zn atoms in the 1 S and 3 P states with N2 molecules in the X 1Σ g + and A 3Σ u + states at moderate distances between the atom and molecule

An asymptotic method was used to derive analytical expressions for the matrix elements of interaction between the N₂ molecule in the X ¹Σ _g ⁺ and A ³Σ _u ⁺ electronic states and the Zn atom in the ¹ S and ³ P states. Quadrupole-quadrupole, dispersion, and exchange interactions were taken into consideration. The character of the set of diabatic vibronic potential energy surfaces of the system suggests that the energy transfer in the process N₂(A ³Σ _u ⁺ ) + Zn(¹ S) → N₂(X ¹Σ _g ⁺ ) + Zn(³ P) may prove to be rather effective.     

Doubly excited resonances of positronium negative ions

Some lower-lying doubly excited ¹S^e and ³S^e resonances of positronium negative ions associated with N = 2 up to N = 5 positronium thresholds are calculated by a method of complex-coordinate rotation. Hylleraas-type wave functions with N = 203 terms are used to represent the system.     

Spontaneous compactification in generalized Candelas-Weinberg models

In their recent work on the dimensional reduction, Candelas and Weinberg considered a model which is compactified into a direct product space of the Minkowski space (M₄) and an N-dimensional sphere (S_N). In the present paper we investigate generalized models of their type which are compactified into M₄ × S_M × S_N and M₄ × S_M × CP₂. The compactification is caused by the quantum loop effect due to a large number of matter fields. The conditions for the vacuum stability are studied. Numerical computation of the loop effect is undertaken, and it is shown that some of the models of the type M₄ × S_M × S_N admit a stable solution which has finite circumferences of both of the extra spaces and positive coupling constants of the Einstein-Yang-Mills theory in four dimensions.     

Rovibrational spectrum and potential energy surface of the N2-N2O van der Waals complex

The rovibrational spectrum of the N₂-N₂O van der Waals complex has been recorded in the N₂O ν₁ region (∼1285 cm⁻¹) using a tunable diode laser spectrometer to probe a pulsed supersonic slit jet. The observed transitions together with the data observed previously in the N₂O ν₃ region are analyzed using a Watson S-reduced asymmetric rotor Hamiltonian. The rotational and centrifugal distortion constants for the ground and excited vibrational states are accurately determined. The band-origin of the spectrum is determined to be 1285.73964(14) cm⁻¹. A restricted two-dimensional intermolecular potential energy surface for a planar structure of N₂-N₂O has been calculated at the CCSD(T) level of theory with the aug-cc-pVDZ basis sets and a set of mid-bond functions. With the intermolecular distance fixed at the ground state value R = 3.6926 Å, the potential has a global minimum with a well depth of 326.64 cm⁻¹ at θ_N2 = 11.0° and θ_N2O = 84.3° and has a saddle point with a barrier height of 204.61 cm⁻¹ at θ_N2 = 97.4° and θ_N2O = 92.2°, where θ_N2(θ_N2O) is the enclosed angle between the N-N axis (N-N-O axis) and the intermolecular axis.     

Das integrale Reflexionsvermögen von gebogenen Quarzkristallen für Röntgenstrahlen im Transmissionsfall

A calculation procedure is described which permits evaluation of the material functions (electrical conductivityσ and radiation densityu as a function of the heat flux potentialS)from the measured arc characteristicsE(I) andU(I) (field strength and radiated power per unit arc length as a function of current strength). Hereto must be employed the additional relationship of energy balance and the current transport equation. The procedure is applied to N₂ and Ar. If furthermore the radial temperature distribution is known the temperature dependence ofσ, u.S andκ (thermal conductivity) may also be determined. In this way the material functions of the N₂-plasma are evaluated from available measurements.     

Structure of higher order corrections to the Lipatov asymptotic form

High orders of perturbation theory can be calculated by the Lipatov method, whereby they are determined by saddle-point configurations, or instantons, of the corresponding functional integrals. For most field theories, the Lipatov asymptotic form has the functional form ca ^NΓ(N+b) (N is the order of perturbation theory) and the relative corrections to it are series in powers of 1/N. It is shown that this series diverges factorially and its high-order coefficients can be calculated using a procedure similar to the Lipatov one: the Kth expansion coefficient has the form const[ln(S ₁/S ₀)]^?K Γ(K+(r ₁? r ₀)/2), where S ₀ and S ₁ are the values of the action for the first and second instantons of this particular field theory, and r ₀ and r ₁ are the corresponding number of zeroth-order modes; the instantons satisfy the same equation as in the Lipatov method and are assumed to be renumbered in order of their increasing action. This result is universal and is valid in any field theory for which the Lipatov asymptotic form is as specified above.     

Selective effects of homogeneous and heterogeneous reactions in the system N21-CO

In the system N₂¹-CO, effects arising only from the reactions in the homogeneous phase have been isolated in a reactor with inert walls. After an induction period of 0.13 s, they involve a stationary rate of enhancement of N₂(B³Π_g) and N(⁴S) concentrations according to the reactions N₂(X¹Σ_g⁺)_v¹+CO→ CO(X¹Σ⁺)_v1 + N₂(X¹Σ_g⁺ and CO(X¹Σ⁺)_v1 + N₂(A³Σ_u⁺) → N (⁴S) + N(⁴S) + CO(X¹Σ⁺).In a reactor with active walls, both the above reactions in the homogeneous phase and heterogeneous reactions due to CO adsorbed on the walls are involved according to CO_ads + N₂(X¹Σ_g⁺)_{v1 ads or not} → CO(X¹Σ⁺)_v1 + N₂(X¹Σ_g⁺ and N(⁴S) + N(⁴S) + CO_ads → N₂(X¹Σ_g⁺) + CO(X¹Σ⁺)N(⁴S) + CO_ads → N₂(X¹Σ_g⁺) + CO(X¹Σ⁺). In this case, the rate of enhancement is not stationary. Furthermore, for cylindrical reactors with large diameters, the two types of reaction do not interact and their effects are additive.     

Duality and quantum-algebra symmetry of the AN−1(1) open spin chain with diagonal boundary fields

We show that the transfer matrix of the A_N−1⁽¹⁾ open spin chair with diagonal boundary fields has the symmetry U_q(SU(l)) × U_q(SU(N−l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S-matrices in the regime with q real.     

Specific heats and phase transition in TMMC

The specific heats of the nearly one-dimensional antiferromagnet TMMC showed a sharp discontinuity in the temperature range ?(≡∥1?T/T_N∥) ≈ 2 × 10^-3 at T_N =0.835 ± 0.010 K. The remaining magnetic entropy below T_N is about 1% of its total for S = $\text{5}\text{2}$.     

Manifestation of the vibronic analogue of the Fermi resonance in quasi-line spectra of porphyrins: Experiment and theoretical analysis

The quasi-line low-temperature (4.2 K) fluorescence excitation spectra of two porphyrins, meso-tetraazaporphin and meso-tetrapropylporphin introduced into an n-octane matrix are measured in the range of the S ₀ → S ₂ electronic transition. A characteristic feature of these spectra is that a conglomerate of quasi-lines—a structured complex band—is observed instead of one 0–0 quasi-line of the S ₀ → S ₂ transition. In this band, the intensity distributions for the two main types of impurity centers considerably differ from each other. The occurrence of such conglomerates is interpreted as a result of nonadiabatic electronic-vibrational interactions between vibronic S ₂ and S ₁ states (the complex vibronic analogue of the Fermi resonance). The frequencies and intensities of individual transitions determined from the deconvolution of complex conglomerates are used as the initial data for solving the inverse spectroscopic problem: the determination of the unperturbed electronic and vibrational levels of states involved in the resonance and the electronic-vibrational interaction matrix elements between them. This problem is solved with a method developed previously. The energy intervals between the S ₂ and S ₁ electronic levels of the two main types of impurity centers formed by molecules of a given porphyrin in the crystal matrix are found to significantly differ from each other (～100 cm^?1). At the same time, the energies of the unperturbed vibrational states of the S ₁ electronic level partcipating in the resonance are very close to each other for these two types of impurity centers.     

Electron-vibrational energy exchange in collisions of electronically excited N2(A 3Σ u + ) molecules with Zn(X 1 S) atoms

The interaction matrix between the N₂ molecule in the X ¹Σ _g ⁺ and A ³Σ _u ⁺ states and the Zn atom in the ¹ S and ³ P states calculated earlier by the asymptotic method was used to find the rate constants for the electron-vibrational energy exchange N₂(A ³Σ _u ⁺ , v) + Zn(¹ S) → N₂(X ¹Σ ₈ ⁺ , v′) + Zn(³ P). The calculations were performed by the transition state method, and the probabilities of transitions between intersecting electron-vibrational terms of the system in motion along the reaction coordinate were determined by the Landau-Zener equation. The calculated electron excitation transfer constants between N₂(A ³Σ _u ⁺ , v = 1, 0) and Zn(¹ S) over the temperature range 300–900 K were on the order of 10^?11?10^?12 cm³/s.     

Correlation analysis of the shifts of the electronic spectra of anthracene, phenanthrene, and fluorene as functions of the temperature in the gas phase and of the refractive index in n-paraffin solvents

The temperature-induced shifts of the maxima of the longest-wavelength bands of the S ₁ ← S ₀ and S ₂ ← S ₀ transitions in phenanthrene and the S ₁ ← S ₀ transition in fluorene in the gas phase are measured. A correlation analysis of these data and similar data on the S ₁ ← S ₀ and S ₁ → S ₀ transitions in anthracene is fulfilled. The positions of the maxima of analogous bands of the S ₁ ← S ₀ transition in anthracene, S ₁ ← S ₀ and S ₂ ← S ₀ transitions in phenanthrene, and S ₁ ←S ₀ transition in fluorene dissolved in liquid n-paraffins are also measured and analyzed as functions of (n ² ? 1)/(n ² + 2), where n is the refractive index of the solvent. The results confirm the conclusion of the Mirumyantz-Demchuk theory about the linear temperature dependence of the wave number of a band maximum but contradict the prediction that, upon extrapolation to T = 0 K, the positions of the maxima correspond to the electronic transitions in the molecule unperturbed by out-of-plane vibrations of the aromatic core.