Note on the two inequivalent spin 1/2 baryon field operators

There are two inequivalent spin 1/2 local baryon field operators that can be constructed from 3 quarks. A priori theJ ^P =1/2⁺ baryons can couple to any linear combination of these operators. We show however that the coupling of the 1/2⁺ baryons to these operators is determined by the value of theSU(3) ratio ofF toD type pseudoscalar-baryon couplings. The experimental value of this ratio implies, for example, that the proton couples strongly to (u ^T C _γ d)u and weakly to (u ^T C d)γ _s u. This is of interest in QCD sum rule applications.     

Invariant subspaces of clustering operators

A class of clustering operators is defined which is a generalization of a transfer matrix of a Gibbs lattice field with an exponential decay of correlations. It is proved that for small values of the clustering operator has invariant subspaces which are similar tok-particle subspaces of the Fock space. The restriction of the clustering operator onto these subspaces resembles the operator exp(-H _k, whereH _k is thek- particle Schrödinger Hamiltonian in nonrelativistic quantum mechanics. The spectrum of eachH _k,k1, is contained in the interval (C ₁^k,C ₂^k). These intervals do not intersect with each other.     

Systems with separable many-particle interactions. I

In this paper we give an exact evaluation of the free energy per particle for systems with separable many-particle interactions described by a hamiltonian of the type ? = ∑_kT(k) + NP (N^-1 ∑_kV(k)), where P is an arbitrary polynomial. In the proof use is made of a fundamental theorem due to Bogoliubov Jr. for ferromagnetic quadratic operators. The free energy can be obtained from a trial hamiltonian, which is linear in the operators T and V.     

A new ℋ -space formalism

The equations governing geometrical objects in ? space are written in terms of operators adapted to families of left shear-freeσ ⁰= 0) cross sections of complexified null infinity (C I ⁺). The concept of ?-conformai weight (HCW) is introduced, and a derivative operatorI _a ^′ , which is closely connected with the covariant derivative but which (unlike the covariant derivative) maps objects having well-defined HCW to other such objects, is defined. A function ?, derived from the Gaussian curvature of left shear-free slicings ofC I ⁺ and having a well-defined HCW, is shown to contain all the curvature information for ? space.     

Degenerate asymptotic perturbation theory

Asymptotic Rayleigh-Schrödinger perturbation theory for discrete eigenvalues is developed systematically in the general degenerate case. For this purpose we study the spectral properties ofm×m—matrix functionsA(κ) of a complex variable κ which have an asymptotic expansion εA _k κ ^k as τ→0. We show that asymptotic expansions for groups of eigenvalues and for the corresponding spectral projections ofA(κ) can be obtained from the set {A _κ} by analytic perturbation theory. Special attention is given to the case whereA(κ) is Borel-summable in some sector originating from κ=0 with opening angle >π. Here we prove that the asymptotic series describe individual eigenvalues and eigenprojections ofA(κ) which are shown to be holomorphic inS near κ=0 and Borel summable ifA _k ^* =A _k for allk. We then fit these results into the scheme of Rayleigh-Schrödinger perturbation theory and we give some examples of asymptotic estimates for Schrödinger operators.     

Large transverse momenta in the multiperipheral model

A unified picture of small and large transverse momenta is provided by the multiperipheral model in its original version. The large k_T spectrum is k_T^?p times a scaling function. Results are in agreement with ISR data and testable predictions are made.     

Simplified closed form expressions for irreducible tensor operators

A general closed form expression is derived which enables one to write a spherical tensor of rank L and projection k, T_uk^L, in terms of the familiar angular momentum operators, S_z and S². The simplicity of this expression results from an intriguing relationship between these spherical tensor operators (diagonal operator equivalents) and successive derivatives of Tchebichef orthogonal polynomials.     

Measurement of collision broadening of the P1(5) line of (0,0) band of OH AΣ←XΠ transition at high temperatures

Even for the well-studied and ubiquitous species, OH, the current state of theoretical development of broadening theory does not allow extrapolation from low-temperature laboratory measurements to the range of practical combustion devices. We performed a series of experiments at typical combustion conditions to determine the collision broadening of the P₁(5) line of the (0,0) band of OH A²Σ⁺←X²Π transition by Ar in shock-heated H₂-O₂-Ar mixtures and by air in H₂-air flames over a wide range of stoichiometry (φ=0.01-10.0), temperature (T=780-2440 K), and pressure (p=0.7-10.0 atm). The values of the collision width, Δν_C, were acquired by fitting Voigt profiles to the measured spectral line shapes in flames and to the peak absorption coefficients (k_ν0) in shock tube experiments. Collision broadening parameters (2γ_Ar, 2γ_N2, and 2γ_H2O) were then calculated assuming the linear dependence of Δν_C with pressure—the 2γ_N2 and 2γ_H2O values were inferred from 2γ_Air and the equilibrium concentration of N₂ and H₂O of a given flame. The temperature dependences of 2γ_i in our temperature range are, respectively, 1.0, 0.75, and 0.87 for Ar, N₂, and H₂O. The collision broadening cross sections (σ) deduced from 2γ_i values are expressed with an assumed form, σ_i(T)=σ_i,₀(T₀/T)^k, T₀=1000 K: for Ar, σ_Ar,0=63.3 (Ų), k=0.50; for N₂, σ_N2,0=68.0 (Ų), k=0.25; for H₂O, σ_H2O,0=188.8 (Ų), k=0.37.     

Solvent aided NMR microscopy of γ-irradiatedcis 1,4-polybutadiene

Cross-linked structure of γ-irradiatedcis 1,4-polybutadiene (PBi) was studied by NMR microscopy with the aid of deuterated benzene. After PBi was swollen (PBiS) in C₆D₆, the¹H NMR linewidth of the polymer was reduced from 4 to 2 kHz. The images show that the relaxation times,T ₁ andT ₂, of PBiS are longer than those of PBi. The simultaneous increase ofT ₁ andT ₂ implies that the molecular chains of PBi become more mobile upon swelling. The enhanced mobility of the molecular chains may provide a possibility of the increase in space resolution.     

Exact expressions for the energy current and stress tensor operators in many-particle systems

For some purposes in statistical physics, such as, for example, the calculation of various transport coefficients, it is necessary to have expressions for the energy current operatorS and stress tensor operatorT _lm . In this work it is shown that by using a simple identity, exact expressions forS andT _lm which satisfy the conservation laws for the energy density? and momentum densityP, respectively, exist.S andT _lm can each be written as a sum of two parts,S=S ^(A) +S ^(B) T _lm =T _lm ^(A) +T _lm ^(B) . The “A” part is the ordinary convective or kinetic part while the “B” part is shown to be expressible as a gradient and hence its homogeneous component vanishes identically. The expressions are compared with approximate forms found in the literature. The operators are Fourier analyzed and written in terms of the field operators in the second quantization formalism.     

On the temperature behavior of second sound and Poiseuille flow

The linearized Peierls equation for the phonon densityN (k λ,r t) is solved by replacing the collision operator in the subspace orthogonal to the collision invariants byk-dependent relaxation rates. For the normal process relaxation time the behaviorτ _N (k λ)∝|k|^?p for smallk is assumed. Taking into account thisk-dependence ofτ _N explicitly and avoiding an expansion with respect toΩτ _N (kλ) before performing the necessary integration overk yields new, non-analytic, terms in the hydrodynamic equations describing second sound and Poiseuille flow. It is shown that this may lead to a temperature dependence of second sound damping and thermal conductivity in the Poiseuille flow region differing from the usual theoretical predictions and in better agreement with experiments.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.     

Paramagnetic centres in tungstate powders

The EPR-powder spectrum ofV _k -centres in CaWO₄ is simulated using the experimentally obtained principal values of theg-tensor. The influence of the finite linewidth ΔH on the resulting EPR-pattern is taken into account. With these results the existence ofV _k -centres in x-rayed microcrystalline tungstate powder is proved. The resonance of the² S _1/2-state of Pb³⁺-ions substitutionally incorporated on Ca²⁺-sites in CaWO₄ is measured in the powder spectrum. The optically and thermally stimulated valence state changes of the centres are studied and are shown to be correlated with the thermoluminescence glow curve.     

Investigation of LiFeAs by means of “break-junction” technique

In our tunneling investigation using Andreev superconductor-normal metal-superconductor contacts on LiFeAs single crystals we observed two reproducible independent subharmonic gap structures at dynamic conductance characteristics. From these results, we can derive the energy of the large superconducting gap ??_L = (2.5?C3.4) meV and the small gap ??_S = (0.9?C1) meV at T = 4.2 K for the T _C ^local ?? (10.5?C14) K (the contact area critical temperature which deviation causes the variation of ??_L). The BCS-ratio is found to be 2??_L/k _B T _C = 4.6?C5.6, whereas 2??_S/k _B T _C ? 3.52 results from induced superconductivity in the bands with the small gap.     

On the thermodynamic formalism for the gauss map

We study the generalized transfer operator ? _β f(z)= \(\sum\limits_{n = 1}^\infty {\left( {\frac{1}{{z + n}}} \right)^{2\beta } \times f\left( {1/\left( {z + n} \right)} \right)} \) of the Gauss mapTx=(1/x) mod 1 on the unit interval. This operator, which for β=1 is the familiar Perron-Frobenius operator ofT, can be defined for Re β>1/2 as a nuclear operator either on the Banach spaceA _∞(D) of holomorphic functions over a certain discD or on the Hilbert space ? _Reβ ⁽²⁾ (H _-1/2 of functions belonging to some Hardy class of functions over the half planeH _?1/2. The spectra of ? _β on the two spaces are identical. On the space ? _Reβ ⁽²⁾ (H _-1/2 ? _β is isomorphic to an integral operatorK _β with kernel the Bessel function \(\mathfrak{F}_{2\beta - 1} (2\sqrt {st} )\) and hence to some generalized Hankel transform. This shows that ? _β has real spectrum for real β>1/2. On the spaceA _∞(D) the operator ? _β can be analytically continued to the entire β-plane with simple poles atβ=β _k =(1-k)/2,k=0, 1, 2,..., and residue the rank 1 operatorN ^(k) f=1/2(1/K!)f ^(k)(0) . From this similar analyticity properties for the Fredholm determinant det (1-? _β ) of ? _β and hence also for Ruelle's zeta function follow. Another application is to the function \(\zeta _{\rm M} (\beta ) = \sum\limits_{n = 1}^\infty {\left[ n \right]^\beta } \) , where [n] denotes the irradional [n]=(n+(n ²+4)^1/2)/2.ζ _M (β) extends to a meromorphic function in the β-plane with the only poles at β=±1 both with residue 1.     

Four-wave mixing and hyper-Raman scattering in CuCl

Non-degenerate four-wave mixing using two non-collinear laser beams with frequencies (wavevectors) ω_p, ω_t (k_p, k_t) respectively is studied in CuCl. Two emission lines at frequencies ω⁽¹⁾=2ω_t-ω_p, and ω⁽²⁾=2ω_p-ω_t are observed. Their excitation spectrum is sharply peaked if the phase-match condition k⁽¹⁾=2k_t-k_p is fulfilled. This is the case, if ω_p coincides with the hyper-Raman lines (R⁺_T, R^-_T) of the laser labelled (t) in a well-defined geometrical configuration.     

On the mechanism of decomposition of the benzyl radical

The C₇H₇ potential energy surface was studied from first principles to determine the benzyl radical decomposition mechanism. The investigated high temperature reaction pathway involves 15 accessible energy wells connected by 25 transition states. The analysis of the potential energy surface, performed determining kinetic constants of each elementary reaction using conventional transition state theory, evidenced that the reaction mechanism has as rate determining step the isomerization of the 1,3-cyclopentadiene, 5-vinyl radical to the 2-cyclopentene,5-ethenylidene radical and that the fastest reaction channel is dissociation to fulvenallene and hydrogen. This is in agreement with the literature evidences reporting that benzyl decomposes to hydrogen and a C₇H₆ species. The benzyl high-pressure decomposition rate constant estimated assuming equilibrium between the rate determining step transition state and benzyl is k₁(T) = 1.44 × 10¹³T^0.453exp(−38400/T) s⁻¹, in good agreement with the literature data. As fulvenallene reactivity is mostly unknown, we investigated its reaction with hydrogen, which has been proposed in the literature as a possible decomposition route. The reaction proceeds fast both backward to form again benzyl and, if hydrogen adds to allene, forward toward the decomposition into the cyclopentadienyl radical and acetylene with high-pressure kinetic constants k₂(T) = 8.82 × 10⁸T^1.20exp(1016/T) and k₃(T) = 1.06 × 10⁸T^1.35exp(1716/T) cm³/mol/s, respectively. The computed rate constants were then inserted in a detailed kinetic mechanism and used to simulate shock tube literature experiments.     

Measurement of fast neutron induced fission cross section of thorium using Lexan plastic track detector

Fission-track registration characteristics of Lexan solid state nuclear track detectors have been used to measure the fast neutron induced fission cross section of²³²Th. The fast neutrons (?14.2MeV) were produced with the help of an AN-400 model Van-de-Graaff accelerator at Banaras Hindu University laboratory using³H(²H,n)⁴He reaction and were used to irradiate the fissile target deposited on the plastic detector. The track densityT, registered on the plastic detector is related to the fission cross sectionσ _f, through the relationT=knσ _føt wheren is the number of fissile atoms per cm² in the deposit, ø is the neutron flux,k is fission track registration efficiency andt is the time of irradiation. The fission cross sectionσ _f of²³²Th, relative to the well measured fission cross section of²³⁸U, was found to be 0.36±0.04 barn.     

The determination by an independent method ofP k electron capture probabilities in133Ba and139Ce decays gamma decay of133Ba

The electron capture decays of¹³³Ba (10.4 y) and¹³⁹Ce (140 d) were investigated with high resolution Ge(Li) detectors. By x-ray — γ-ray coincidences values of the quantityP _k ω _k ? _k for various transitions in the decay of¹³³Ba and¹³⁹Ce are obtained. The factor ω _k ? _k was measured independently by means ofK-conversion electron-K x-ray coincidences and was then used to determineP _k , theK-capture probability. The independent measurement of the product ω _k ? _k , together with recent accurate values of ω _k , provides a new method for the accurate calibration of semiconductor x-ray detectors. In the decay of¹³⁹Ce, a value ofP _k =0.78±0.03 is found (where the error represents twice the standard deviation) from whichQ _ec =326 _?30 ⁺⁷⁰ keV to the¹³⁹La ground-state is found by use of theory. In¹³³Ba decay, values are found ofP _k 1=0.72±0.04 for theEC transition to the 437 keV level in¹³³Cs,P _k 2=0.80±0.07 to the 384 keV level, and from an independent measurement, the ratioP _k 1/P _k 2=0.87±0.07. From these results the ground-state value ofQ _ec =522 _?10 ⁺²⁰ keV is derived from theory for¹³³Ba decay. The gamma spectrum of¹³³Ba also was remeasured. From the present gamma intensities and previous conversion electron intensities, new values forK-shell conversion coefficients are obtained. Previously reported γ-rays at 35 and 391 keV are not confirmed.