Unitarity and the inhomogeneous equations method for identical particle scattering

A K-matrix solution to the coupled, inhomogeneous equations describing the scattering of a particle by a system of identical particles is developed. It is shown that K is a sum of two terms, one arising from the homogeneous solution and one from the particular integral. The former is a direct contribution, i.e., with no exchange, while the latter is a pure exchange contribution. Thus, as in the previously studied case of the T matrix arising from this system of equations, the direct and exchange portions of K are additive, and can be computed separately. A unitary S matrix is obtained from K in the usual way: S = (1 + iK)(1 − iK)⁻¹. The problem of how to calculate K when an apparent two-channel problem is actually a two-particle problem with the channels referring to the identical particle labels is also solved.     

Change in the states of optically excited Rb atoms near sapphire surface

The changes in the states of excited Rb atoms approaching a single-crystal sapphire surface have been investigated by methods of laser-excitation spectroscopy and luminescence of Rb vapor in a cell with sapphire windows, the gap between which was varied from 250 to 500 nm. Upon resonant excitation of Rb atoms by two semiconductor lasers with powers of 20 and 40 mW, luminescence from optically excited 5D _3/2 and 5D _5/2 states and optically unexcited 6P _1/2 and 6P _3/2 states is observed. It is established that the luminescence intensity from unexcited states is only a few times lower than that from excited states, with allowance for the fact that excited atoms are rapidly and almost completely quenched on the sapphire surface. The found anomalously strong luminescence from optically unexcited 6P _J states is explained by their nonradiative occupation near the sapphire surface from optically excited 5P _J states, in which atoms fail to reach the sapphire surface because of the repulsion from it. This repulsion is due to the polarization interaction between sapphire and the atoms in the 5P _J states near the surface. Nonradiative transition from the 5P _J state to the 6P _J ^?1 state is accompanied by excitation of two optical phonons in sapphire.     

Fluorine Kα radiation for the excitation of electron spectra

The applicability of the F Kα X-ray line (hv = 676 eV) from potassium fluoride for the excitation of electron spectra is demonstrated. Relative photoionization cross-sections in Au and gaseous Hg have been measured. The F Kα radiation from KF, RbF and CsF has been studied. The Ba Mζ line (hv = 602 eV) is found to be too broad for use in ESCA, even when emitted from metallic barium.     

Scattering of Hawking photons as a barrier to particle absorption by black holes

Electromagnetic scattering interactions between photons emanating from a Schwarzschild black hole and an incident charged particle should generate a repulsive force between the particle and black hole. The net scattering cross-section is calculated here as a function of the mass M of the black hole and the mass m of the particle for scenarios in which the particle is point-like and initially stationary, with proper energy ε=m, at some location far from the black hole. It follows from comparing the repulsive scattering force to the corresponding gravitational force that, in order for the particle to be drawn to the black hole, ε/Tbh must be greater than a certain lower bound that is of the order ¹⁰−3 for spin-1/2 or spin-0 particles with unit-charge. Although the scattering restriction is weaker than the requirement ε/Tbh?1 obtained independently from field-theoretic and thermodynamic treatments, the recurrence of a lower bound on the Boltzmann factor ε/Tbh in limitations on particle absorption suggests a physical unity whose nature is fundamentally thermodynamic.     

Laser probing of OH production in catalytic oxidation of NH3byNO2 and no over a polycrystalline Pt surface at high temperatures

Catalytic ammonia denox reactions over a polycrystalline Pt surface in the temperature range 800–1330 K have been investigated by laser-induced-flourescence detection of the OH radical produced on and subsequently desorbed from the surface. For the NO₂-NH₃ system, strong curvature is observed in the low temperature region of the Arrhenius plots, which could be attributed to the presence of different desorption processes. The two extracted apparent OH desorption energies increase from 30 to 49 kcal/mol and from a surprisingly low value of 2 to 27 kcal/mol as the NO₂NH₃ reactant mixture ratio is decreased from 70 to 0.037. On the other hand, for the NO-NH₃ system, no such curvature in the Arrhenius plots is observed and the OH desorption energy decreases from 38 to 26 kcal/mol as the NO/NH₃ ratio is decreased from 70 to 0.4. The different trends in the apparent OH desorption energies as a function of the NO_x/NH₃ ratio in the present two systems can be rationalized by the degree of coverage of chemisorbed O atoms relative to that in the earlier studied O₂-NH₃ system.     

Occupancy Distributions Arising in Sampling from Gibbs-Poisson Abundance Models

Estimating the number n of unseen species from a k-sample displaying only p≤k distinct sampled species has received attention for long. It requires a model of species abundance together with a sampling model. We start with a discrete model of iid stochastic species abundances, each with Gibbs-Poisson distribution. A k-sample drawn from the n-species abundances vector is the one obtained while conditioning it on summing to k. We discuss the sampling formulae (species occupancy distributions, frequency of frequencies) in this context. We then develop some aspects of the estimation of n problem from the size k of the sample and the observed value of P _n,k , the number of distinct sampled species. It is shown that it always makes sense to study these occupancy problems from a Gibbs-Poisson abundance model in the context of a population with infinitely many species. From this extension, a parameter γ naturally appears, which is a measure of richness or diversity of species. We rederive the sampling formulae for a population with infinitely many species, together with the distribution of the number P _k of distinct sampled species. We investigate the estimation of γ problem from the sample size k and the observed value of P _k . We then exhibit a large special class of Gibbs-Poisson distributions having the property that sampling from a discrete abundance model may equivalently be viewed as a sampling problem from a random partition of unity, now in the continuum. When n is finite, this partition may be built upon normalizing n infinitely divisible iid positive random variables by its partial sum. It is shown that the sampling process in the continuum should generically be biased on the total length appearing in the latter normalization. A construction with size-biased sampling from the ranked normalized jumps of a subordinator is also supplied, would the problem under study present infinitely many species. We illustrate our point of view with many examples, some of which being new ones.     

Can HERA data improve the LEP constraints on the WWV vertex?

The combined results from ep → νWX, ep → eWX, and ep → νγX processes at HERA are used to constrain anomalous three-boson couplings. The effective model for anomalous couplings where there is no light Higgs boson and where interactions responsible for the breakdown of electroweak symmetry are strongly coupled is considered. Bounds on the couplings L _9L and L _9R , which parametrize contributions from the anomalous WWγ (WWZ) vertices, attainable from an analysis of the distributions for the processes in question are presented. The results are compared with the bounds resulting from the LEP I and LEP II data. It is shown that the bounds coming from HERA significantly reduce the parameter region allowed by the analysis of the LEP I and LEP II data.     

Nearest-neighbour spacing distributions of the β-Hermite ensemble of random matrices

The evolution with β of the distributions of the spacing ‘s’ between nearest-neighbour levels of unfolded spectra of random matrices from the β-Hermite ensemble (β-HE) is investigated by Monte Carlo simulations. The random matrices from the β-HE are real symmetric and tridiagonal where β, which can take any positive value, is the reciprocal of the temperature in the classical electrostatic interpretation of eigenvalues. The distribution of eigenvalues coincide with those of the three classical Gaussian ensembles for β=1, 2, 4. The use of the β-HE ensemble results in an incomparable speed up and efficiency of numerical simulations of all spectral characteristics of large random matrices. Generalized gamma distributions are shown to be excellent approximations of the nearest-neighbor spacing (NNS) distributions for any β while being still simple. They account both for the level repulsion in ∼s^β when s→0 and for the whole shape of the NNS distributions in the range of ‘s’ which is accessible to experiment or to most numerical simulations. The exact NNS distribution of the GOE (β=1) is in particular significantly better described by a generalized gamma distribution than it is by the Wigner surmise while the best generalized gamma approximation coincides essentially with the Wigner surmise for β>∼2. They describe too the evolution of the level repulsion between that of a Poisson distribution and that of a GOE distribution when β increases from 0 to 1. The distribution of ln (s), related to the electrostatic interaction energy between neighbouring charges, is accordingly well approximated by a generalized Gumbel distribution for any β?0. The distributions of the minimum NN spacing between eigenvalues of matrices from the β-HE, obtained both from as-calculated eigenvalues and from unfolded eigenvalues are Brody distributions which are classically used to characterize the spectral fluctuations of various physical systems.     

NMR hyperfine spectrum of 143Nd in ferromagnetic cubic intermetallic NdAl2

The hyperfine spectrum of ¹⁴³Nd in NdAl₂ measured at T = 1.4 K provides values of ∣a_t∣ = 786 ± 0.5 MHz and ∣P_t∣ = 3.25 ± 0.03 MHz. The latter value is in agreement with the expected calculated value obtained from the 4f ground state wave function in a crystal field plus molecular field model, which may be deduced from inelastic neutron scattering experiments combined with susceptibility measurements, or from polarized neutron diffraction experiments. It is shown that the 4f electronic moment can be directly obtained from zero field NMR with good accuracy.     

The effective potential and the bound states for a class of two dimensional gauge theories

The effective potential is calculated for a two dimensionalU(N) gauge theory with scalar quarks to leading order in the 1/N expansion. If there is noφ ⁴ interaction present, the potential is unbounded from below. If theφ ⁴ interaction is present, the potential is bounded from below and there is an unbroken and a spontaneously broken symmetry phase. The bound state spectrum of the unbroken phase is very similar to that of anU(N) gauge theory without theφ ⁴ term.     

Neutrino mixing and leptonic CP phase in neutrino oscillations

Oscillations of the Dirac neutrinos of three generations in vacuum are considered with allowance made for the effect of the CP-violating leptonic phase (analogue of the quark CP phase) in the lepton mixing matrix. The general formulas for the probabilities of neutrino transition from one sort to another in oscillations are obtained as functions of three mixing angles and the CP phase. It is found that the leptonic CP phase can, in principle, be reconstructed by measuring the oscillation-averaged probabilities of neutrino transition from one sort to another. The manifestation of the CP phase as a deviation of the probabilities of direct processes from those of inverse processes is an effect that is practically unobservable as yet.     

Is there a low-p T “anomaly” in the pion momentum spectra from relativistic nuclear collisions?

The influence of resonance production in relativistic hadron-hadron and nucleus-nucleus collisions, and their role in explaining the so-called “anomalous” behaviour of the hadronic transverse momentum spectra at lowp _T is studied qualitatively and quantitatively in the framework of a simple thermodynamical model. In the discussion effects from the different kinematics in 2- and 3-body decays and from the finite width of the resonances are included. We compare our results with data from the NA35 collaboration for pion, kaon, proton and Λp _T -spectra from 200 A GeV S+S collisions and withpp data at similar energies. The model can successfully describe both S+S andpp data withT=200 MeV, μ _b =250 MeV andT=180 MeV, μ _b =250 MeV, respectively. We discuss the consistency of these parameters by comparing with measured particle ratios and checking the freeze-out conditions. We conclude that the low-p _T part of the pion spectra is dominated by resonance decays, and that there is no low-p _T “anomaly”. We also find, that the flattening of the high-p _T tail in central nuclear collisions compared topp data is probably not of thermal origin but caused by other effects, e.g. collective transverse flow.     

Effective pinning barriers of NdFeAsO0.88F0.12 superconductor

Resistivities of polycrystalline iron-based NdFeAsO_0.88F_0.12 superconductors prepared via solid-state reaction in ambient pressure (AP) and high pressure (HP) were measured in various magnetic fields ranging from 0 to 9 T. Different resistivity broadening behaviors of the AP and HP samples, which may originate from the anisotropic superconductivity, the vortex motion, or the connectivity, were investigated in detail. The effective pinning barriers of both the AP and HP samples were obtained from the Arrhenius plot of the resistivity data by two analytic methods of which one assuming the prefactor 2ρ_cU/T of the thermally activated ?ux ?ow (TAFF) resistivity ρ=(2ρ_cU/T)exp(−U/T) is a constant, while the other assuming the prefactor is temperature dependent. The results determined from the two methods were compared and analysed, and the true effective pinning barriers were obtained. The origin of different pinning barriers of the AP and HP samples is discussed.     

Evaluation of error in the measurement of displacement vector components by using electronic speckle pattern interferometry

We report on the errors obtained by comparing in- and out-of-plane displacements calculated from the sensitivity matrix with all its components, and when only the component from the largest contributing of each one of the three interferometers is considered. Divergent illumination is considered in the evaluation of sensitivity vector to measure displacement vector components. This analysis is performed for a flat elastic target which is loaded in the x-direction and after in the z-direction. The technique applied is electronic speckle pattern interferometry.     

Coordination number in liquid argon

Structure of liquids is discussed in terms of Voronoi figures and Delaunay polyhedra. Equations of the respective models and precise experimental data recently available for argon lead to calculated values of the coordination number z and the geometric parameter μ. The relation between z and μ is thus found empirically. Further, calculated values of coordination numbers are compared with those coming from thermal-neutron and X-ray scattering data. A selection among the existing methods of obtaining z from the radial distribution function g(R) is made. The method chosen enables one to find z[g(R)] corresponding to the Voronoi structure.     

Real space and configuration space wave function in the intermediate valence problem

This paper analyses the behavior of intermediate valence compounds, from the point of view of wave functions. They are expressed in a linear combination of cellular orbitals (LCCO) basis for SCF plus correlation introduced in the configuration interaction (CI) scheme, suitable to describe the different spatial extension in real space and the correlation between different fⁿ possibilities. This allows the discussion of the large variety of interesting phenomena which arises from the changes of the f electron configuration space wave functions: fⁿ → fⁿ⁺¹ of from the changes of the electronic charge from atomic-like to the different condensed matter-like boundary conditions. In particular an analysis is included of the correspondence between the actual properties in this type of materials and the amount of atomic-like f character n_f^atomic ?n_f^total in some rare earth and actinide compounds, concluding that the experimental evidence is consistent with a large distortion of the actual f-wave functions from their atomic-like forms.     

The width of the Δ-isobar in chiral soliton models

The strong decay width Δ→πN is estimated using a linear meson-nucleon coupling derived from a constrained quantization of the ω-stabilized version of the Skyrme model. Due to the inherent gauge conditions, this coupling is subleading in N_c and differs from the one proposed by Adkins, Nappi and Witten in the context of soliton models.     

A dynamical theory for the off-shell continuation of the πNt-matrix

A dynamical theory, based on analyticity and dispersion theory, for the half-off-shell continuation of the on-shell πNt-matrix is proposed and developed. The resulting half-shell t-matrix is covariant, unitary, crossing symmetric, and based on a field-theoretic foundation. The dynamical information required to continue half off shell is obtained from field theory and consists of the off-shell amplitudes corresponding to the exchanges of the nucleon in the s- and u-channels and the ? and σ mesons in the t-channel. A coupled system of integral equations is derived for the partial wave half-shell t-matrix, which is truncated at the S- and P-waves and solved numerically. The results are compared with those obtained from various separable models of the πNt-matrix. The half-shell t-matrix is examined for separability and is found to be approximately separable in the P₃₃ and P₃₁ states. The dynamical content of the half-shell t-matrix is further illustrated by modeling the dynamical equation.     

Viscosity: From air to hot nuclei

After a brief review of the history of viscosity from classical to quantal fluids, a discussion of how the shear viscosity η of a finite hot nucleus is calculated directly from the width and energy of the giant dipole resonance (GDR) of the nucleus is given in this paper. The ratio η/s with s being the entropy volume density, is extracted from the experimental systematic of GDR in copper, tin and lead isotopes at finite temperature T. These empirical results are compared with the results predicted by several independent models, as well as with almost model-independent estimations. Based on these results, it is concluded that the ratio η/s in medium and heavy nuclei decreases with increasing T to reach \((1.3 - 4) \times \hbar /(4\pi k_{\mathrm {B}})\) at T = 5 MeV, which is almost the same as that obtained for quark-gluon plasma at T > 170 MeV.     

Diffraction properties of opaque disks outside and inside a laser cavity

Diffraction of symmetrical Laguerre-Gauss TEM_p0 beams incident on an opaque disk known as a stop is considered. The near- and far-field patterns are studied. Thanks to zero-field occluding, conversion from TEM₁₀ beam to dark hollow beam can be achieved with better efficiency than from a TEM₀₀ beam. It is shown that the fundamental mode of a laser cavity including a diaphragm and a stop can be TEM₀₀- or TEM₁₀-like in shape depending on their size. This result is interpreted from the new divergence hierarchy, which characterises the diffracted TEM_p0 beams emerging from the stop.