Absorptionsquerschnitte und Transmissionskoeffizienten für Protonen und Neutronen nach dem optischen Modell

T _l -values and absorption cross sections for protons and neutrons are calculated with optical potentials, which have been fitted to experimental scattering data. Values are given forZ=10, 20, 30, 50, 70, 90, and energies between 0.1 und 25 MeV. For protons we used the local optical potential ofPerey and for neutrons the nonlocal optical potential ofPerey andBuck. The results are compared with those of other optical potentials. In addition it is shown, that the spin-orbit-interaction leads toT _{l j} -values which sometimes differ appreciably depending whetherj equalsl+1/2 orl?1/2.     

On a modified separation method for nuclear potentials

In order to obtain a regular but energy-dependent nuclear potential, the following modification of the separation method ofMoszkowski andScott is used: we replace the nuclear potentialv _c (r) by a long-range potentialv _l (r)=v _c (r) Θ(r? d ₀) together with a short-range energy dependent repulsionv _s =h(k) Θ(r _c ?r), whered ₀ is the separation distance for vanishing energy andr _c is the hard-core radius. The potentialv=v _s +v _l (r) is fitted to theS-wave scattering data and the binding energy of the deuteron.h(k) turns out to be almost proportional to the scattering energyE _rel for energiesE _rel<150 MeV.     

On double polarization asymmetries in the elastic electron-proton scattering

Double polarization asymmetry D_p^(M) for the process of elastic electroweak scattering of the longitudinally polarized electrons by polarized proton target is considered with account of anapole G_1p and electric dipole moment (EDM) G_2p proton form factors. This asymmetry is only due to T-parity violating form factor G_2p, but does not directly depend on it, and having a significant value, allows to confirm the existence of the EDM of the proton.     

Microwave photoresistance of a two-dimensional electron gas in a ballistic microbar

The effect of millimeter microwave radiation on the electron transport of two-dimensional (2D) ballistic microbars formed on the basis of individual GaAs quantum wells at a temperature of T = 4.2 K in magnetic fields B < 0.6 T has been investigated. Differences have been revealed in the magnetic field dependences of the microwave photoresistance of a 2D electron gas in Hall bars with a length L and a width W for the cases L, W > l _p and L, W < l _p , where l _p is the electron mean free path for momentum. The microwave photoresistance in macroscopic bars (L, W > l _p ) is a periodic alternating function of the inverse magnetic field; in microbars (L, W < l _p ), it is a periodic positive function of 1/B. The experimental results indicate that the mechanisms of the microwave photoresistance of a 2D electron gas are different for macroscopic and microscopic bars.     

Solving the relativistic inverse scattering problem with allowance for inelasticity effects on the basis of <Emphasis Type="Italic">N/D</Emphasis> equations and application of the resulting solution to an analysis of nucleon-nucleon interaction

A manifestly Poincaré-invariant approach to solving the inverse scattering problem is developed with allowance for inelasticity effects. The equations of the N/D method are used as dynamical equations in this approach. Two versions of the approach are considered. In the first version (method A), the required equations are constructed on the basis of the maximal-analyticity principle, which constitutes the basis of dynamical S-matrix theory. In formulating the second version of equations (method B), it is assumed that a partial-wave scattering amplitude may develop dynamical singularities that violate the requirement of maximal analyticity. The dynamics of interaction components that violate maximal analyticity is described within the model of a nonlocal separable potential. The method is used to analyze nucleon-nucleon interaction in the ¹S₀ and ³S₁ states. The results obtained by solving the inverse scattering problem for potential functions are compared with the predictions of the one-boson-exchange model.     

Low-energy scattering by singular potentials in the linearized approximation to Calogero's equation

The linearized Calogero equation for tanδ _l (r) has never been applied to singular potentials with a repulsive core. It is shown that the solution can be written in the form of integrals. Even in the low-energy limit rough estimates can at least be obtained. This can be seen from a comparison of scattering-lengths calculated, both exactly and approximately, for negative-power potentials.     

Elastic scattering of electrons by nuclei of half-integer spin and discrete symmetries

Analytical expression is obtained for the right-left asymmetry A _RL ^(3/2) for the process of elastic scattering of the longitudinally polarized electrons by nuclei with spin 3/2, described in the framework of Rarita-Schwinger formalism by invariant form factors of electromagnetic and weak vertex functions. It is shown, that this asymmetry directly depends on the nuclear anapole form factors G ₁ ⁽ⁿ⁾, and structurally is equivalent to asymmetry A _RL ^(1/2), which arises in electron scattering by proton.     

<Emphasis Type="Italic">K</Emphasis><Superscript>±</Superscript><Emphasis Type="Italic">p</Emphasis> elastic scattering in the QCD inspired eikonalized model

Based on our previous study of the QCD inspired eikonalized model for describing vector meson photoproduction, pp, and \(\bar p\) p elastic scattering at high energies, we apply the mode to high energy K ^± p elastic scattering. The total cross section σ _tot(s), differential cross section dσ/dt, the ratio of the real part to imaginary part of the forward scattering amplitude ρ(s), and nuclear slope parameter function β(s) are calculated in the model. Our results show that the theoretical prediction for σ _tot(s) is in a good agreement with the experimental data within error bars of the data. For the other theoretical predictions there are no data to test the predictive power of the model. We need the corresponding experimental data to examinate the validity of our QCD inspired eikonalized model. However, our calculations clearly show that the Odderon exchange in the process makes a significant contribution to the observable of ρ(s) and β(s). Therefore, we may conclude that there is a good opportunity to find the QCD Odderon in the K ^± p elastic scattering at high energies.     

Zur Klassifikation der Zustände des 5-dimensionalen harmonischen Oszillators

A classification of the eigenstates of the harmonic quadrupole oscillator is given within the framework of the Lie-AlgebraB ₂ ofR(5). There still exists the problem of complete classification, since the multiplicityd _v (l ₂) for seniority numbersv≧6 may be greater than one. For these multiplicitiesd _v (l ₂) easily managable recursion formulae are derived and therefore their explicit calculation for arbitraryv andl ₂ is easily possible.     

<Emphasis Type="Italic">nd</Emphasis> scattering at low energies in the two-body potential model

The S-wave phase shift δ(E) for the spin-doublet nd scattering at low energy E is calculated in the framework of the two-body approach. The effective-range-theory formula k cot δ = (1+k²/k ₀ ² )^?1(?1/α+C₂k²+C₄k⁴) is used to obtain approximate analytical results with different potentials. The corresponding coefficients C₂ and C₄ are obtained from our previous calculations of the asymptotic normalization parameter function C _t ² (aκ), where κ is the triton wave number and a is the doublet nd scattering length. The model reasonably describes δ(E), the results being quite sensitive to the choice of the effective nd potential.     

Rayleigh-Brillouin scattering in chalcogenide glasses of the Ge-As-S system

Rayleigh-Brillouin scattering in chalcogenide glasses of the Ge-As-S system was investigated for the (As₂S₃)_100?x (GeS₂)_x (x=0–100) series. The longitudinal hypersonic velocities, adiabatic elasto-optical constants (p ₁₂)_ad at frequencies of about 15 GHz, and Landau–Placzek ratios (R _LP) were determined.     

Compositions,Random Sums and Continued Random Fractions of Poisson and Fractional Poisson Processes

In this paper we consider the relation between random sums and compositions of different processes. In particular, for independent Poisson processes N _α (t), N _β (t), t>0, we have that \(N_{\alpha}(N_{\beta}(t)) \stackrel{\mathrm{d}}{=} \sum_{j=1}^{N_{\beta}(t)} X_{j}\), where the X _j s are Poisson random variables. We present a series of similar cases, where the outer process is Poisson with different inner processes. We highlight generalisations of these results where the external process is infinitely divisible. A section of the paper concerns compositions of the form \(N_{\alpha}(\tau_{k}^{\nu})\), ν∈(0,1], where \(\tau_{k}^{\nu}\) is the inverse of the fractional Poisson process, and we show how these compositions can be represented as random sums. Furthermore we study compositions of the form Θ(N(t)), t>0, which can be represented as random products. The last section is devoted to studying continued fractions of Cauchy random variables with a Poisson number of levels. We evaluate the exact distribution and derive the scale parameter in terms of ratios of Fibonacci numbers.     

Heat capacity and thermopower coefficient of the carbon preform of sapele wood

This paper reports on measurements of the heat capacity at constant pressure C _p in the 80–300-K temperature interval and the thermopower coefficient S at 5–300 K of the carbon preform of sapele wood, which was prepared at the carbonization temperature of 1000°C. Measurements of C _p (T), our previous data on the phonon thermal conductivity, and literature information on the sound velocity have been used to calculate the phonon mean free path l(T) for this material. It has been shown that within the temperature interval 200–300 K, l is constant and equal to 11 Å, a figure matching the size of the nanocrystallites (“graphite fragments”) making up the carbon framework of the sapele carbon preform. The high-temperature parts of S(T) have been found to follow a linear course characteristic of diffusive thermopower for the degenerate state of charge carriers, with only one type of charge carriers present. The anisotropy of the thermopower coefficient has been estimated.     

Limit of Fluctuations of Solutions of Wigner Equation

We consider fluctuations of the solution W _ε (t, x, k) of the Wigner equation which describes energy evolution of a solution of the Schrödinger equation with a random white noise in time potential. The expectation of W _ε (t, x, k) converges as ε → 0 to \({\bar{W}(t,x,k)}\) which satisfies the radiative transport equation. We prove that when the initial data is singular in the x variable, that is, W _ε (0, x, k) = δ(x)f(k) and \({f\in {\mathcal{S}}(\mathbb{R}^d)}\), then the laws of the rescaled fluctuation \({Z_\varepsilon(t):=\varepsilon^{-1/2}[W_\varepsilon(t,x,k)-\bar{W}(t,x,k)]}\) converge, as ε → 0+, to the solution of the same radiative transport equation but with a random initial data. This complements the result of [6], where the limit of the covariance function has been considered.     

Scattering and bound state solutions for a class of nonlocal potentials (s-wave)

Thes-wave scattering solution is discussed for a class of nonlocal (non-separable) potentials. Existence and uniqueness theorems are given and the analyticity domain in thek-variable (k = wave number in the C.M. system) is determined. Furthermore it is proved that solutions of the bound state problem exist and a discussion of the square-integrable solutions, which can occur for a real positive value of the energy, is given. In this last case the scattering solution also exists but it is not unique. Finally theS-matrix is introduced and it is proved that it is unambigously defined even if the scattering solution is not unique.     

A comparison on absorption coefficients for secondary electron emission obtained from two different formulas

In this work, the absorption coefficients for secondary electron emißsion, α and β, that appeared respectively in the two different formulas, \(\delta (E_p ) = k\int_0^\infty {\left( {\frac{{dE}}{{dz}}} \right)E_p \exp ( - \alpha z)dz} \) and \(\delta (E_p ) = k\int_0^\infty {\left( {\frac{{dE}}{{dz}}} \right)E_p \exp ( - \alpha z)dz} \), were derived with a standard deviation rate analysis method based on a Monte Carlo simulated secondary electron yield, δ(E_p). Both the energy dissipation in depth for primary electrons, \(\left( {dE/dz} \right)E_p \), and the depth distribution for the number of secondary electrons including cascade electrons, n(z, E_p), were obtained by the same Monte Carlo method, in which the discrete inelastic scattering model was employed. The calculation results for Cu and Mg show that the n(z, E_p)-curve differs significantly from the \(\left( {dE/dz} \right)E_p \)-curve, and thus as well as a from b, for varied incidence angles (0°–80°) and low-energy primary electrons (up to 3 keV). The absorption coefficient β-values derived from a realistic depth distribution of cascade secondary electrons, n(z, E_p), then describe more accurately the nature of attenuation behavior of secondary electrons than a-values that associated with the approximate formula.     

On resonance and nonresonance interactions between electrons and spatially periodic clusters

The effects of resonance and nonresonance interactions between electrons and spherical structures with spatial periodicity in the radial direction (clusters) were studied. It was shown analytically and by numerical calculations that the δ _l phase shift of the wave function, which arises in resonance electron scattering by such a periodic structure of a fairly large radius r₀, was not small even at a small ratio between the U₀ amplitude of the periodic potential and scattered electron energy E(ε₀=U₀/E?1) and equaled |δ _l |=π/4 (modulo π). This phase shift corresponded to the limiting case of a large Born parameter for the cluster, ξ₀=r₀U₀/?v?1, where v is the characteristic velocity of the electron. The effect of nonresonance electron scattering by a periodic potential whose spatial period was incommensurate with the Brillouin wavelength of the scattered electron was considered analytically. The effect of nonresonance scattering was shown to be of a higher order in the ε₀?1 parameter than resonance scattering. The cross section of electron scattering by a cluster was calculated, which allowed the conductivity of a medium containing clusters to be estimated.     

Die Winkelverteilung der Protonen der Reaktion B11 (d,p 0,1 B12 im Energiebereich von 0,7 ... 1,7 MeV

Angular distributions of the protons in this low-energy region have been measured by only few groups for obvious reasons: the energy of the emitted protons is very low. It will be shown that by using non-supported targets of B¹¹ with very little oxygen contamination the angular distributions can be obtained between approximately 5 and 165 degrees (cm.,p ₀-group) and between 20 and 165 degrees (cm.,p ₁) with high accuracy. The Butler-fits givel=1,r _B =5.2 fm forp ₀ andl=1,r _B =4.7 fm forp ₁. All angular distributions seem to exhibit strong participation of non-stripping mechanism.