Analysis of the elastic scattering of 12C on 11B in the framework of the molecular wave function method

The elastic scattering of ¹²C on ¹¹B has been analyzed in the framework of the molecular wave function method. It turns out that a coherent sum of the direct and transfer amplitudes gives better agreement with the experimental data than an incoherent sum. Non-adiabatic and Coriolis coupling terms seem to be of little importance in this particular case.     

Multiple diffractive analysis of elastic and inelastic scattering by 1 GeV protons on 12C, 58Ni,and 208Pb

Recent elastic and inelastic scattering experiments of 1 GeV protons on ¹²C, ⁵⁸Ni, and ²⁰⁸Pb have been analyzed using multiple diffractive scattering theory.Elastic angular distributions have been calculated, including pair correlations in many-particle densities. There is evidence from the Ni and Pb data for the presence of correlations, but some evaluated correlation corrections do not produce detailed agreement.It is shown that the Glauber series for coherent inelastic scattering can be approximately summed to yield an eikonal form of the DWIA. In particular the smaller angle parts of the inelastic distributions are well described in this approximation.The expression for the summed incoherent inelastic cross section is considered as a sum rule. It is found that for ¹²C the excitation of the three lowest excited states exhaust ? 25 % of the sum rule up to ?t ? 1 fm^?2. For larger t quasi-elastic knock-out largely exhausts the sum rule.     

Noneikonal effects in spin-dependent proton-nucleus interactions

Simple expressions are derived for the non-eikonal corrections to the Glauber diffraction approximation for the proton-nucleus scattering amplitudes, with the spin dependence of the proton-nucleon amplitudes taken into account. As an example, we study the numerical importance of these corrections for elastic p ⁵⁸Ni scattering at 800 MeV.     

Dispersion corrections to the forward Rayleigh scattering amplitudes around the L‐shell of tantalum and lead

Dispersion corrections to the forward Rayleigh scattering amplitudes of tantalum and lead in the photon energy range 6.4–24.14 keV were determined by a numerical evaluation of the dispersion integral that relates them through the optical theorem to the photoelectric cross‐sections. The photoelectric cross‐sections were extracted by subtracting the coherent and incoherent scattering contribution from the measured total attenuation cross‐section, using a high‐resolution, high‐purity germanium detector in a narrow‐beam good geometry setup. The real part of the dispersion correction to which the relativistic corrections calculated by Kissel and Pratt (S‐matrix approach) or Creagh and McAuley (multipole corrections) have been included are in better agreement with the available theoretical values than those values to which the relativistic corrections calculated by Cromer and Liberman (dipole corrections) are added. Copyright © 2006 John Wiley & Sons, Ltd.     

Photon interaction cross-sections and anomalous scattering factors of Cu and Ag

Total attenuation cross sections of copper and silver have been measured in the energy range 5 to 85 keV in a narrow beam good geometry set up using X- andγ-rays emitted from radio isotopes, by employing a high resolution hyper pure germanium detector. From the measured values, the photoeffect cross-sections have been derived by subtracting a small contribution of the sum of the theoretical coherent and incoherent scattering cross sections. The photoeffect cross-sections so obtained are found to be in better agreement with the unrenormalized values of Scofield [10]. These photoeffect cross-sections have been used to evaluate the dispersion corrections (also called anomalous scattering factors)f ⁺ andf″ for the forward Rayleigh scattering amplitude by a numerical evaluation of the dispersion integral that relates them at the energies at which the cross-sections have been measured. To thef ⁺ values so obtained, the relativistic corrections proposed by different investigators are included separately and the valuesf′ so obtained are compared with the available data and discussed. Possible conclusions are drawn from the present study.     

Regge Models and Dispersion Relations for Partial Waves

The asymptotic behaviour of partial wave amplitudes is calculated supposing various Regge models for the total scattering amplitude A(s, t, u). The high energy partial wave behaviour obtained is combined with the validity of partial wave dispersion relations. It is shown that consistency of these assumptions can only be achieved by demanding. 1) a definite asymptotic behaviour of the discontinuity of the left hand cut of partial wave amplitudes. 2) the validity of partial wave sum rules of similar kind as the well-known finite energy sum rules for the total amplitude. All steps of the derivation shall first be demonstrated for elastic scattering of identical scalar particles. Then within the helicity formalism the results are generalized for particles with arbitrary spin and different masses. Finally the question is studied whether the sum rules can be employed to determine unknown CDD-pole parameters in an N/D approach for the I = J = 1/2 state in πN scattering. It is shown that the sum rules of highest order are able to do that.     

Scattering of low-energy atoms by metallic surfaces

The problem of a neutral low-energy atom impinging on a well-defined metallic surface is approached from first principles. The solid and its potential energy of interaction with the incident atom is treated in the most general way, but under the following assumptions: (a) the conduction electrons interact adiabatically with the lattice ions and the gas atom; (b) no chemical reactions occur; (c) the one-phonon approximation is valid. The scattering amplitudes for surface and bulk mode excitations are obtained in terms of the dynamical properties of the metallic surface. Direct collisions of the incident atoms with the lattice ions are shown to give a negligible contribution to the scattering. The most important contribution comes from the interaction of the gas atom with the surface conduction electrons; the excitation of lattice vibrational modes occurs through the electron-phonon term of the Hamiltonian. The general expressions for the scattering amplitudes obtained show that the scattering is incoherent. With further assumptions one obtains a separation of the scattering amplitude into a coherent and incoherent part.     

A Mössbauer Effect Powder Diffractometer

An automated, high-sensitivity Mössbauer powder diffractometer is described, and its performance demonstrated with a bcc ⁵⁷Fe foil sample. Useful diffraction patterns are acquired in about 10 hours. The incoherent and coherent parts of the scattering are readily identified. Both are affected by thickness distortion, but the incoherent part is affected more strongly.     

Time-dependent photon correlations for incoherently pumped quantum dot strongly coupled to the cavity mode

The time dependence of correlations between the photons emitted from a microcavity with an embedded quantum dot under incoherent pumping is studied theoretically. Analytic expressions for the second-order correlation function g ⁽²⁾(t) are presented in strong and weak coupling regimes. The qualitative difference between the incoherent and coherent pumping schemes in the strong coupling case is revealed: under incoherent pumping, the correlation function demonstrates pronounced Rabi oscillations, but in the resonant pumping case, these oscillations are suppressed. At high incoherent pumping, the correlations decay monoexponentially. The decay time nonmonotonically depends on the pumping value and has a maximum corresponding to the self-quenching transition.     

X-ray scattering from a randomly rough surface

Abstract

On the basis of the method of reduced Rayleigh equations we present a simple and reciprocal theory of the coherent and incoherent scattering of x-rays from one- and two-dimensional randomly rough surfaces, that appears to be free from the limitations of earlier theories of such scattering based on the Born and distorted-wave Born approximations. In our approach, the reduced Rayleigh equation for the scattering amplitude(s) is solved perturbatively, with the small parameter of the theory η(ω) = 1 - ε(ω), where ε(ω) is the dielectric function of the scattering medium. The magnitude of η(ω) for x-rays is in the range from 10^?6 to 10^?3, depending on the wavelength of the x-rays. The contributions to the mean differential reflection coefficient from the coherent and incoherent components of the scattered x-rays are calculated through terms of second order in η(ω). The resulting expressions are valid to all orders in the surface profile function. The results for the incoherent scattering display a Yoneda peak when the scattering angle equals the critical angle for total internal reflection from the vacuum-scattering medium interface for a fixed angle of incidence, and when the angle of incidence equals the critical angle for total internal reflection for a fixed scattering angle. The approach used here may also be useful in theoretical studies of the scattering of electromagnetic waves from randomly rough dielectric-dielectric interfaces, when the difference between the dielectric constants on the two sides of the interface is small.     

Nuclear resonant scattering using synchrotron radiation

A one-dimensional quantum model for nuclear resonant scattering using synchrotron radiation has been developed. This model gives a clear physical interpretation of the most prominent features of the coherent forward scattering process namely, the “speed-up” and “dynamical beat” effects. The form of the solution, for the time-dependent forward scattered intensity of the resonant radiation from the resonant medium after synchrotron radiation excitation, is a finite series. This unique solution can be interpreted in terms of a summation over all multiple forward scattering paths the radiation takes in reaching the detector. The resonant medium is represented by a linear chain of N effective resonant nuclei. The analysis starts from a coupled set of quantum mechanical equations for the relevant amplitudes in frequency space. Transformation to the time domain gives an analytical expression for the forward scattered intensity. The contribution of every order of the multiple scattering processes from the N effective nuclei appears naturally. The expression gives a clear physical understanding of all relevant aspects of resonant forward nuclear scattering. Furthermore, the present formalism allows the consideration of incoherent processes. This permits the study of processes in which there is gamma emission with recoil or emission of internal-conversion electrons. This revised version was published online in August 2006 with corrections to the Cover Date.     

Higher multipole polarizabilities of hadrons from compton scattering amplitudes

Starting with partial wave projections of the Compton scattering invariant amplitudes free of kinematical singularities or zeros, generalized electric and magnetic multipole polarizabilities of spin-0 and $\text{spin}\text{-}\text{1}\text{2}$ hadrons are introduced as threshold limits of the non-Born parts of the corresponding electric and magnetic Compton multipoles. These objects, which enter the higher low-energy theorems for elastic γ-hadron scattering, are shown to be acceptable quantum field theoretical generalizations of the usual static multipolar polarizabilities encountered in classical electrodynamics or non-relativistic quantum mechanics. Using the analyticity properties of the amplitudes, sum rules for the generalized electric and magnetic quadrupole polarizabilities of the proton and the pions are written down and evaluated numerically within the two-particle unitarity approximation.     

Discording power of Hamiltonian interactions

In this paper, we report the coherent scattering cross sections of some lanthanides at low momentum transfer in four angular ranges of (0°?4°), (0°?6°), (0°?8°) and for ²⁴¹Am (59.54 keV) and ¹³⁷Cs (661.6 keV) gamma rays. The coherent scattering cross sections were derived by subtracting the small contribution of the corresponding angle integrated incoherent scattering cross sections from the experimentally measured total (coherent + incoherent) scattering cross sections for the elements and energies of interest. The coherent scattering cross sections were found to agree with the corresponding theoretical cross sections within the range of experimental errors. The theoretical coherent scattering cross sections were computed by numerically integrating the S-matrix data of the elements in the angular ranges of interest. The incoherent scattering cross sections were based on the compilations which make use of the non-relativistic Hartree-Fock (NRHF) model for the atomic charge distribution.     

Dispersion-relation analysis of K+p scattering below 2 GeV/c

We have obtained K⁺p scattering amplitudes that fit a large body of data below 2 GeV/c, satisfy phenomenological partial-wave backward dispersion relations, and are consistent with forward dispersion relations for the spin-non-flip amplitude, and forward dispersion-relation sum rules for the K⁺p P-wave scattering lengths. This has been achieved by firstly making an energy-dependent phase-shift analysis of 1 660 pieces of K⁺p data below 2 GeV/c, using parameterised partial-wave dispersion relations, with the additional constraints of forward dispersion relations and P-wave scattering lengths obtained from forward dispersion-relation sum rules, and then checking the resulting solutions for consistency with backward K⁺p dispersion relations.     

Electrodynamics of a Scalar Particle in a Plane Electromagnetic Wave Field

In the present paper, compact expressions are derived for the probability of photon emission by a scalar particle and for the probability of creating pairs of scalar particles in an arbitrary plane electromagnetic wave field. Based on these general expressions, the amplitude of elastic scattering of a scalar particle and the amplitude of elastic scattering of a photon are derived by the method of dispersion relations (in the first-order approximation for the fine-structure constant ₀ = e ²/4). The real components of these amplitudes determine the radiative corrections for particle masses in the examined fields. Some particular cases of the plane wave field are examined. In particular, the above-indicated amplitudes in the external electromagnetic field being a superposition of a constant crossed field and a plane elliptically polarized electromagnetic wave propagating along the direction orthogonal to the magnetic and electric components of the constant crossed field are investigated. The amplitude of elastic scattering of a scalar particle in an arbitrary plane electromagnetic wave field is also obtained by direct calculations of the corresponding mass operator of the scalar particle in this field.     

The incoherent scattering function and related correlation functions in hard sphere fluids at short times

For a classical fluid of hard spheres and hard disks exact expressions for all densities and wave vectors are derived for the coefficients oft ⁿ in the short-time expansion of the incoherent intermediate scattering function (n = 0, 1,..., 4) and the velocity correlation function (n=0,1,2). Similarly, we obtain the coefficient of the leading term in the short-time behavior of the cumulants of the displacements. Furthermore,S(k, ) has a high-frequency tail ^–4, characteristic for the hard-sphere fluid, which leads to a modification of the standard sum rules. We present estimates for the frequency range, in which this tail may be observed in neutron scattering off noble gases. The results are also compared with Enskog's theory and molecular dynamics calculations.     

OPE analysis of the nucleon scattering tensor: a review including weak interactions and finite mass effects

We perform a systematic operator product expansion of the most general form of the nucleon scattering tensorW _μν including electro-magnetic and weak interaction processes. Finite quark masses are taken into account and a number of higher-twist corrections are included. In this way we derive relations between the lowest moments of all 14 structure functions and matrix elements of local operators. Besides reproducing well-known results, new sum rules for parity-violating polarized structure functions and new mass correction terms are obtained.     

Nature of charge transport in quantum-cascade lasers

The first global quantum simulation of semiconductor-based quantum-cascade lasers is presented. Our three-dimensional approach allows us to study in a purely microscopic way the current-voltage characteristics of state-of-the-art unipolar nanostructures, and therefore to answer the long-standing controversial question: Is charge transport in quantum-cascade lasers mainly coherent or incoherent? Our analysis shows that (i) quantum corrections to the semiclassical scenario are minor and (ii) inclusion of carrier-phonon and carrier-carrier scattering gives excellent agreement with experimental results.     

Summation of partial waves for large-angle scattering

For large-angle elastic scattering different methods of summing partial wave amplitudes are investigated for their accuracy and simplicity of computation. It is found that among the approximations considered, the method of expanding the T-matrix in terms of the weighted orthogonal polynomials proposed by Brysk is the most accurate way of calculating the scattering amplitude in the backward direction. If the two-particle interaction is assumed to be a Yukawa potential, then the lth partial sum of the T-matrix with the weighted polynomials can be expressed as the lth partial sum with the Legendre polynomials and a correction term which depends on the phase shift for the lth partial wave.     

Determination of coupling constants from superconvergence sum rules in vector meson — Vector meson scattering

Dynamical relations between masses and coupling constants have been studied using the superconvergent sum rule technique in vector meson — vector meson scattering. Unessential complications due to the spin have been removed by defining a set of 25 KSF invariant amplitudes. Commonly accepted analyticity properties and asymptotics estimated arguing along the line of unitarity then lead to superconvergent sum rules for three amplitudes. Their saturation by one-intermediate-particle contributions in the processesωρ→ ωρ, ωB→ωB andωA ₁→ωA ₁ results in a system of nine coupled equations which have been approximately solved for coupling constants and aρ-ω-B- A ₁ mass sum rule.