Two-body scattering without angular-momentum decomposition: Fully off-shell T-matrices

Two-body scattering is studied by solving the Lippmann-Schwinger equation in momentum space without angular-momentum decomposition for a local short-range interaction plus Coulomb. The screening and renormalization approach is employed to treat the Coulomb interaction. Benchmark calculations are performed by comparing our procedure with a configuration space calculation, using the standard partial-wave decomposition, for ¹²C - ¹⁰Be elastic scattering. The fully off-shell T -matrices are also calculated for the final goal of studying the three-body scattering by solving Faddeev/AGS equations.     

On-shell methods in perturbative QCD

We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider.     

On-shell baryon-baryon semi-local duality relations

Zeitschrift für Physik C Particles and Fields - Parent-parent on-shell semi-local duality relations betweens − andu-channel resonances in πN amplitudes are studied. The duality...     

On-shell improved lattice gauge theories

By means of a spectrum conserving transformation, we show that one of the 3 coefficients in Symanzik's improved action can be chosen freely, if only spectral quantities (masses of stable particles, heavy quark potential etc.) are to be improved. In perturbation theory, the other 2 coefficients are however completely determined and their values are obtained to lowest order.Heisenberg foundation fellow     

Low-order light scattering in multiple scattering disperse media

Light scattering has been investigated in systems in which both single and higher order scattering occur. The Monte Carlo simulation technique for studying light scattering in randomly inhomogeneous, strongly scattering disperse media was employed. The reliability of the data obtained has been checked by comparing the results of the computer simulation with analytical calculations for the intensity of doubly scattered light. The first several scattering orders have been analyzed for different geometries of the optical experiment. It has been shown, in particular, that, depending on the detector aperture, the contribution of multiple scattering can vary by almost an order of magnitude.

     

Off-energy-shell effects in multiple scattering

The elastic scattering from a two-body bound system is investigated in order to determine what information about the nuclear structure and the projectile-nucleon interaction may be obtained at intermediate energies. Emphasis is placed on the kinematics and the importance of properly treating the overlapping potential region. The kinematics of the “fixed scatterer” and “impulse” approximations result in differences which are still significant at intermediate energies. As far as scattering information is concerned, the overlapping potential region is the interesting one since it requires explicit knowledge of the interaction. Our results suggest that for nucleon scattering at intermediate energies the corrections due to properly taking into account off-energy-shell effects are likely to be comparable with the contributions due to the short-range two-body correlations. The relevance of the above results to various models currently employed in analyzing high- and intermediate-energy nuclear scattering is also discussed.     

On multiple small-angle scattering

An analytical approach has been taken for analyzing the multiple scattering effects in small angle scattering (SAS) from both monodisperse and polydisperse systems. Two limiting regions, viz the Guinier region and the Porod region have been studied. A modified form of Guinier law has been deduced for the scattered intensity distribution in the region of small wave vector transfer, q. In the regionq(=|q|)→∞, it is shown that the effect of multiple scattering does not alter the Porod (q ⁻⁴) law. In the case of polydisperse systems, a correlation has been established between the size distribution of the inhomogeneities and the experimentally extractable parameters. The validity of the formalism has been examined by reinterpretation of the multiple SANS data (Hardman-Rhyne and Berk 1985) on polydisperse Al₂O₃ samples. This formalism is useful in characterizing the inhomogeneities from SAS measurements, particularly when thick samples are used.     

Theory of multiple scattering

Consideration is given to problems of obtaining exact and approximate solutions of kinetic equations in the multiple scattering problem. For cross sections which are rational functions of χ² (χ = 2sin(δ/2), δ is the scattering angle) exact solutions are obtained as a series in terms of Legendre polynomials. The limits of validity of the kinetic equation for the distribution function in terms of the variable q = 2sin(?/2) are refined [1] and the solutions of this equation are compared with the exact solutions of the Rutherford and Mott cross sections. The problem of convergence of approximate solutions in the form of a series in terms of Legendre polynomials and a series in powers of 1/B is solved. These approximations are obtained and their limits of validity are determined.     

On-shell renormalization for particles with mixing

The subject of our discussion are the on mass-shell renormalization conditions in any order of the perturbative calculations with particle mixing. The imaginary parts of the propagators which are connected with the particle decay width are taken into account. The phenomenological LSZ relation for unstable particles is discussed. The on-shell renormalization condition for the mixing of particles with spins 0+0, 0+1. and 1+1 is presented.     

Inelastic shadowing effects in multiple scattering

The projectile-nucleon scattering amplitudes used as input into multiple scattering theories of projectile-nucleus scattering naturally include the effects of coupling to inelastic (i.e., production) channels. We employ a multichannel separable potential to describe the projectile-nucleon interaction and show that within the fixed nucleon framework we can obtain the nuclear elastic scattering amplitude. This includes terms outside the conventional formalisms, corresponding to intermediate propagation in the inelastic channels both above and below inelastic threshold. We refer to this as inelastic shadowing. In a two-channel approximation, we show that knowledge of the projectile-nucleon elastic scattering phase shifts plus specification of the inelastic threshold energy are sufficient to determine the off-shell coupled-channel transition matrix, implying that the nuclear amplitude can be calculated within this model without any detailed information about the inelastic channels. We study this solution quantitatively for some model problems and for pion scattering, with the general result that inelastic shadowing can be significant whenever the elementary interaction has important channel coupling. For pion scattering in the energy regime characterized by strongly absorptive resonances, we find, for example, that the effect of inelastic shadowing is much more important than that due to two-nucleon correlations.     

On-shell and conformal N = 4 supergravity in superspace

We discuss the superspace geometries which are necessary to describe on-shell O(4) and SU(4) supergravity. The relation of central charge field strengths to physical spin-zero fields is exhibited and a “new” O(4) theory is shown to exist. The version of SU(4) supergravity which uses an antisymmetric tensor gauge field is found to require modifications of ordinary superspace. Finally the Poincaré supergeometry which admits the conformal N = 4 supermultiplet is constructed. It is shown that consistency of the Bianchi identities implies the existence of dimension zero auxiliary fields which are components of a non-linear multiplet.     

LIDAR multiple scattering from clouds

Multiple-scattering LIDAR return calculations obtained by seven different models for the same specified numerical experiment are compared. This work results from an international joint effort stimulated by the workshop group called MUSCLE for MUltiple SCattering Lidar Experiments. The models include approximations to the radiative-transfer theory, Monte-Carlo calculations, a stochastic model of the process of multiple scattering, and an extension of Mie theory for particles illuminated by direct and scattered light. The model solutions are similar in form but differ by up to a factor of 5 in the strength of the multiple-scattering contributions. Various reasons for the observed differences are explored and their practical significance is discussed.     

Gamma holography from multiple scattering

Since the introduction of heterodyne methods for synchrotron radiation (Cousesement et al. in Phys. Rev. B 54:16003, 1996; Callens et al. in Phys. Rev. 67:104423, 2003) one observes interferences between two scattering amplitudes; the scattering amplitude of resonant nuclei in a reference sample and the scattering amplitude of nuclei in the sample under investigation. Theses interferences can easily been observed as resonances in velocity spectra when one uses a time integrated method. They can also been observed as quantum beats, when one would use the time differential method. For both methods it is important that one uses a reference sample and therefore both methods disserved the name “heterodyne methods.” As theses interferences are a product of two scattering amplitudes, the amplitude of a wave scattered form the investigated sample can be known with its phase. But it is assumed that the reference wave is known in advance by a proper choice of the reference sample. At first sight it is very likely that multiple scattering would add more complexity but in this paper it is claimed that on the contrary it provide a bonus, especially for single crystals. It provokes only a line broadening and a line shift of the resonances in the velocity spectra (or a change in the damping and frequency of the quantum beats when the time spectra are registered). Moreover these changes in the line shapes can easily be measured and they provide all the information needed to reconstruct a 3-D picture of the atomic arrangement of resonant nuclei and moreover they distinguish between different hyperfine sites. The method may be more practical for measurements on synchrotron radiation but it does also apply to velocity spectra obtained from resonant scattering with strong sources. The use of radioactive sources suffer from the disadvantage of poorer statistics or much longer accumulation times but they enjoy the advantage to be table-top and at-home experiments. As strong sources are now commercially available this possibility to measure not only the hyperfine fields but also the corresponding crystal structure could give a renewed impetus to the investigations with Moessbauer spectrometry, with “at home and table top” instrumentation.     

On multiple Compton scattering in plasma clouds

Inverse Compton scattering of low energy photons in a nonrelativistic electron gas is considered. The angle dependence in the Thomson cross section is neglected and spatial and energy transport are separated in a multiple scattering development of the emerging spectrum. The energy transport is determined by a Green function G which may be obtained from the single scattering spectrum for small optical depth or from the Kompaneets equation in the optically thick medium (τ ? 1). The electron cloud is assumed to be spherical and homogeneous with constant temperature $\text{?}{}_{\mathrm{e}}\text{=}\text{kT}{}_{\mathrm{e}}\text{m}{}_{\mathrm{e}}\text{c}{}^2$. Photon escape probabilities P_N from the cloud after N scatterings are calculated from a random flight problem with absorbing walls and alternative methods are mentioned and compared in the limit of large optical depth.     

Evanescent modes in a multiple scattering factorization

We discuss differences between the exactS-matrix for scattering on serial structures and a known factorized expression constructed of single-elementS-matrices. As an illustration, we use an exactly solvable model of a quantum wire with two point impurities. The work has been partially supported by the Grants AS No. 148409 and GA CR No. 202-93-1314.     

Quantum signatures in laser-driven relativistic multiple scattering

The dynamics of an electronic Dirac wave packet evolving under the influence of an ultraintense laser pulse and an ensemble of highly charged ions is investigated numerically. Special emphasis is placed on the evolution of quantum signatures from single to multiple scattering events. We quantify the occurrence of quantum relativistic interference fringes in various situations and stress their significance in multiple-particle systems, even in the relativistic range of laser-matter interaction.