On complete sets of polarization observables

A new criterion is developed which provides a check as to whether a chosen set of polarization observables is complete with respect to the determination of all independent T-matrix elements of a reaction of the type a + b → c + d + … As an illustrative example, this criterion is applied to the longitudinal observables of deuteron electrodisintegration.     

Derivation of extended boundary condition method from general definition of -matrix elements and Lippman–Schwinger equation for transition operator

Waterman's surface-integral expressions for the T-matrix elements are derived on the basis of the quantum-mechanical potential scattering approach in electromagnetic scattering problem. We use general definition of the elements of the T-matrix as the matrix elements of the dyadic transition operator and Lippman–Schwinger volume integral equation for the dyadic transition operator. The interrelations of the Q- and Waterman's T-matrix with the transition operator are shown.     

Relations between polarization observables and complete sets for deuteron photodisintegration

The polarization observables for deuteron photodisintegration are given as Hermitean forms of theT-matrix elementst _i . By inversion we are able to express a given productt _i ^* t _j in terms of polarization observables. This allows (i) to derive linear relations between observables for unpolarized, circularly and linearly polarized photons, (ii) to construct explicitly complete sets of polarization observables, and (iii) to derive quadratic relations between observables.Supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

General formulae for polarization observables in two-body break-up of deuteron photodisintegration

The formal expressions of all possible polarization observables ind(,N)N with polarized photons and oriented deuterons are derived in terms of thet-matrix elements. Furthermore, using the multipole expansion of thet-matrix, all observables are expanded in terms of Legendre polynomials or associated functions, the coefficients of which are given as bilinear forms of the multipole moments and allow a model independent analysis of experimental data.Supported by the Deutsche Forschungsgemeinschaft (SFB 201)     

Complete Sets of Polarization Observables in Electromagnetic Deuteron Breakup

 For deuteron photo- and electrodisintegration the selection of complete sets of polarization observables is discussed in detail by applying a recently developed new criterion for the check of completeness of a chosen set of observables. The question of ambiguities and their resolution by considering additional observables is discussed for a numerical example, for which the role of experimental uncertainties is also investigated. Furthermore, by inversion of the expressions of the observables as Hermitean forms in the t-matrix elements a bilinear term of the form can be given as a complex linear form in the observables from which an explicit solution for in terms of observables can be obtained. These can also be used to select sets of observables for the explicit representation of the t-matrix. Received May 15, 1999; accepted for publication August 30, 1999     

General multipole expansion of polarization observables in deuteron electrodisintegration

Formal expressions are derived for the multipole expansion of the structure functions of a general polarization observable of exclusive electrodisintegration of the deuteron using a longitudinally polarized beam and/or an oriented target. This allows one to exhibit explicitly the angular dependence of the structure functions by expanding them in terms of the small rotation matrices d ^j _m'm(θ), whose coefficients are given in terms of the electromagnetic multipole matrix elements. Furthermore, explicit expressions for the coefficients of the angular distributions of the differential cross-section including multipoles up to L _max = 3 are listed in tabular form. Received: 19 November 2002 / Accepted: 7 May 2002     

Modified T-matrix formulation for multiple scattering of acoustic waves

Abstract

In studying the multiple scattering of acoustic waves by distributed discrete scatterers, the ‘two-exterior’ T-matrix or the modified T-matrix is needed. In this paper, the modified T-matrix formulae for a scatterer of arbitrary shape are derived, based on Huygen's principle and the method of optimal truncation (MOOT), respectively. Analytical expressions are given for the modified T-matrix elements of a spheroid in the low-frequency limit. The agreement with the existing results is shown to be exact to the given order of ka. It is also shown that the results based on Huygen's principle are merely the special cases of those based on MOOT.     

Elastic <Emphasis Type="Italic">Nd</Emphasis> scattering at intermediate energies as a tool for probing the short-range deuteron structure

A calculation of the deuteron polarization observables A _y ^d , A _yy , A _xx , A _xz and the differential cross section for elastic nucleon-deuteron scattering at incident deuteron energies 270 and 880 MeV in lab is presented. A comparison of the calculations with two different deuteron wave functions derived from the Bonn-CD NN-potential model and the dressed-quark-bag model is carried out. A model-independent approach, based on an optical-potential framework, is used in which a nucleon-nucleon T matrix is assumed to be local and taken on the energy shell, but still depends on the internal nucleon momentum in a deuteron. The text was submitted by the author in English.     

Polarization observables in elastic electron deuteron scattering including parity- and time-reversal-violating contributions

The general formalism for polarization observables in elastic electron deuteron scattering is extended to incorporate parity- and time-reversal-violating contributions. Parity-violating effects arise from the interference of γ and Z exchange as well as from the hadronic sector via a small parity-violating component in the deuteron. In addition we have allowed for time-reversal-invariance-violating contributions in the hadronic sector. Formal expressions for the additional structure functions are derived, and their decomposition into the various multipole contributions are given explicitly. Received: 19 December 2000 / Accepted: 14 February 2001     

A spin-isospin-dependent 3N scattering formalism in a 3D Faddeev scheme

We introduce a spin-isospin-dependent three-dimensional approach for the formulation of the three-nucleon scattering. The Faddeev equation is expressed in terms of vector Jacobi momenta and spin-isospin quantum numbers of each nucleon. Our formalism is based on connecting the transition amplitude T to momentum-helicity representations of the two-body t -matrix and the deuteron wave function. Finally, the expressions for nucleon-deuteron elastic scattering and full breakup process amplitudes are presented.     

The dependence of the photodisintegration cross section on the off-shell T-matrix

Nucleon-nucleon scattering phase shifts determine the diagonal element of the transition matrix. The off-diagonal elements are not completely arbitrary but have conditions imposed on them by the range and the tail of the potential. Electromagnetic interaction can also be used to place restrictions on the off-diagonal elements. We find that the cross section of the deuteron photodisintegration is sensitive to the off-shell transition matrix. The integrated cross section can be varied by as much as 30 % or more, and the matrix element for the El transition by a factor of 2. While the matrix element for the photodisintegration depends on the off-shell elements of the T-matrix, it cannot be used to discriminate between alternative off-shell T-matrices. We have constructed classes of different off-shell T-matrices, which produce identical photo-disintegration cross sections and other two-body scattering and bound-state properties.     

Relativistically invariant analysis of -isobar production in deuteron electrodisintegration: : General analysis of polarization effects

The differential cross-section and the polarization observables for Δ-isobar production in the deuteron electrodisintegration process, e^-+d→e^-+Δ+N, are calculated in a general formalism based on structure functions. The obtained expressions have a general nature, hold for one-photon-exchange, assuming P-invariance of the electromagnetic interaction and the conservation of the hadron electromagnetic current. The dependence of the differential cross-section of the e^-+d→e^-+Δ+N reaction on the vector and tensor polarizations of the deuteron target with unpolarized and longitudinally polarized electrons is considered. The general dependence of the asymmetries on two of five kinematic variables, the azimuthal angle φ and (linear polarization of the virtual photon) is calculated. A similar analysis is performed for the polarization of the nucleon produced in γ^*d→ΔN reaction provided the electron beam is unpolarized or longitudinally polarized. Polarization effects, which are due to the strong ΔN-interaction in the final state are calculated. The photoproduction of the Δ-isobar on the deuteron target has been considered in detail, as a particular case. The differential cross-section and various polarization observables have been derived in terms of the reaction amplitudes. The polarization observables due to the linear and circular polarizations of the photon, when the deuteron target is arbitrarily polarized have been derived in terms of the reaction amplitudes. The polarization of the final nucleon is also considered.     

R-matrix approach to the 3-body problem

The asymptotic form of the Faddeev amplitude in coordinate space is derived in various orders. This form and the structure of the Faddeev equations allow by aR-matrix method to establish a set of equations directly for the 3-body on-shellT-matrix elements. The procedure is equally well suited for local and nonlocal interactions.     

Reactions p(d, p)d and p(d, p)pn as a tool for studying the short-range internal structure of the deuteron

In recent years, the deuteron structure at short distances has often been treated from the point of view of nonnucleonic degrees of freedom. In this study, measurements of T-odd polarization observables by using a tensorially polarized deuteron beam and a polarized proton target or a proton polarimeter are proposed as a means for seeking quark configurations inside the deuteron.     

Extraction of Astrophysical Cross Sectionsin the Trojan-Horse Method

 The Trojan-horse method has been proposed to extract S-matrix elements of a two-body reaction at astrophysical energies from a related reaction with three particles in the final state. This should be useful in cases where the direct measurement of the two-body reaction at the necessary low energies is experimentally difficult. The formalism of the Trojan-horse method for nuclear reactions is developed in detail from basic scattering theory including spin degrees of freedom of the nuclei and we specify the necessary approximations. The energy dependence of the three-body reaction is determined by characteristic functions that represent the theoretical ingredients for the method. In a plane-wave Born approximation of the T-matrix the differential cross section assumes a simple structure. Received August 31, 1999; revised June 14, 2000; accepted for publication June 30, 2000     

Change in the structure of colliding deuterons

The effect of the fields of two colliding deuterons on the deuteron wave functions is investigated within the algebraic version of the resonating-group method. The problem of determining the continuum of the K-matrix elements at a given c.m. energy of the deuterons is formulated and solved on the basis of this approach.     

The T-matrix for particle with arbitrary permittivity tensor and parallelization of the computational code

Using the T-matrix approach electromagnetic scattering by a non-axisymmetric particle with an arbitrary permittivity tensor is studied. The electromagnetic fields inside the scatterer are expressed by a system of quasi-spherical vector wave functions which are derived by the use of inverse Fourier transform. Using this expansion a solution of the light scattering problem in the framework of the null-field method is obtained. The implemented T-matrix program is parallelized using both OpenMP and MPI parallel paradigms. Numerical scattering results for anisotropic ellipsoids are presented.     

Renormalized Perturbation Expansion in Kinetic Theory

Ladder summation techniques are applied to the recently developed c-number diagram expansion for kinetic equations describing the relaxation of quantum fluids. By way of the resummation, the kinetic equations are reformulated in terms of a T-matrix which describes the scattering of two particles influenced by the remaining particles of the system via the particle statistics (Bose or Fermi). At sufficiently high temperatures (Maxwell-Boltzmann statistics), the T-matrix introduced coincides with the usual T-matrix of conventional two-body scattering theory in free space. In low-temperature Fermi systems, the T-matrix differs from the reaction matrix of the Brueckner-Goldstone theory because the “healing” property of the two-body wave function does not obtain.