An exorcized, factorizing dual amplitude for six charged pions

We further study the amplitudes proposed by two of us which possess the πA₁ three-body trajectory and the f trajectory in the two-body channels. We deduce the π^±o→π^±o amplitude. This amplitude has no parity doubling on any of the leading trajectories. By using the positivity and the Adler conditions we show that the possible forms of the amplitude are severely restricted. We predict degeneracy of the levels along the leading πA₁ trajectory with the exception of spin 0 and spin 1. The positivity conditions have only been imposed on the parent trajectory, so that the overall consistency of the π amplitude has not been fully checked. If we further require the A₁ to be a single level, the amplitude has no free parameters. We regard the existence of an amplitude which obeys the bootstrap condition, which has positivity and no parity doubling along the parent trajectory, and which satisfies the Adler condition as a remarkable consistency test for the N-point function.     

Exchange interaction and elastic 16O + 12C scattering

The effect of core exchange on the potential of interaction between the ¹⁶O and ¹²C nuclei is considered. The amplitudes corresponding to nonlocal exchange interactions are calculated in the Born approximation. It is shown that the inclusion of exchange processes leads to the growth of the elasticscattering amplitude in in the region of large scattering angles. The dependence of amplitudes on the parity of relative motion is analyzed.     

Time-reversal invariance-like relations for spin-effects in elastic and inelastic reactions; vector-meson photoproduction versus compton scattering from nucleons

For elastic scattering, relations between spin-effects (for example, the well-known asymmetry-polarization equality) follow from time-reversal invariance. We show that if certain amplitude combinations vanish, there are strikingly similar relations between spin-effects for elastic and also inelastic reactions. This vanishing of amplitude combinations (denoted M-purity) corresponds asymptotically to purely natural or purely unnatural parity in the crossed channel. The M-purity relations hold for spin-configurations much more general than do the corresponding time-reversal invariance relations.The experimental evidence for purely natural parity exchanges in high energy vector meson photoproduction from nucleons is shown to be good for all amplitudes involving nonzero meson helicity, but less conclusive for the zero helicity ones. Using time-reversal invariance and a vector meson-dominance argument, this implies no unnatural parity contributions in high energy Compton scattering from nucleons.Because of this empirical evidence for M-purity in these two processes, a detailed application to spin-effects in Compton scattering and in vector meson photoproduction is made. Some time-reversal invariance relations in Compton scattering resemble the corresponding M-purity relations though the applicability of the two is different, and there are examples where only one of the two exists. Out of our illustrations, the only M-purity relations which change in form due to the extra amplitudes present in the inelastic reaction are the M-purity analogue and extensions of the asymmetry-polarization equality (of Compton scattering) referring to the photon; the change is the appearance of the elements ?⁰⁰ of the vector meson density-matrix ?. Our other examples of M-purity relations do not change in form in going over from the elastic reaction (Compton scattering) to the inelastic reaction (vector meson photoproduction).     

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.     

Interference effects in proton scattering on <Superscript>15</Superscript>N nuclei at intermediate energies

The differential cross section for proton scattering on ¹⁵N nuclei is calculated within Glauber diffraction theory at energies of 0.2, 0.6, and 1.0 GeV. Use is made of the shell-model wave function for the ¹⁵N nucleus. The contribution of single and double collisions to the Glauber operator Ω is taken into account. The sensitivity of the differential cross sections to the contributions of scattering on nucleons from different shells, to the parameters of the elementary pN amplitude, and to the energy of projectile protons is investigated. It is shown that the interference between amplitudes corresponding to different collision multiplicities, as well as between the amplitudes for scattering on nucleons from different shells, determines special features of the cross section.     

Pion-Nucleon Interaction and Two-Pion-Exchange Three-Nucleon Forces

We compare the πN scattering amplitudes that underlie 2π-exchange three-nucleon forces (TBFs) with the experimental πN amplitudes in the form of partial-wave phase shifts and subthreshold invariant amplitudes. The amplitudes of the Tucson-Melbourne and Brazil TBFs when taken on-pion-mass-shell predict scattering lengths at threshold and phase shifts (slightly) above threshold which are in good agreement with the experimental amplitudes, except for the S-waves. Partial wave amplitudes from separable potentials, recently employed in a 2π-TBF calculation, were continued below threshold, summed into invariant amplitudes, and compared with the experimental amplitudes in this kinematic region, which is most relevant to the kinematics of TBFs. The separable-potential invariant amplitudes, in contrast to those of TM and Brazil TBFs, do not compare well quantitatively with the experimental amplitudes in this region but have a similar qualitative behaviour. The very small TBF effect in the triton of the separable-potential amplitude appears to be due to the πNN vertex function rather than the πN amplitude itself. Received April 27, 1994; revised August 2, 1994; accepted for publication August 31, 1994     

Amplitudes of two-channel scattering by a two-dimensional potential barrier with a constant height

The immersing method is used to solve the two-channel scattering problem in the case of concrete potential. In particular, we consider the particle scattering by a two-dimensional barrier which is constant in the scattering direction and is arbitrary in the transverse direction. For this case the scattering amplitudes t ₁, t ₂, r ₁, and r ₂ are determined. Expressions for the transmission and reflection amplitudes are obtained for the case of δ-potential. The behavior of the scattering amplitudes in the limit k ₂ → 0 is studied. It is also shown that the ratio of products of transmission and reflection amplitudes for two channels does not depend on the coordinate of the middle of coordinate.     

Symmetry constraints in optimal polarization formalisms with an application to p−p scattering

The paper contains results (a) for the general optimal polarization formalism with constraints from time reversal invariance, identical particles, and parity conservation, (b) for the specific reaction involving four $\text{spin}\text{-}\text{1}\text{2}$ particles, (c) for the application of the formalism to elastic p?p scattering at 6 GeV/c and at 800 MeV. The choice of the orientation axes under various symmetry constraints is discussed for the general optimal formalism, showing the narrowing of the choices which nevertheless retains an infinite continuum of possibilities. The transformation properties of amplitudes among these various optimal frames are specified. The transformation of observables among these frames is also discussed for the reaction with four $\text{spin}\text{-}\text{1}\text{2}$ particles. Then the relationship between the observables and the bilinear combination of amplitudes is given for the reaction with four $\text{spin}\text{-}\text{1}\text{2}$ particles, for the constraints of identical particles, identical particles and time reversal invariance, and identical particles and time reversal invariance and parity conservation. The results are applied to the analysis of the Argonne data at 6 GeV/c, t = ?0.6 GeV²/c², for elastic p?p scattering. The amplitudes are easily determined when the proper optimal frame is used, and the display of the amplitudes in other optimal frames suggest some features that may be significant in searching for dynamics. Another application is presented to 800 MeV elastic p?p scattering at several angles, showing that in the proper optimal frame very accurate results can be obtained about a subset of amplitude parameters on the basis of an incomplete set of data. Such an analysis is shown to be helpful in the design of future experiments.     

Dual resonance model with two fermions

Multiparticle Veneziano amplitudes with two fermions are constructed. Factorization holds along the leading trajectory without parity doubling.     

On the analytic properties of the reggeon-reggeon amplitude

The analytic properties of the reggeon-reggeon amplitude in the missing-mass like variable are discussed. (This amplitude is defined through the suitable high-energy limit of the eight-point amplitude). It is shown on the basis of simple Feynman diagrams that it is possible to define reduced amplitudes which are free from kinematical singularities provided that the eight-point amplitude is expressed in a form explicitly consistent with Steinmann relations. In a simple model which is considered in this paper, the reduced amplitudes have the singularity structure of ordinary two-body scattering amplitudes. The finite energy sum rules and four reggeon vertices are also briefly discussed.     

Dual Pomeron Amplitude with External Spin Particles

On the basis of the operator-formulation of the conventional dual resonance model we derive an expression for the one-loop Pomeron exchange amplitude with four external excited particles lying on the parent Regge trajectory. Evaluation of the high energy behaviour leads to the definition of spin-spin-Pomeron form factors. There is a leading Pomeron contribution only if the sum of external spins is even. The dual Pomeron does not exhibit any helicity conservation properties except for s-channel forward scattering. The extension to multiloop amplitudes is briefly discussed.     

Sommerfeld-watson representation for double-spectral functions

We discuss, for the case of pion-pion scattering, a closed system of equations which may be used for a self-consistent calculation of partial-wave amplitudes. It is shown that, for a given sufficiently small input function, the equations have a locally unique solution in a particular Banach space of doubly Hölder continuous partial wave amplitudes. At a fixed point, the scattering amplitude is shown to satisfy both a crossing symmetric unsubtracted Mandelstam representation and the elastic unitarity condition. In this initial study the partial-wave amplitudes are holomorphic in the right half complex angular-momentum plane.     

Compton scattering on a target with degeneracy states

An additional pole term and the contributions to it from intermediate states with the same mass but with different spins is calculated for the Compton scattering amplitude on a two-particle system with zero total angular momentum. It is shown that the decomposition of invariant amplitudes on the generalized polarizabilities of the system does not take place if this term is taken into account.     

A partial-wave analysis for proton compton scattering in the Δ(1232) energy region

Based on the nowadays available phenomenological multipoles for pion photoproduction, a systematic dispersion theoretic calculation of Compton partial amplitudes has been performed. By comparing with the new experimental data in the Δ(1232) region it is found that the hitherto existing discrepancies between the data and theory remain. Our results allow us to isolate the basis of this problem. It is due to the fact that the imaginary parts of the Compton amplitudes determined already by unitarity, give too large contributions to the cross section thus leaving no space for real parts required by the dispersion integrals.Therefore a simultaneous partial-wave analysis for Compton scattering and pion photoproduction was carried through employing only the unitarity connections between both. The resulting amplitudes give a good fit to the Compton cross section and all photoproduction data; moreover the photoproduction multipoles agree essentially with those of the previous analyses. On the other hand for Compton scattering, phenomenological amplitudes are obtained for the first time and a model independent test of dispersion theoretic amplitudes can be carried out. For the resonating f_MM¹⁺ amplitude which describes the M1 excitation and deexcitation to the Δ-isobar, large discrepancies have been found. Possible consequences especially for the forward scattering amplitude and the validity of the Kramers-Kronig relation are discussed.     

Method for solving the problems of multiple scattering by several bodies in a homogeneous unbounded medium

A method is developed for solving problems of multiple scattering by an aggregate of bodies in a homogeneous unbounded medium. For this purpose, the problem on the multiple scattering produced by two bodies in the field of a plane wave is first considered under the assumption that the initial unperturbed scattering amplitudes of both scatterers are known. The solution is constructed by considering plane waves multiply rescattered by the scatterers. Integral equations are obtained that allow one to calculate the resulting scattering amplitude of each scatterer and the combined scattering amplitude of the system of two scatterers. It is shown that knowledge of the solution to this problem is sufficient to solve the problem on the scattering field of a system consisting of an arbitrary number of scatterers. Expressions for the scattering amplitude in the case of an arbitrary primary field are presented. The relationship between the integral equations describing the multiple scattering in a homogeneous space and the multiple scattering by a single scatterer located near an interface is demonstrated. Approximate expressions are given for calculating the scattering amplitude in the case of multiple scattering.     

Angular correlation for nuclear muon capture

Formulae for the capture rates, gamma-neutrino correlations, and angular distributions of recoil in muon capture processes J_i J_f by an unpolarized nucleus for J_i ≦ 3 and J_f ≦ 5/2, with and without change of parity of nuclear levels, are given explicitely in terms of the multipole amplitudes. Relation of helicity amplitudes for muonic atom decay to the multipole amplitudes and to amplitudes introduced by other authors is presented. The derivation is based on kinematics only, and the formulae are strictly valid for the muon capture by any nuclei. The formulae are convenient for model calculations of partial transitions with realistic nuclear and muon wave functions and for the phenomenological analysis of a weak interaction.     

Scattering of spin waves by a rectilinear edge dislocation

The propagation of volume spin waves in an unbounded easy-axis magnet containing a rectilinear edge dislocation is studied theoretically. The spin-wave scattering amplitudes are calculated in the Born approximation. It is shown that the spin-wave scattering amplitude vanishes for certain values of the scattering angle. The dependence of the scattering angle on the angle of incidence of the spin waves is found for this case. The transport scattering cross section of spin waves is found. Fiz. Tverd. Tela (St. Petersburg) 40, 2056–2058 (November 1998)     

Bound and Scattering States of Extended Calogero Model with an Additional PT Invariant Interaction

Here we discuss two many-particle quantum systems, which are obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the Calogero model with and without confining potential. It is shown that the energy eigenvalues are real for both of these quantum systems. For the case of extended Calogero model with confining potential, we obtain discrete bound states satisfying generalised exclusion statistics. On the other hand, the extended Calogero model without confining term gives rise to scattering states with continuous spectrum. The scattering phase shift for this case is determined through the exchange statistics parameter. We find that, unlike the case of usual Calogero model, the exclusion and exchange statistics parameters differ from each other in the presence of PT invariant interaction.     

Behavior of the hadron potential at large distances and properties of the hadron spin-flip amplitude

The impact of the form of the hadron potential at large distances on the behavior of the hadron spin-flip amplitude at small angles is examined. The t-dependence of the spin-flip amplitude of high-energy hadron elastic scattering is analyzed under different assumptions on the hadron interaction. It is shown that the long tail of the nonGaussian form of the hadron potential of the hadron interaction in the impact parameter representation leads to a large value of the slope of the spin-flip amplitude (without the kinematical factor ) as compared with the slope of the spin-nonflip amplitude. This effect can explain the form of the differential cross-section and the analyzing power at small transfer momenta. The methods for the definition of the spin-dependent part of the hadron scattering amplitude are presented. A possibility to investigate the structure of the hadron spin-flip amplitude from the accurate measure of the differential cross-section and the spin correlation parameters is shown. Received: 14 December 2001 / Accepted: 17 January 2002     

Spin dependence of the parity non-conserving neutron-nucleus interaction

We show that the spin dependence of the parity violating amplitudes can provide a clue to the precise origin of the large parity non-conserving effects observed in neutron scattering on nuclei. The polarization asymmetries for longitudinal and transverse polarization of the incoming neutrons allow the separation of these spin amplitudes. In the mechanism of parity admixing of the virtually excited compound nucleus states, the spin dependence of the weak amplitudes is determined by the spin dependence of the strong interaction amplitudes for the elastic channel of the decay of the p-wave resonance