Interplay of quark and meson degrees of freedom in a near-threshold resonance: Multi-channel case

We investigate the interplay of quark and meson degrees of freedom in a physical state representing a near-threshold resonance for the case of multiple continuum channels. The aim is to demonstrate the full complexity of possible near-threshold phenomena. It turns out that those are especially rich, if both quark and meson dynamics generate simultaneously weakly coupled near-threshold poles in the S-matrix. We study the properties of this scenario in detail, such as t-matrix and production amplitude zeros, as well as various effects of the continuum channels interplay.     

On the Connection between Particles and Poles of the S-Matrix

In axiomatic S-matrix theory it is usually assumed that stable particles give rise to simple poles of the S-matrix for real negative energies while unstable particles give rise to poles close to the real axis on an unphysical sheet of the energy Riemann surface. The stable particle — pole association has been known for a long time not to be always true. For example in potential scattering what is relevant in this case in fact is not the S-matrix but the Jost function. The zeroes of this function for real negative energies are in fact in one-to-one correspondence with the bound states, while the correspondence may break down for the poles of the S-matrix. On the other hand it has recently been pointed out that there also is in general no connection between unstable particles and poles of the S-matrix.     

Separable energy-dependent approximation to local potentials

An extension of the single-pole separable approximation of a two-body t-matrix in which the effects of several poles are included is made. The simple form for the t-matrix derived from a single separable potential is retained. However, the separable potential is constructed using an energy-dependent superposition of the states corresponding to the various poles. The energy dependence is chosen so as to obtain the correct residue of both the on-shell and off-shell t-matrices at each of these poles, while preserving unitarity. The formalism is specialized to the case of s-wave scattering from an attractive square well. Comparison to the exact s-wave cross section gives good results.     

Separation of Variables for the Ruijsenaars System

We construct a separation of variables for the classical n-particle Ruijsenaars system (the relativistic analog of the elliptic Calogero-Moser system). The separated coordinates appear as the poles of the properly normalised eigenvector (Baker-Akhiezer function) of the corresponding Lax matrix. Two different normalisations of the BA functions are analysed. The canonicity of the separated variables is verified with the use of the r-matrix technique. The explicit expressions for the generating function of the separating canonical transform are given in the simplest cases n=2 and n=3. Taking the nonrelativistic limit we also construct a separation of variables for the elliptic Calogero-Moser system. Received: 10 January 1997 / Accepted: 1 April 1997     

Optical-model description of the fragmentation of a single-particle state

Several possible definitions of thel = 0 neutron strength function are examined. Their energy dependence is investigated and particular attention is paid to threshold effects when the single-particle state lies in the vicinity of the elastic threshold. Among other results, it is shown that, in actual physical situations, the S-matrix strength function never exhibits a cusp at threshold.     

Three-Body Phase Shift in One-Dimensional 2 + 1 Scattering

For a model of three particles on a line, subject to attractive delta-function interactions, we consider the phase shift. We do this from the point of view of the calculation of the S-matrix in a hyperspherical adiabatic basis (an adiabatic S-matrix), and for energies ranging from the (negative) energy of the two-body bound state to a total energy of zero. We derive analytical expansions and present numerical work, for different approximations, and compare with the exact results that we obtain from the work of McGuire, whose model we have borrowed. We show that the simplest adiabatic approximation gives results that are qualitatively wrong, but that better approximations yield, for most of our range, excellent agreement with the exact result. Understanding the threshold behaviour, however, requires a zero-energy three-body bound state, or resonance, previously unsuspected for this model. The methods developed for the case of the simplest adiabatic approximation also yield threshold and low-energy results applicable to the two-body problem in two dimensions. Received December 23, 1996; revised May 13, 1997; accepted for publication June 19, 1997     

Study of theS-matrix near bound states in the continuum

The behaviour ofS-matrix for potentials generating bound states in continuum in the neighbourhood of the positive bound state energies is studied. It is shown that unlike the case of usual negative energy bound states, theS-matrix does not have a pole at the positive bound state energy but becomes unity at the energy corresponding to bound states in continuum. Calculations ofS-waveS-matrix for a local potential constructed by Stillinger and Herrick and a separable nonlocal potential constructed by the present authors verify these results. Our results indicate that the bound states embedded in continuum constructedvia the von Neumann and Wigner procedure cannot be interpreted as resonances with zero width.     

T-matrix analysis of biexcitonic correlations in the nonlinear optical response of semiconductor quantum wells

A detailed numerical analysis of exciton-exciton interactions in semiconductor quantum wells is presented. The theory is based on the dynamics-controlled truncation formalism and evaluated for the case of resonant excitation of 1s-heavy-hole excitons. It is formulated in terms of standard concepts of scattering theory, such as the forward-scattering amplitude (or T-matrix). The numerical diagonalization of the exciton-exciton interaction matrix in the 1s-approximation yields the excitonic T-matrix. We discuss the role of the direct and exchange interaction in the effective two-exciton Hamiltonian, which determines the T-matrix, evaluated within the 1s-subspace, and also analyze the effects of the excitonic wave function overlap matrix. Inclusion of the latter is shown to effectively prevent the 1s-approximation from making the Hamiltonian non-hermitian, but a critical discussion shows that other artefacts may be avoided by not including the overlap matrix. We also present a detailed analysis of the correspondence between the excitonic T-matrix in the 1s-approximation and the well-known T-matrix governing two-particle interactions in two dimensional systems via short-range potentials. Received 3 August 2001 and Received in final form 26 December 2001     

Analytic properties of the scattering amplitude and resonances parameters in a meson exchange model

The analytic properties of scattering amplitudes provide important information. Besides the cuts, the poles and zeros on the different Riemann sheets determine the global behavior of the amplitude on the physical axis. Pole positions and residues allow for a parameterization of resonances in a well-defined way, free of assumptions for the background and energy dependence of the resonance part. This is a necessary condition to relate resonance contributions in different reactions. In the present study, we determine the pole structure of pion–nucleon scattering in an analytic model based on meson exchange. For this, the sheet structure of the amplitude is determined. To show the precision of the resonance extraction and discuss phenomena such as resonance interference, we discuss the S₁₁ amplitude in greater detail.     

Channeling problem for charged particles produced by confining environment

Channeling problem produced by confining environment that leads to resonance scattering of charged particles via quasistationary states imbedded in the continuum is examined. Nonmonotonic dependence of physical parameters on collision energy and/or confining environment due to resonance transmission and total reflection effects is confirmed that can increase the rate of recombination processes. The reduction of the model for two identical charged ions to a boundary problem is considered together with the asymptotic behavior of the solution in the vicinity of pair-collision point and the results of R-matrix calculations. Tentative estimations of the enhancement factor and the total reflection effect are discussed. The text was submitted by the authors in English.     

Investigation of the photothermally modulated ferromagnetic resonance signal from magnetostatic modes in yttrium iron garnet films

The conventional and photothermally modulated (PM) ferromagnetic resonance (FMR) of magnetostatic modes (MSM) in yttrium iron garnet (YIG) films have been investigated as a function of temperature. Approaching the ferrimagnetic transition at T _c=560 K a strong enhancement of the PM-FMR signal amplitude is observed which is accompanied by a change of the signal shape. The observations are discussed in the framework of a model that takes into account the temperature derivatives of those quantities that contribute to the high-frequency susceptibility. At temperatures still below T _c a paramagnetic line emerges. The MSM disappear in a state of finite magnetization which is explained on the basis of damping of the MSM being important in the vicinity of the magnetic phase transition. Additionally, frequency and power dependent measurements are presented and the imaging ability of PM-FMR is demonstrated.     

The (d,p)-reaction treated by the formalism of Green's functions

The full energy dependence of the two-particle Green's function is taken into account in deriving theS-matrix for a (d, p)-reaction leading from an even-even nucleus in the ground state to a single-particle residual state in the even-odd nucleus. The resultingT-vertex of many-body theory is discussed with the Bethe-Salpeter equation in the particle-particle channel, which allows for a renormalization in the same sense as for bound state problems but now in a different range of energy. Special attention is paid to the problems arising in expanding the deuteron (two particles in the continuum) into shell model wave functions.     

Pion-nucleon scattering in the K-matrix approach

The K-matrix approach with effective Lagrangians is used to describe the S and P pion-nucleon partial-wave amplitudes in the energy range E _lab≤ 1 GeV. It is demonstrated, that treating the resonance as K-matrix a pole gives the natural way to separate the resonance and non-resonance parts of the πN amplitude. The model includes all the four-star πN resonances, the non-resonance contributions are calculated from relevant Feynman graphs without any phenomenological form factors. Different contributions to the inelastic π⁻ p→ηn amplitude are estimated. Received: 9 July 1998     

Ferromagnetic resonance and bistability field in a uniaxial magnetic film

Peculiarities of ferromagnetic resonance (FMR) corresponding to bias along the “hard” magnetic axis of a film with 2D uniaxial anisotropy are studied based on numerical solution of magnetic moment dynamics equations. It is shown that an additional resonance peak is formed in the FMR spectrum in the vicinity of “bistability field” H _b . The dependence of this field on the amplitude of the microwave field and damping parameters is analyzed.     

Interplay of quark and meson degrees of freedom in a near-threshold resonance

We investigate the interplay of quark and meson degrees of freedom in a physical state representing a near-threshold resonance for the case of a single continuum channel. We demonstrate that such a near-threshold resonance may possess quite peculiar properties if both quark and meson dynamics generate weakly coupled near-threshold poles in the S -matrix. In particular, the scattering t -matrix may possess zeros in this case. We also discuss possible implications for production reactions as well as studies within lattice QCD.     

Resonances and Fluctuations in Nuclear Reaction Cross Sections

On the basis of the continuum shell model, an expression for the S-matrix is derived. The external mixing between shape resonances and resonance states of complicated nuclear structure is investigated. It is shown that the doorway properties of the shape resonances may lead to an l-dependent transparency of the optical potential and, consequently, to an energy dependence of large back angle scattering if the unitarity of the S-matrix is taken into account.     

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     

J-Plane Analysis of the Veneziano Amplitude with Nonlinear Trajectories

The structure of singularities of the Veneziano amplitude in the complex angular momentum plane is studied. The introduction of a nonlinear term in the trajectory essentially changes the properties of the partial amplitude as compared to the case of linear trajectories. In the J-plane, besides simple poles lying on the leading and on the conventional daughter trajectories, additional poles lying on mirage trajectories (situated below the leading trajectory) emerge. In the partial amplitude also non-reggeised poles in the s-plane emerge whose position is independent of the angular momentum. Such are, for example, the ancestors.     

Nearly separable potentials

It is shown that an investigation of the on-shell T-matrix as a function of the strength of the interaction can provide much information on the off-shell behaviour of its T-matrix. In particular it is found that a large class of so-called realistic potentials is “nearly separable”.