K −-Proton atomic transitions

The relation between theK ^}-P scattering length and the X-ray spectrum for the 2p → 1s electromagnetic transition inK ^?-P atoms is examined. A coupled-channel potential model is used to explicitly calculate the energy of theS-matrix pole in the 1s channel, which is then compared with the energy obtained from the scattering lengths via the standard equation. The X-ray spectrum is calculated and compared with the Lorentzian shape associated with the complex energy of theS-matrix pole. In addition, theK ^?p branching ratios are compared at threshold and at the complexS-matrix pole energy.     

P-Matrix analysis of the dibaryon1 D 2 resonance

We study the relation between intermediate energy nucleon-nucleon scattering and the eigenstates of the bag model using theP-matrix formalism. Data of existing phase-shift analyses are employed to calculate theP-matrix for the coupled¹ D ₂(pp) and⁵ S ₂(NΔ) channels in the energy region above the Δ-isobar production threshold. TheP-matrix calculated for the equivalent hadronic bag radiib=1.4?1.5 fm is shown to have a pole in the mass range 2.31–2.34 GeV in agreement with the MIT bag model prediction of theI=1,J ^P =2⁺ 6-quark state with the mass 2.34 GeV. The hadronic shift of this state is shown to be ≈200 MeV; the dibaryon pole of theS-matrix is located at the energy 2.15–2.17 GeV with the width ≈100–200 MeV.     

Analyticity and ergodicity in the maximum-entropy approach to statistical nuclear reactions

In the maximum-entropy approach to statistical nuclear reactions one imposes naturally the constraints of unitarity and symmetry of theS-matrix, and of a fixed expectation value ofS. We show that the analytical structure of theS-matrix and the requirement that the problem be ergodic (so that energy averages can be replaced by ensemble averages) impose certain restrictions on the distribution of statisticalS-matrices. Some of these additional constraints are then imposed numerically in a two-channel calculation, and are shown to improve the results for the fluctuation cross sections, the elastic enhancement factor, etc.     

A new approach to potential scattering

An approximate integral-representation of theS-matrix in partial-wave expansion is derived for a scalar Schrödinger particle in a central field. The method consists of linearizingCalogero's Riccati equation for the interpolatingS-matrix in such a way that the solution of the linearized equation deviates as little as possible from the exact one. TheS-matrix thus obtained exhibits exact crossing-symmetry and uniform convergence independent of the coupling constant of the scattering potential. In the weak coupling limit it is especially shown thatour method is more accurate than the second Born approximation. In the second part of the paper we specialize ourS-matrix to low and large energies. At low energies, a general integral for the scattering length is obtained and at large energies the summation over all angular momenta is carried out yielding an expression for the scattering amplitude.     

Analytical properties of theS-matrix in many-channel-scattering

This work is an extension of previous work byNewton ^1–3 andWeidenmüller ^4,5 to a more realistic case of many-channel scattering: We consider arbitrary orbital angular momenta and a potential matrix of the Yukawa type. The analytical properties of the modifiedS-matrix are investigated. The modifiedS-matrix is meromorphic in certain strips around the real axes of the Riemann surface. This surface is determined solely by the kinematical branchpoints. The region of analyticity can be extended further for the diagonal and the squared nondiagonal elements of theS-matrix to include the entire Riemann surface except cuts on the imaginary axes. These cuts can possibly include part of the real axes. The one-pole approximation of theS-matrix is of a Breit-Wigner form. An exact expression for the partial widths and a sum rule for the partial widths are derived. A generalized Levinson theorem is proved.     

Geometric-symmetry consideration on magneto-conductance oscillations in purely ballistic quantum rings

We report an analysis of the magneto-conductance oscillations in two-dimensional mesoscopic ring structures with different geometric symmetry. In particular, we demonstrate that the h/2e magneto-conductance oscillations may be absent or present in purely ballistic quantum rings depending on their geometric symmetry. A detailed analysis of the results is carried out by expanding the transmission amplitudes with backscattering terms. The role of interchannel scattering, which is an essential element of multichannel ballistic transport, is stressed.     

Scattering and infinite dimensional symmetry schemes

We examine the recently proposed non-trivial binding of the Poincare group with internal symmetry groups, which leads to mass splitting without symmetry breaking, from the point of view of scattering. We give a very general realization of the corresponding infinite dimensional Lie algebra in the Fok space of asymptotic states built from two scalar nucleons. Assuming that the algebra describes the exact symmetry of theS-matrix we conclude that no elastic NN scattering exists.The author is indebted to Professor V. Votruba and Dr. J. Formánek for many stimulating discussions.     

Statistical reactions with memory and thermalized-nonequilibrated nuclear states

Starting from the Feshbach S-matrix pole expansion we modify the standard statistical model for compound reactions by introducing correlations between fluctuating S-matrix elements with different J (total spin) and π (parity) values. The S-matrix (J, π)-correlations are obtained at the expense of introducing infinitesimally small entrance-exit channel off-diagonal (J, π)-correlations between the random variables of the statistical model. Although later on these correlations are switched off by means of a properly applied limiting procedure, the S-matrix (J, π)-correlations do not vanish and can be strong. The physical origin of the S-matrix (J, π)-correlations resembles the effect of spontaneous symmetry breaking while S-matrix (J, π)-decoherence is due to quantum chaos. Novel reaction mechanism results in the excitation of peculiar nuclear states: The intermediate system is thermalized so that the shape of the spectrum is angle-independent and Maxwellian with angle-independent slope, yet the intermediate nucleus is not equilibrated since the angular distribution is forward-peaked, i.e., memory of the direction of the initial beam is not lost. The existence of thermalized-nonequilibrated nuclear states is supported by data on the 50–100% forward peaking of neutrons in the typically evaporation (1–3.5 MeV) part of the spectrum observed in the ⁹³ N b(n, n′) scattering with E _n = 7 MeV.     

Construction ofS-matrix from scattering data

A method of construction of the scatteringS-matrix from scattering data is proposed. The scattering matrix is expressed in the form of a rational fraction and takes fully into account the analytic properties of theS-matrix. The method generates a unique and stable analytic continuation of theS-matrix into the complex energy plane. The method is applied to calculation of energy and widths of several resonances in nuclear and atomic physics. Its efficiency is compared with some recently proposed methods.     

On the regular holonomic character of theS-matrix and microlocal analysis of unitarity-type integrals

The previously proved results that every analytically renormalized Feynman integral is a regular holonomic function suggests that theS-matrix should be locally expressible as an infinite sum of regular holonomic functions. A regularity propertyR is formulated that expresses the condition that theS-matrix be locally expressible near each physical pointp as a convergent sum of regular holonomic functions, with each term enjoying some of the regularity properties of a corresponding Feynman integral. This propertyR holds at every physical pointp that has yet been analyzed by the methods of axiomatic field theory orS-matrix theory. Some analyticity properties of unitarity-type integrals are then examined under the assumption that theS-matrix satisfies propertyR and a weak integrability condition. These results rest heavily on some recently proved properties of regular holonomic functions.     

Entwicklung der Streuamplituden nach irreduziblen Spintensoroperatoren

The scattering amplitude for elastic or inelastic scattering of nonrelativistic particles with spin is calculated from the angular momentum representation of theS-matrix. Application of Racah algebra techniques allows a representation in terms of irreducible spin-tensor operators. Only two particle channels are considered. The physical significance of the invariant expansion coefficients of that representation is illustrated in the well known case of nucleon nucleon scattering.     

Scattering and bound state solutions for a class of nonlocal potentials (s-wave)

Thes-wave scattering solution is discussed for a class of nonlocal (non-separable) potentials. Existence and uniqueness theorems are given and the analyticity domain in thek-variable (k = wave number in the C.M. system) is determined. Furthermore it is proved that solutions of the bound state problem exist and a discussion of the square-integrable solutions, which can occur for a real positive value of the energy, is given. In this last case the scattering solution also exists but it is not unique. Finally theS-matrix is introduced and it is proved that it is unambigously defined even if the scattering solution is not unique.     

Long-range tail produced by the CDD ambiguity in a static model

An aspect of a potential-model analogy of the customary CDD ambiguity is studied. Starting from the idea that the known CDD ambiguity in theS-matrix produces an ambiguity in the determination of potentials, the influence of CDD poles upon the long-range behaviour of potentials in the relativistic (Klein-Gordon) static model is demonstrated. Generation of the long-range tail by CDD poles is investigated in terms of a scattering inversion-problem formalism, based on theN/D equations extended off the mass shell.     

Large-angle scattering of heavy ions: (I). General structure of elastic cross section

Closed-form expressions are derived for the differential cross section of elastic heavy-ion scattering at large angles. The derivation is based on the general form of the elastic partial-wave S-matrix in real l-space. By a generalization of analytic techniques developed in earlier work, it is shown that the large-angle scattering cross section has a universal structure involving combinations of Bessel functions and the Fourier transforms of the rapidly varying parts of the S-matrix, irrespective of their dynamical origin. Anomalous large-angle scattering is attributed to deviations of the S-matrix from its “normal strong-absorption profile”, and general conditions for backward-angle enhancement are given. Our model-independent formulation provides the framework for an “inductive” method of analyzing experimental angular distributions and excitation functions aimed at identifying, as uniquely as possible, the dynamical mechanisms that operate in large-angle heavy-ion scattering. Extensions of the formalism to inelastic scattering and transfer reactions, and applications of the analytic method, will be described in subsequent papers.     

Gravitational waves as string vacua II

Classical propagation of (super)strings through gravitational shock waves is analyzed. The exact classical solutions are used for quantization and for the identification of the exact quantumS-matrix describing string scattering by the wave. ThisS-matrix coincides with theS-matrix of the string-string scattering in theflat space-time for particular profile of the shock wave! This is interpreted as the generation of curved geometry from the flat space-time string theory. The quantum consistence of (super)string motion in gravitational plane wave backgrounds is then studied. It turns out that for the standard dimensionsD=26 (D=10) the vanishing of the Ricci tensor for the plane wave is sufficient condition for vanishing of the Weyl (superWeyl) anomaly. Thus, plane wave solutions of the Einstein equations are automatically the classical (super)string vacua. For particular plane waves the anomaly can be evaluated even nonperturbatively.This is the second part of the review based on the PhD thesis of the author defended in 1989 at SISSA, Trieste.     

A relationship between Gel'fand-Levitan and Marchenko kernels

A new integral equation which relates the output kernels of the Gel'fand-Levitan and Marchenko inverse scattering equations in a continuous range of their variables is specified. Structural details of this integral equation are studied when theS-matrix is a rational function, and the output kernels are separable in terms of Bessel, Hankel and Jost solutions.     

On the Regge-pole description of nucleus-nucleus scattering

The properties of the Regge poles of theS-matrix for scattering of strongly-absorbed nuclear particles are considered. Simple formulae are obtained for describing the Regge trajectories in terms of the nuclear radius, the quasi stationary levels in the combined nuclear-Coulomb-potential and the widths of these levels. The predictions of these formulae are compared with the Regge trajectories obtained previously, for a Woods-Saxon potential, and with those required to fit¹⁶O-¹²C backward scattering.     

Spin-polarized transmission through a mesoscopic ring with a magnetic impurity

Based on one-dimensional quantum waveguide theory we study the symmetry of the spin-polarized transmission through an Aharonov–Bohm ring with a magnetic impurity, in which the spin-exchange interaction between an incident electron and the magnetic impurity leads to spin–flip scattering. It shows that for some special Fermi energies, both spin-up and spin-down transmission coefficients are symmetric under the flux reversal in the spin–flip scattering process and the spin-polarized conductance also is symmetric. In above case, AB oscillations of spin-down transmission and reflection are perfectly identical. The effect of the exchange interaction strength and Fermi wave vector on transmission behavior of spin-state electrons is examined.     

Ground state energy for a model gas in one dimension

Ground state energies of many-body systems in one dimension in the thermodynamic limit are calculated. We use relations between the ground state energy and the scattering phase, which are exact for a delta-function potential, and are fulfilled approximately for other interactions. This will be applied to a model of quantum field theory, for which theS-matrix can be calculated exactly by means of a property which is called factorization.