Pion-nucleon scattering: Chiral symmetry and unitarity

The chiral quark models which have been constructed over the past five years generally preserve chiral symmetry in the tree approximation. However, unitarity is then violated. We examine the problem of going beyond the tree approximation for s-wave pion-nucleon scattering within the context of the cloudy bag model.     

Pion-nucleon backward scattering: The location of the amplitude zeros

The complex zero trajectories for the πN helicity amplitudes with definite u-channel isospin are determined from phase shifts. Some of these trajectories display systematic behaviour, having fixed values of (u?u₀), where u₀ corresponds to the backward direction, and small values of Im u. On the assumption that this systematic behaviour will persist to higher energies one can make predictions about the locations of zeros in these helicity amplitudes at high energies. These zero locations are very relevant to an understanding of the mechanisms involved in πN backward scattering. The results, which show quite a striking pattern for the zero positions in the various amplitudes, are discussed from the point of view (a) of the experimental data for πN backward scattering and (b) of a theoretical interpretation of the interaction mechanism.     

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     

Pion-nucleon scattering amplitudes from data and fixedt-analyticity

Summary of recent work of the Karlsruhe group on the determination of N amplitudes at high energies from experimental data and fixed-t analyticity.Presented at the Symposium on Hadron-Hadron Scattering at High Energies, Liblice, Czechoslovakia, June 16–21, 1975. Supported by Bundesministerium für Forschung und Technologie.The author is very grateful toJ. Fischer, J. Piút, O. Dumbrajs and other participants of the symposium for discussions.     

Pion-nucleon scattering in the Brown-Rho bag model

Pion-nucleus scattering in the (3,3) resonance region is described using a version of the Brown-Rho bag model. Terms involving iterations of the crossed Born graphs, as well as excitation of the three-quark delta, both give significant contributions to the scattering amplitude.     

The ratio of K-capture to positon emission in the decay of P

The ratio of K-capture to positon emission in the 2.5 min decay of ³⁰P has been measured by a proportional counter-flow technique. The experimental value of the K/β⁺ was found to be (1.24 ± 0.04) × 10⁻³ in agreement with the conventional theoretical ratio i.e. apparently supporting the view that exchange and overlap effects are small.     

Coupled channel T-operator equations with connected kernels: (II). N coupled two-body channels

A time-independent theory of rearrangement collisions involving transitions between two-body states is presented. It is assumed that the system of interest consists of particles that may be partitioned into two-body systems in N ways, including interchanges of particle labels without changing the kind of channel. An infinite family of sets of N coupled T-operator equations is derived by use of the channel coupling array, as in previous work on the three-body problem. Specialization to the channel-permuting arrays guaranteeing connected (N?1)th iterates of the kernel of the coupled equations is made in the N-channel case (N > 3) and the nature of the solutions to the coupled equations is discussed. Various approximation schemes to be used with numerical calculations are suggested. Since the transition operators for all rearrangement channels are coupled together, no problems concerning non-orthogonality of the eigenstates of different channel Hamiltonians are encountered; also the presence of the outgoing wave boundary condition in all channels is made explicit. The close resemblance of the equations in matrix form to those of one-channel scattering is exploited by introducing Møller wave operators and associated channel scattering states, an optical potential formalism that leads to rearrangement channel optical potential operators, and a variational formulation of the coupled equations using a Schwinger-like variational principle. A brief comparison with other many-body formalisms is also given.     

Test of vibrational current distributions in transverse electron scattering

The transition current distribution for the low-lying 2⁺ state at 4.085 MeV in ²⁰⁸Pb obtained in a realistic cranked shell-model calculation is used to calculate the transverse PWBA form factor for inelastic electron scattering to this state. By keeping the same density but changing the velocity field to that of irrotational, incompressible flow the sensitivity of the form factor to the dynamics of nuclear vibrational motion is explored. It is found that the two flow patterns lead to significant, observable differences in the form factors.     

Calculations of the critical angular momentum in the entrance reaction channel

A dynamic model, based on the force equilibrium concept, is proposed to estimate the critical angular momentum in the entrance channel for reactions between complex nuclei. The nucleus-nucleus force is derived from simple surface-energy considerations. Good agreement with the experimental data on complete-fusion cross sections is obtained.     

Quasi-elastic pion scattering on 16O: A comparison between the Δ-hole approach and a standard first-order calculation

We present calculations of quasi-elastic pion scattering on ¹⁶O in both the Δ- hole model and a standard first-order theory. The basic approach is a modified “DWIA”, where the same in-medium πN t-operator is used for the transition and the optical potential generating the distorted pion wave functions. In order to allow a meaningful comparison with the recent SIN data, all technical complications such as background interactions, non-static vertex-corrections, 1/A effects, are taken into account, and the DWIA amplitude is evaluated without further numerical simplification like, e.g., factorization. In contrast to the closure approximation, the Δ-hole model predicts correctly the doubly differential cross sections for (π, π') on ¹⁶O over a wide range of angles and energy-losses.     

Folding-model analysis of elastic and inelastic α-particle scattering using a density-dependent force

A folding model with a density-dependent form of the semi-realistic M3Y effective interaction is applied to α-particle scattering. A previous analysis of elastic scattering at 140 and 172 MeV is now applied to data at other energies from 25 to 120 MeV. The model is also extended to inelastic scattering, using both the collective model and a valence-plus-core-polarization model for the transition densities. The proton transition densities were normalized to measured B(EL) values. When necessary, the neutron transition densities were rescaled to fit the (α, α′) data, providing a source of information on the neutron contributions. The neutron transition multipole moments thus obtained are compared to those derived from (p, p′) data at 800 MeV, as well as from other sources.     

Magnetic dipole moments near Sn: Measurement on isomeric 11/2 states in odd-A Te and Te by NMR/ON

On-line low temperature nuclear orientation (OLNO) experiments have been performed on the odd-A Te isotopes ¹³¹Te and ¹³³Te using the technique of nuclear magnetic resonance on oriented nuclei (NMR/ON). The magnetic moments of the isomeric 11/2⁻ states have been measured extending the known data on these states in the Te isotopes up to the neutron shell closure at N = 82. The contribution to the 11/2⁻ magnetic moment in ¹³³Te due to core polarisation is calculated using an RPA shell model as well as corrections to the magnetic dipole operator caused by mesonic exchange currents. The neutron number dependence of the magnetic moments of the 11/2⁻ isomers in heavy Te isotopes is discussed in terms of particle-core coupling model (PCM) calculations.     

Nuclear matter distributions for 16,17,18O from a microscopic analysis of elastic proton scattering

An analysis of 65 MeV elastic proton scattering by ^16,17,18O has been made in terms of a reformulated optical model. Matter distributions for ¹⁷O and ¹⁸O have been obtained relative to ¹⁶O. The results for the rms matter radii are R₁₇?R₁₆ = 0.04±0.03 fm and R₁₈?R₁₆ = 0.35± 0.07 fm.