The free-field Lagrangian as well as the propagator for spin-; particles contains an arbitrary parameter A . However, the S-matrix elements for the interaction of a spin-9 field with other fields are always independent of this parameter, provided the interaction Lagrangian is properly chosen. For a system of a spin-; field coupled to a nucleon field and a pion field, a two-parameter (A,Z) interaction Lagrangian is introduced in such a way that it is invariant under a point transformation of the spin-4 field. The transition amplitude for such an interaction is independent of the parameter A. However, it does depend on the second parameter Z. By requiring the interaction to be consistent with the principles of second quantization, the value of the second parameter has been fixed. Therefore, the A (1238) contribution to the elastic 7iN scattering amplitudes can be uniquely determined. Using this model for the evaluation of the A(1238) contribution and the chiralinvariant Lagrangians for the calculation of the nucleon pole and p-pole contributions, the TN scattering lengths have been computed and compared with the experimental data. The calculated results are in good agreement with experiment.

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The curvature potential arising from confining a particle initially in three-dimensional space onto a curved surface is normally derived in the hard constraint q → 0 limit, with q the degree of freedom normal to the surface. In this work the hard constraint is relaxed, and eigenvalues and wave functions are numerically determined for a particle confined to a thin layer in the neighborhood of a toroidal surface. The hard constraint and finite layer (or soft constraint) quantities are comparable, but both differ markedly from those of the corresponding two dimensional system, indicating that the curvature potential continues to influence the dynamics when the particle is confined to a finite layer. This effect is potentially of consequence to the modelling of curved nanostructures.

Total cross sections (elastic plus inelastic) are reported for electron-Ar and Kr scattering at energies 10-6000 eV. A model complex-optical-potential (COP) approach is employed in which the real and imaginary parts are expressed in terms of the target electron density. For the real part of the COP, the static potential is determined exactly at the Hartree-Fock level, the exchange potential is approximated in the free-electron-gas model and the polarisation effects are included via the parameter-free correlation polarisation potential. The imaginary part of the COP, i.e. the absorption potential, is a function of projectile energy, target charge density, mean excitation energy of the atom, and static and the exchange potential terms. The charge density of the atom is obtained accurately from the numerical self-consistent Hartree-Fock procedure. The complex potential scattering problem is solved exactly under the variable-phase-approach. Our total cross sections compare very well with the measured values at all energies considered here. We also present differential cross sections (DCS) with and without absorption effects. We found that absorption effects improve the elastic DCS at all energies above the excitation threshold.

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