A scheme of parametrization ofππ S andP partial wave amplitudes is proposed. Analytic, crossing and unitarity properties are rigorously satisfied. The analyticity property is made explicit by the use of a conformally mapped variable. Our expressions fit excellently with both phase shift and inelastic curves for centre of mass energy up to 1·4 GeV.

On the basis of crossing symmetry a new set of exact relations involving theππ partial wave amplitudes have been derived, using Roskies’ amplitudes.

A novel approach to energy dependent phase shift analysis ofππ scattering is proposed. Optimised polynomial expansions of Roskies’ amplitudes are given. The parameters of these expansions are searched out by making a fit to the differential cross-sections. Then the transformation matrix between Roskies’ amplitudes and the conventional partial waves is used to compute the phase shifts and inelasticities. Significant improvement is observed in so far as the number of free parameters for a fixed energy phase shift analysis is concerned. Value for the effective Chew-Mandelstam coupling constant, λ_CM, is also estimated.

The forces of interaction as reflected in the cosθ plane analytic structures of the helicity amplitudes of Σ⁻-p and Λ-p scattering are optimally exploited using the conformal mapping technique of Cutkosky and coworkers. A suitable parametrization of these amplitudes in the mapped variable is then chosen so that it can see the zeros better. These zeros are then located by making a good fit to the differential scattering cross-section curves. The effect of these zeros upon the cross-sections is discussed. Values for the phase shifts and coupling parameters between channels of fixedJ values are also computed.

The lowest momentum at which the total scattering cross-section data are available for Σ⁺p and Σ⁻p scattering is 145 MeV/c and 142.5 MeV/c respectively. Thus extracting low energy parameters amounts to extrapolating the data to still lower energies. Using the analytic structure of foward scattering amplitude to advantage a parameterization of theσ_T is presented which is hoped to be more reliable and stable for deriving results through extrapolation. The scattering lengths and effective ranges for the Σ⁺p and Σ⁻p are also estimated.

Optimally exploiting the analytic structure of the helicity amplitudes of Σ⁺-p scattering we locate their zeros by making a fit to the differential cross-section curves at 40, 100 and 150 MeV energies. Minute changes in the positions of the zeros produced detectable noises in the fit. It was observed that quite reliable predictions for the phase shifts can also be obtained from this analysis.

A relatively stable method of phase shift analysis of hyperon-nucleon scattering proposed by us is applied to Σ⁺p and Λp scattering. The analytic cutt-planes of analyticity of the helicity amplitudes are mapped into the interior of unifocal ellipses. The helicity amplitudes are then expressed as accelerated convergent expansions in the mapped variable. A definite economy is observed in the number of free parameters for fixed energy phase shift analysis of Σ⁺p and Λp scattering at 40 and 100 MeV and 100 MeV respectively. Twenty six more phase shifts and coupling parameters corresponding to higherJ values are also predicted.

The claim of Mohapatra and Maharana thattb(s) is a better scaling variable thant(lns)² is put to test in the case of Λ-p scattering, after parametrizingb(s) asC₁ +C₂(lns)α. It was observed that in this case the data also prefer anα value which is close to those obtained by Mohapatra and Maharana for other scattering processes.