Dynamical Theory for Strong Interactions at Low Momentum Transfers but Arbitrary Energies

Starting from the Mandelstam representation, it is argued on physical grounds that "strips" along the boundaries of the double spectral regions are likely to control the physical elastic scattering amplitude for arbitrarily high energies at small momentum transfers. Pion-pion scattering is used as an illustration to show how the double spectral functions in the nearest strip regions may be calculated, and an attempt is made to formulate an approximate but "complete" set of dynamical equations. The asymptotic behavior of the solutions of these equations is discussed, and it is shown that if the total cross section is to approach a constant at large energies then at low energy the S-dominant ππ solution is inadmissible. A principle of "maximum strength" for strong interactions is proposed, and it is argued that such a principle will allow large low-energy phase shifts only for l<~lmax, where lmax~1

On the analysis of nucleon-nucleon scattering experiments

A method of perturbation calculation, especially adapted to nucleon-nucleon scattering problems, is described. Any contribution to the energy of the system which is relatively small where the nuclear potential is large may be treated as the perturbation. Two principal examples are discussed. (1) Energy as the perturbation: An expansion of the phase shifts in powers of the energy is written down which extends earlier results of Schwinger, Blatt, and Jackson. (2) The Coulomb field as the perturbation in the proton-proton problem: Expansions are given which relate the nuclear phase shifts in a combined nuclear and Coulomb field to the corresponding phase shifts for a purely nuclear problem. Attention is confined to central forces throughout

The scattering of elementary particles by complex nuclei -— A generalization of the impulse approximation

By a systematic iteration procedure it is shown how the problem of the scattering of an elementary particle by a complex nucleus (or any many-particle target system) can be expressed in terms of two-body operators. The results are related to the previous work of Chew and Wick on the impulse approximation, with special attention given to multiple scattering effects which have heretofore not been formulated in a rigorous way. An explicit formula for the double scattering terms is presented