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It is proved that for a particle enclosed in a large box, a potential shifts the energy levels by an amount which, as the volume v of the enclosure tends to infinity in a suitable manner, becomes proportional to ${E}^{\frac{1}{2}}\ensuremath{\delta}(E){v}^{\ensuremath{-}\frac{1}{3}}$, where $\ensuremath{\delta}$ is the corresponding phase shift. Application of this result to the many-particle problem is discussed.

The asymptotic distribution of poles of the nonrelativistic S matrix for potential scattering in the complex angular momentum plane is investigated, and so is the nature of the pole trajectories near E = 0. As a consequence of the behavior of the distant poles and of their residues the S matrix is shown to be representable in the form of an infinite (Weierstrass-Hadamard) product as well as in the form of a (Mittag-leffler) series of partial fractions. (auth)

The study of the structure of the two-particle S matrix as a function of the angular momentum in potential theory is extended to spin-dependent interactions between two spin 1/2 particles, including the tensor force. The results reveal considerable similarity with the spin zero case, including the symmetry properties. The main differences are two branch points at j = 0 and j = -1 and a pole at j = -1/2. It is shown that judicious combinations of S-matrix elements contain none of these singularities, and, as a result, neither do the scattering amplitudes. Certain modifications of the canonical situation are found in the presence of spin-orbit forces or other orbital angnlar momentum- dependent potentials. The factorization of the residue of the S matrix is also discussed. (auth)

The possibility of obtaining threshold anomalies in reactions leading to three-particle channels was studied in detail. It was found that a threshold cusp or rounded step existed in reactions whose final three-body channels have at least one particle in common. The effect appeared as a function of the momentum of the common particle while the total energy was fixed. (auth)

Polarization effects in the scattering of high-energy electrons by charges and magnetic moments are discussed. A double scattering experiment using targets with lined-up nuclear spins should be a sensitive means of obtaining information about a possible difference in the charge and magnetic moment distributions of nuclei.

Central, tensor, and spin-orbit potentials are calculated for the neutron-proton triplet state. They allow explicit solution of the Schr\"odinger equation and fit the low-energy data: effective range, scattering length, deuteron binding energy, quadrupole moment, and $D$-state probability. The deuteron wave function as well as scattering wave functions which result from these potentials are also computed. The potential and wave functions which fit the low-energy singlet state data are also obtained.

A method of avoiding all infrared divergencies in the radiative effects of a constant electromagnetic field is developed. It is used, without the necessity of resumming a nonintegrable series, to calculate the one photon mass operator up to the third order in the external field. The magnetic susceptibility and field dependence of the rest mass of an electron are thereby exhibited to lowest order. The result is then shown in a simple way to provide charged particles with strong short-range forces against the Coulomb field. Particles of unrealistically small mass and charge would carry a large repulsive core, if Coulomb attractive, or a large attractive shell, if Coulomb repulsive.

The detailed behavior of elastic and inelastic scattering cross sections as functions of the energy at the threshold of a new reaction is derived from general principles. The results lend themselves in certain cases to the experimental determination of spins and parities of reaction products, as well as of not directly observable scattering amplitudes and inelastic cross sections. A number of special cases are treated in detail.

The origin of the spurious eigenvalues of Weinberg's kernel for three particles, discovered by Federbush in a special case, is discussed. They are shown to be generally expected with Weinberg's kernel because of its factorization property. Noble's contention that every complex energy is an eigenvalue of Weinberg's kernel is shown to be incorrect.

This paper comments on a recent paper by Feinberg and describes an experiment in which an effect would precede its cause if there were particles that travel faster than light.