Marvin L. Goldberger

Mandelstam representation for potential scattering

Abstract A proof of the Mandelstam representation for the scattering amplitude in the case of nonrelativistic potential scattering is given for a certain class of potentials. Fredholm theory and the Lehmann representation are employed in the proof. The unitarity condition is used to provide an iteration procedure for the exact determination of the weight function appearing in the Mandelstam representation, independent of the number of subtractions required in the latter. The analytic properties of the partial wave amplitudes can be easily read off from the Mandelstam representation. It is shown that in cases where the partial wave amplitudes can be represented by dispersion integrals without subtractions, they are uniquely determined, together with the energies of any bound states, in terms of the first Born approximation and the Mandelstam weight function, which is in principle known. In these circumstances, in effect, the Mandelstam representation and unitarity, together with the first Born approximation, completely define the nonrelativistic scattering problem in a way which replaces the Schrodinger equation. Some approximation methods are discussed and compared with exact solutions for s -wave amplitudes.

Dispersion relations for nucleon-nucleon scattering

Abstract Dispersion relations for nucleon-nucleon scattering are presented. The general case of nonforward scattering is treated, although the majority of the discussion is confined to the limiting cases of forward scattering and the non-relativistic approximation. It is shown that in the relativistic case the dispersion relations for nucleon-nucleon scattering necessarily involve the nucleon-antinucleon amplitude. Some qualitative conclusions are drawn about the differences between the nucleon-nucleon and nucleon-antinucleon interactions. The concept of a potential in quantum field theory is discussed briefly.

The bound states of weakly coupled long-range one-dimensional quantum hamiltonians

Abstract We study the small λ behavior of the ground state energy, E ( λ ), of the Hamiltonian −( d 2 dx 2 ) + λV(x) . In particular, if V ( x ) ∼ − ax −2 at infinity and if 69-1, we prove that (−E(λ)) 1 2 = −[ 1 2 λ + aλ 2 lnλ] ∫ dxV(x) + O(λ 2 ) .

Elastic neutron-deuteron scattering

Abstract The process of elastic neutron-deuteron scattering is discussed from the standpoint of dispersion theory. Aside from the appearance of anomalous thresholds, there seems to be no difficulties in principle, although no derivation of the relations is attempted. Certain features of the process, such as the pick-up peak in the backyard direction, appear quite neatly and the general occurrence of such phenomena is discussed. The theory is developed for the general case, but our only application is to forward scattering at low energies where phase shift analyses are available. The agreement with experiment is quite good.

Diffractive dissociation within multiperipheral dynamics

Abstract The relationship of diffractive dissociation to multiperipheral dynamics is explored within the framework of the ABFST model. After splitting the kernel of the integral equation into “resonance” and “Pomeranchuk” components, a variational technique is employed to treat the Pomeranchuk component as a small perturbation. The corresponding perturbed structure of the Fredholm determinant is developed in detail, leading to identification of a small dimensionless parameter η P which measures the strength of the APS branch point and thereby sets the scale of Regge fine structure near J = 1. It is shown that η P also determines the probability of diffractive dissociation into large masses and thus is subject to experimental determination.

Application of dispersion relations to nucleon-nucleon scattering: The two-pion contribution

Abstract The two-pion contribution to the amplitude for nucleon-nucleon scattering is computed in terms of the invariant amplitudes which characterize the four-body Greens function of the pion nucleon system. The dependence of this contribution upon the momentum transfer of the two-nucleon system is completely exhibited. A general method is described for the derivation of symmetry properties for the invariant coefficients in the expansion of the scattering amplitude in spinor space.

Valentine Louis Telegdi

On 8 April 2006, Valentine Louis Telegdi died in Pasadena, California, of complications following surgery for an aortic aneurysm. With his passing the physics community lost one of its most original and distinguished members. Val’s contributions to our understanding of weak and electromagnetic interactions are seminal. Beyond those contributions, though, what made Val unique was the depth of his understanding of the theoretical fine points of the physics, which in his fundamental particle-physics experiments led him to beautiful and far from obvious ways of testing an idea. A Telegdi experiment was always marked as much by the conceptual cleverness of its design as by the importance of its results.