K. L. Kowalski

Unitarity and the optical potential

Abstract The optical potential for the elastic scattering of two nuclear fragments with the full inclusion of the Pauli principle is considered. It is shown using unitarity that the optical potential, defined in terms of the Alt, Grassberger and Sandhas off-shell extension of the transition operator, has no singularities across the elastic unitarity cut. Similar results are obtained for general rearrangement scattering.

Transition Matrix for Nucleon‐Nucleon Scattering

As part of a study of the influence of off‐the‐energy‐shell effects on the optical potential for nucleon‐nucleus scattering, a method is presented for the calculation, via the reactance matrix, of the nucleon‐nucleon transition matrix in terms of an internucleon potential and the scattering amplitude. The singular integral equations for the partial‐wave amplitudes of the reactance matrix are reduced to a Fredholm form which contains the scattering amplitude parametrically. The iteration solution of these Fredholm equations is shown to be generally unreliable; however, the zeroth‐order iteration approximates the exact solution quite well near the energy shell. The replacement of the kernels of these integral equations by separable functions is discussed; the validity of such an approximation is illustrated by a simple example. The requirement that the solutions of the (exact) Fredholm equations be consistent with the original singular integral equations yields a solution for the scattering amplitude in ter...

Search for disoriented chiral condensate at the Fermilab Tevatron

We present results from MiniMax (Fermilab T-864), a small test/experiment at the Fermilab Tevatron designed to search for the production of a disoriented chiral condensate (DCC) in p-p(bar sign) collisions at {radical}(s)=1.8 TeV in the forward direction, {approx}3.4<{eta}<{approx}4.2. Data, consisting of 1.3x10{sup 6} events, are analyzed using the robust observables developed in an earlier paper. The results are consistent with generic, binomial-distribution partition of pions into charged and neutral species. Limits on DCC production in various models are presented. (c) 2000 The American Physical Society.

OPTIMAL EQUATIONS FOR THREE-PARTICLE SCATTERING.

Abstract In this paper we investigate two differing approaches to the three-body scattering problem—that of Faddeev and Lovelace. We find a simple operator connection between the two methods and use this connection to give a physical justification of Faddeevs residue prescription for determining those three-body scattering amplitudes in which a two-particle bound state is in the initial and/or final configuration. Based on these results, we present derivations of a class of integral equations for simple and natural half-off shell extensions of the breakup and rearrangement amplitudes.

Analysis of charged-particle–photon correlations in hadronic multiparticle production

In order to analyze data on joint charged-particle/photon distributions from an experimental search (T-864, MiniMax) for disoriented chiral condensate (DCC) at the Fermilab Tevatron collider, we have identified robust observables, ratios of normalized bivariate factorial moments, with many desirable properties. These include insensitivity to many efficiency corrections and the details of the modeling of the primary pion production, and sensitivity to the production of DCC, as opposed to the generic, binomial-distribution partition of pions into charged and neutral species. The relevant formalism is developed and tested in Monte-Carlo simulations of the MiniMax experimental conditions.

Multiple scattering, optical potential, and N-body approaches to elastic two-fragment collisions

Two-fragment elastic scattering problems are often studied using multiple scattering theories such as those due to Watson along with Feshbach-type optical potentials. These conventional methods are re-examined, rephased, and generalized using the language and techniques of contemporary N-particle scattering theory. A special realization of the latter theory is developed which is especially useful for relating the older and newer methods. This is facilitated by maintaining the same off-shell continuations of the scattering operators in both approaches. In particular, a set of connected-kernel scattering integral equations is introduced which provides a consistent N-particle framework for the calculation of that definition of the optical potential possessing the Feshbach off-shell continuation. These equations exhibit a multiple-scattering substructure and therefore allow the systematic generalization of some of the usual low-order approximations.

Partition combinatorics and multiparticle scattering theory

The recently developed combinatoric methods for handling partition‐labeled operators in N‐particle scattering theory are studied from an abstract point of view. The relation of these methods to approaches of the cluster/cumulant type in many areas of mathematical physics is pointed out. The concept of connectedness is defined abstractly and the mathematical structure of the partition lattice is considered in detail. Many of the useful results of combinatoric scattering theory are shown to be natural expressions of properties of the partition lattice. The conditions on these results can then be stated with precision. A number of new operator theorems are also obtained by means of applying simple extensions and analogs of the known properties of the partition lattice.

Generalization and applications of the sasakawa theory

Abstract The Sasakawa theory of scattering is phrased in the form of a Fredhohn reduction technique for integral equations possessing a fixed-point singularity in their kernels. This permits the generalization of this theory to a large variety of scattering integral equations. Some specific applications include the two-particle off-shell and multichannel scattering problems. In the first instance a rank-three approximation to the fully off-shell transition matrix is derived which is exact on and half-off shell, satisfies off-shell unitarity, and which possesses no unphysical singularities. In the second problem it is shown how the method leads to the generation of a unitary approximation to the multichannel amplitudes.

Partition permuting array approach to few‐body Hamiltonian models of nuclear reactions

The approximate Hamiltonian formulation of many‐body scattering recently proposed by Polyzou and Redish is used to derive approximate Baer–Kouri–Levin–Tobocman (BKLT) integral equations. It is shown that these equations have connected kernels after a finite number of iterations and the approximation defined by them is unitary. Integral equations imbedding the approximation in the exact theory are also given. Some lemmas which relate to the connectivity of operator products are established and are employed to prove the connected‐kernel properties of both the BKLT as well as the imbedding integral equations

N-Body Systems

The designation “N-Body Systems” covers a lot of ground. The exclusion of N = ∞ (nuclear matter, e.g.) and N ≤ 3 helps us somewhat. However, we have to delimit our discussion further in order to represent the emphasis of much of the work carried out in the past few years as well as that reported to this conference. To this end we confine ourselves to the so-called N-particle approach to scattering. By this we mean, essentially, the extension of the Faddeev point of view to the scattering of nonrelativistic systems of finite numbers (≥ 4) of particles which interact through short-range (plus possible Coulomb) potentials. We take this to include the deduction of few-body models of many-particle scattering but not those calculations which only assume such a model as a starting point. The latter work is considered elsewhere in this conference (DS,8). The four-hadron system is also considered elsewhere (DS,7)so that we do not review any of the interesting N = 4 calculations.