Hyperspherical harmonics and the nuclear four-body problem

ANNALS

OF PHYSICS

95, 227-228 (1975)

Abstracts Hyperspherical

lnstituto

of Papers

Harmonics

and the Nuclear

de Fisica, Universidad

National

to Appear Four-Body

in Future Problem.

E.

Issues

CHAC~N

AND

A.

AMAYA.

de Mexico, A. P. 20364, Mexico 20, D.F.

A method proposed earlier by Aguilera, Moshinsky, and Kramer, for adapting a system of translationally invariant four-particle harmonic oscillator functions to the symmetry of the permutation group S(4), is applied to hyperspherical harmonic functions depending on three relative vectors. Except for a few cases in which diagonalization of matrices is required, the method gives closed formulas for orthonormal sets of harmonic functions with good permutational symmetry. The matrix elements of S(4) permutations with respect to the harmonic functions are obtained. Saturation of Isospin ?rN-Scattering. D.

Bounds

and

Constraints

on Experimental

Data

and Amplitude

Analysis

in

B. ION. Joint Institute for Nuclear Research, Dubna, Moscow, P.O. Box 79,

U.S.S.R. In this paper we prove new and interesting isospin bounds in pion-nucleon scattering and we investigate their saturations using the CERN-phase shift analysis. These isospin bounds are saturated exactly along certain lines in the (P bin, cos @-plane and impose strong constraints on experimental data and amplitude analyses. Also, we obtain all constraints on data and amplitude analysis when different isospin bounds are saturated or degenerated. Finite

Concentrations

of Localized

Moments

in Metals.

J.

C.

STODDART.

Department of Physics,

The University, Sheffield, SlO 2TN, England. In earlier work, density functional methods have been used to study the magnetism of pure metals and the problem of local moment formation on a single magnetic impurity. In the present paper these methods are reviewed and applied to the case of an arbitrary concentration of impurity atoms. It is shown that the Hartree-Fock treatment of the system and a local environment effect can be reproduced very easily in the density functional framework. More importantly, the present formulation allows one some insight into the effects of correlation. Although correlation density functionals are difficult to obtain, it is shown that a class of models of the many impurity system can be solved exactly. Use of the Wigner

Representation

in Scattering

College of William and Mary, Williamsburg,

Problems.

Virginia

E. A. 23185

REMLER.

Department of Physics,

The basic equations of quantum scattering are translated into the Wigner representation. This puts quantum mechanics in the form of a stochastic process in phase space. Instead of complex valued wavefunctions and transition matrices, one now works with real-valued probability distributions and source functions, objects more responsive to physical intuition. Aside from writing out certain necessary basic expressions, the main purpose of this paper is to develop and stress the interpretive picture associated with this representation and to derive results used in applications published elsewhere. The quasiclassical guise assumed by the formalism lends itself particularly to approximations of complex multiparticle scattering problems. We hope to be laying the foundation for a systematic application of statistical approximations to such problems.

227 Copyright All rights

0 1975 by Academic Press, Inc. of reproduction in any form reserved.