123004618
Comment on `Failure of the connected-kernel method'
In a recent paper by Komarov et al., the claim is made that the coupled Faddeev-type equations for a system of two noninteracting particles in a fixed potential do not have a unique solution. It is shown here that the claim is not justified. Moreover, it is shown that the phenomenon on which the claim is based occurs even in a true three-body system of three finite-mass particles. Therefore, the property is not, as has been asserted, a consequence of the total Hamiltonian being the sum of commuting sub-Hamiltonians.
122265419
KRAUSS--KOWALSKI CALCULATIONS OF NUCLEON--DEUTERON POLARIZATION.
120648410
MULTIPLE-SCATTERING ANALYSIS ON A SOLUBLE NEUTRON--DEUTERON MODEL.
122386499
Equations for Four-Particle Scattering
119889919
On choosing the points in product integration
A product‐integration rule for the integral Fbak (t)  f (t)  dt is a rule of the form Jni=1wi f (ti), with the weights w1,...,wn chosen so that the rule is exact if f is any linear combination of a chosen set of functions φ1,...,φn . For some choices of {φj}, including the polynomial case, the points {ti} need to be carefully chosen if reliable results are to be obtained. In this paper known convergence results for the polynomial case with well‐chosen points are summarized and illustrated, and extended to some nonpolynomial cases, including one proposed by Y.E. Kim for use in solving the three‐body Faddeev equations. The convergence theorems yield practical prescriptions for choosing the points {ti} .
121372340
Method for three-body equations
A recently proposed degenerate-kernel scheme for solving Fredholm integral equations of the second kind gave very good results for Lippmann-- Schwinger equations. The method is here extended to give a very simple and practical method for the three-body equations with separable two-body interactions. Numerical calculations of the three-body amplitudes are carried out at positive energies for two simple models. In spite of the more complicated singularities in the kernel as well as in the solutions of the equation, satisfactory convergence is achieved.