Three-Body Problem with Separable Potentials. II.n−dScattering

Abstract

The three-body formalism, using separable potentials in s and p states of nucleon pairs, is set up under the conditions of full antisymmetrization of the three-nucleon wave function. The formalism is applied to the problem of n-d scattering, where the effects of "polarization" are fully taken into account. The amplitudes for quartet and doublet scattering are found to satisfy two-and four-coupled one-dimensional integral equations, respectively. The quartet scattering length is found to agree with the figure for the so-called experimental set I for this parameter. The doublet scattering length, on the other hand, is found to be much more sensitive to the details of the potentials, thus preventing a theoretical resolution of its ambiguity within the present formalism without tensor forces.

Exact Calculation of Triton Parameters with Realistic Potentials

“…It is seen that while the inclusion of tensor forces brings about a small increase in the [2,1] or S' part of P 0 , over a calculation with a pure s-wave interaction, this still falls far short of Schiff's 13 requirement of 4% to account for the observed difference in the H 3 and He 3 magnetic form factors. On the other hand, this value is in qualitative agreement with the variational results of Blatt and Delves, 14 using the (more classical) Gammel-Thaler, Hamada-Johnson, and Yale potentials.…”

Faddeev Formalism for Four-Particle Systems

“…(13) simplifies considerably in the case of identical particles when amplitudes of the appropriate symmetry are used. Furthermore, separable two-body interactions, which are known to reduce three-body calculations to ones which are no more difficult than two-body calculations, [9][10][11] should reduce the four-body equations to the level of a three-body problem. In fact a preliminary attempt on similar lines at understanding the a particle as a bound state of four nucleons 12 already indicates the possibility of a tractable numerical scheme when the appropriate symmetries are taken into account in a four-particle Schrodinger equation.…”

The solvable three-dimensional rank-two separable potential model: partial-wave scattering

“…The formation of a resonance, which occurs as an unstable intermediate state in scattering processes, introduces a time delay between the arrival of the incident wave and its departure from the collision region. This property has been examined in many works [13,22]. The partial-wave time delay τ ≡ 2 q dδ l dq can be used to estimate the resonance energy, since τ should rapidly rise as a function of momentum (or energy) and reach its peak near a resonance indicating its location.…”

“…The theory of separable potentials was first proposed for the 3 S 1 nucleon-nucleon interaction by Yamaguchi [9,10]. The behavior of a certain kind of nonlocal potential has been studied by Mitra et al [11][12][13] in the complex angular momentum plane. Tabakin [14,15] used a set of separable potentials with small off-energy-shell T-matrix elements, matching the s, p and d-wave nucleon-nucleon phase parameters without generating the usual strong short-range correlations.…”