Generalization of the Numerov method for solution ofNdbreakup problem in configuration space

Abstract

A new computational method for solving the configuration-space Faddeev equations for three-nucleon systems has been developed. This method is based on the spline decomposition in the angular variable and a generalization of the Numerov method for the hyperradius. The s-wave calculations of the inelasticity and phase shift as well as breakup amplitudes for n-d and p-d breakup scatterings for lab energies 14.1 and 42.0 MeV were performed with the Malfliet-Tjon I-III potential. In the case of n-d breakup scattering the results are in good agreement with those of the benchmark solution [J. L. Friar, B.

Benchmark calculation for proton-deuteron elastic scattering observables including the Coulomb interaction

“…Although there is a long history of theoretical work on the solution of the Coulomb problem in three-particle scattering [1,2,3,4,5,6,7], the work of Refs. [3,4] pioneered the effort on fully converged numerical calculations for proton-deuteron (pd) elastic scattering including the Coulomb repulsion between protons together with realistic nuclear interactions.…”

Publisher's Note: Momentum-space description of three-nucleon breakup reactions including the Coulomb interaction [Phys. Rev. C 72, 054004 (2005)]

“…Whereas it has already been solved for elastic proton-deuteron (pd) scattering with realistic hadronic interactions using various procedures [1,2,3,4,5], there are only very few attempts [6,7,8] to calculate pd breakup, and none of them uses a complete treatment of the Coulomb interaction and realistic hadronic potentials allowing for a stringent comparison with the experimental data.…”

“…References [7,8] have provided first results for pd breakup, but they still involve approximations in the treatment of Coulomb and the employed hadronic dynamics is not realistic. Thus, a benchmark comparison between our breakup results and corresponding configuration space results is, in contrast to pd elastic scattering [16], not possible yet.…”

The general configuration-space Faddeev formalism for studying pd scattering

“…where it is understood that in Φ(i, k, l) particles are grouped as i + (kl) and Φ 1 is antisymmetric in the last pair of arguments: Φ 1 (1, 2, 3) = −Φ 1 (1,3,2). As function Φ 2 (2, 3, 1) has no definite properties under interchange 3 ↔ 1 we encounter permutations which are not cyclic P 12 (231) = (321), P 13 (123) = (321).…”

“…As function Φ 2 (2, 3, 1) has no definite properties under interchange 3 ↔ 1 we encounter permutations which are not cyclic P 12 (231) = (321), P 13 (123) = (321). In terms of these operators and operators P ± we obtain for the independent components Φ 1 and Φ 2 a system (3,1) is the pure nuclear potential:…”