Three-Nucleon Continuum by means of the Hyperspherical Adiabatic Method

TL;DR

This paper explores the use of the Hyperspherical Adiabatic basis to describe three-body scattering states, comparing it with Hyperspherical Harmonic expansion and analyzing different asymptotic coordinate choices through neutron-deuteron scattering examples.

Contribution

It introduces the application of the Hyperspherical Adiabatic basis to three-body scattering states and compares its effectiveness with other methods and coordinate choices.

Findings

Hyperspherical Adiabatic basis is less efficient for scattering states than for bound states.

Comparison shows differences in convergence patterns between coordinate choices.

Numerical examples highlight the method's advantages and limitations.

Abstract

This paper investigates the possible use of the Hyperspherical Adiabatic basis in the description of scattering states of a three-body system. In particular, we analyze a 1+2 collision process below the three-body breakup. The convergence patterns for the observables of interest are analyzed by comparison to a unitary equivalent Hyperspherical Harmonic expansion. Furthermore, we compare and discuss two different possible choices for describing the asymptotic configurations of the system, related to the use of Jacobi or hyperspherical coordinates. In order to illustrate the difficulties and advantages of the approach two simple numerical applications are shown in the case of neutron-deuteron scattering at low energies using s-wave interactions. We found that the optimization driven by the Hyperspherical Adiabatic basis is not as efficient for scattering states as in bound state applications.