Three-Nucleon Continuum by means of the Hyperspherical Adiabatic Method

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.

29 pages, 5 figures, accepted for publication in Few-Body Systems (in press)

References in corpus (6)

• Study of bound and scattering states in three-nucleon systems
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• Variational description of the Helium trimer using correlated hyperspherycal harmonic basis functions
• The complex Kohn variational method applied to N-d scattering
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Cited by in corpus (9)

• Non-symmetrized hyperspherical harmonic basis for $A$-bodies
• The helium trimer with soft-core potentials
• Integral relations for three-body continuum states with the adiabatic expansion
• Variational description of continuum states in terms of integral relations
• Breakup of three particles within the adiabatic expansion method
• General integral relations for the description of scattering states using the hyperspherical adiabatic basis
• Integral relations and the adiabatic expansion method for 1+2 reactions above the breakup threshold: Helium trimers with soft-core potentials
• Nuclear Reactions: A Challenge for Few- and Many-Body Theory
• Hyperspherical approach to atom--dimer collision with the Jacobi boundary condition