Breakup of three particles within the adiabatic expansion method

Abstract

General expressions for the breakup cross sections in the lab frame for $1+2$ reactions are given in terms of the hyperspherical adiabatic basis. The three-body wave function is expanded in this basis and the corresponding hyperradial functions are obtained by solving a set of second order differential equations. The $\mathcal{S}$-matrix is computed by using two recently derived integral relations. Even though the method is shown to be well suited to describe $1+2$ processes, there are nevertheless particular configurations in the breakup channel (for example those in which two particles move away close to each other in a relative zero-energy state) that need a huge number of basis states. This pathology manifests itself in the extremely slow convergence of the breakup amplitude in terms of the hyperspherical harmonic basis used to construct the adiabatic channels. To overcome this difficulty the breakup amplitude is extracted from an integral relation as well. For the sake of illustration, we consider neutron-deuteron scattering. The results are compared to the available benchmark calculations.

References in corpus (16)

• Momentum-space treatment of Coulomb interaction in three-nucleon reactions with two protons
• Momentum-space description of three-nucleon breakup reactions including the Coulomb interaction
• Polarization observables in p-d scattering below 30 MeV
• Three-body halos. V. Computations of continuum spectra for Borromean nuclei
• Benchmark calculation for proton-deuteron elastic scattering observables including Coulomb
• Bound state techniques to solve the multiparticle scattering problem
• Integral relations for three-body continuum states with the adiabatic expansion
• proton-deuteron elastic scattering above the deuteron breakup
• The Kohn Variational Principle for Elastic Proton--Deuteron Scattering above Deuteron Breakup Threshold
• Variational description of continuum states in terms of integral relations
• N-d scattering above the deuteron breakup threshold
• General integral relations for the description of scattering states using the hyperspherical adiabatic basis
• Recombination rates from potential models close to the unitary limit
• Integral relations and the adiabatic expansion method for 1+2 reactions above the breakup threshold: Helium trimers with soft-core potentials
• Three-Nucleon Continuum by means of the Hyperspherical Adiabatic Method
• Boundary Conditions for Three-Body Scattering in Configuration Space

Cited by in corpus (6)

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• Three-body recombination of two-component cold atomic gases into deep dimers in an optical model
• The $p\Lambda$ and $pp\Lambda$ correlation functions
• Deuteron-alpha scattering: separable vs nonseparable Faddeev approach
• Convergence of the $ppp$ correlation function within the hyperspherical adiabatic basis
• Direct and sequential four-body recombination rates at low temperatures