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 (1)

• Three-Nucleon Continuum by means of the Hyperspherical Adiabatic Method

Cited by in corpus (5)

• Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons
• Three-body recombination of two-component cold atomic gases into deep dimers in an optical model
• The $p\Lambda$ and $pp\Lambda$ correlation functions
• Convergence of the $ppp$ correlation function within the hyperspherical adiabatic basis
• Direct and sequential four-body recombination rates at low temperatures