General integral relations for the description of scattering states using the hyperspherical adiabatic basis

Abstract

In this work we investigate 1+2 reactions within the framework of the hyperspherical adiabatic expansion method. To this aim two integral relations, derived from the Kohn variational principle, are used. A detailed derivation of these relations is shown. The expressions derived are general, not restricted to relative $s$ partial waves, and with applicability in multichannel reactions. The convergence of the $\mathcal{K}$-matrix in terms of the adiabatic potentials is investigated. Together with a simple model case used as a test for the method, we show results for the collision of a ${}^4$He atom on a \dimer dimer (only the elastic channel open), and for collisions involving a ${}^6$Li and two ${}^4$He atoms (two channels open).

Accepted for publication in Physical Review A

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Cited by in corpus (12)

• Effective Field Theory Analysis of Three-Boson Systems at Next-To-Next-To-Leading Order
• ${}^4\mathrm{He}$+$n$+$n$ continuum within an ab initio framework
• The helium trimer with soft-core potentials
• Ab initio calculations of nuclear widths via an integral relation
• Breakup of three particles within the adiabatic expansion method
• 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
• Theoretical description of three- and four-nucleon scattering states using bound-state-like wave functions
• Three-body continuum wave functions with a box boundary condition
• Combined few-body and mean-field model for nuclei
• Three-body continuum states and Efimov physics in non-integer geometry
• Hyperspherical approach to atom--dimer collision with the Jacobi boundary condition