Variational description of continuum states in terms of integral relations

Abstract

Two integral relations derived from the Kohn Variational Principle (KVP) are used for describing scattering states. In usual applications the KVP requires the explicit form of the asymptotic behavior of the scattering wave function. This is not the case when the integral relations are applied since, due to their short range nature, the only condition for the scattering wave function $\Psi$ is that it be the solution of $(H-E)\Psi =0$ in the internal region. Several examples are analyzed for the computation of phase-shifts from bound state type wave functions or, in the case of the scattering of charged particles, it is possible to obtain phase-shifts using free asymptotic conditions. As a final example we discuss the use of the integral relations in the case of the Hyperspherical Adiabatic method.

34 pages, 7 figures, accepted in Phys. Rev. C

References in corpus (7)

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• Quantum Monte Carlo calculations of neutron-alpha scattering
• Four-nucleon scattering: Ab initio calculations in momentum space
• Proton-${}^3$He elastic scattering at low energies
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Cited by in corpus (13)

• Bound state techniques to solve the multiparticle scattering problem
• Solution of n-${}^4$He elastic scattering problem using Faddeev-Yakubovsky equations
• Non-symmetrized hyperspherical harmonic basis for $A$-bodies
• ${}^4\mathrm{He}$+$n$+$n$ continuum within an ab initio framework
• The helium trimer with soft-core potentials
• Exploring continuum structures with a pseudo-state basis
• Ab initio calculations of nuclear widths via an integral relation
• 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
• The $p\Lambda$ and $pp\Lambda$ correlation functions
• Theoretical description of three- and four-nucleon scattering states using bound-state-like wave functions
• Selected Topics in Three- and Four-Nucleon Systems