908887 SzGeCERN 20060612114351.0 eng Sitnikov, G V Quantum-mechanical and semiclassical study of the collinear three- body Coulomb problem resonances 2005 This paper continues a quantum-mechanical (QM) and semiclassical (SC) study of the collinear three-body Coulomb problem "O. I. Tolstikhin and C. Namba, 70, 062721 (2004)", extending it to resonances. Our QM treatment is based on the theory of Siegert pseudostates (SPS) implemented in hyperspherical coordinates by means of the slow/smooth variable discretization method. A consistent formulation of this approach for arbitrary dimension of configuration space and number of open channels is given. Not only resonance energy and total width, but also partial widths are defined in terms of the SPS; for the cases of one and two open channels, they are expressed in terms of the SPS eigenvalues only. The SC results are obtained in the leading- order approximation from the asymptotic solution of the problem for h to 0, where h is a dimensionless parameter that depends only on the masses of particles, varies in the interval 0<or=h<or=1, and has the meaning of an effective Planck's constant for the motion in hyperradius. It is shown that resonance widths as functions of 1/h oscillate with an exponentially decaying amplitude and almost constant period. The SC theory qualitatively explains such a behavior as a manifestation of interference effects in the nonadiabatic process of decay of the resonance state and provides surprisingly good quantitative results even for systems with h~1. SIS INSP2005 8344380 SzGeCERN Other Fields of Physics INSPEC Siegert pseudostates eigenvalues INSPEC asymptotic solution INSPEC collinear three body Coulomb problem INSPEC configuration space INSPEC effective Plancks constant INSPEC exponentially decaying amplitude INSPEC hyperradius INSPEC hyperspherical coordinates INSPEC interference effects INSPEC leading order approximation INSPEC nonadiabatic process INSPEC open channels INSPEC particle masses INSPEC quantum mechanical study INSPEC resonance energy INSPEC resonance widths INSPEC semiclassical theory INSPEC slow variable discretization method INSPEC smooth variable discretization method ARTICLE INSPEC N-body-problems INSPEC Schrodinger-equation INSPEC resonant-states Tolstikhin, O I 10.1103/PhysRevA.71.022708 22708-1-12 2 Phys. Rev. A 71 2005 Moscow Inst of Phys & Technol, Dolgoprudnyi, Russia n 200552 13 20071119 1301 CER01 20051121 PUBLIC 002578807CER ARTICLE