Browsing by Subject "Quantum scattering theory"

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    Multi-variate Bateman method for two-body scattering without partial-wave decomposition
    (Springer Netherlands, 2014) Kuruoğlu, Z. C.
    The use of Bateman method for solving the two-variable version of the two-body Lippmann-Schwinger equation without recourse to partial-wave decomposition is investigated. Bateman method is based on a special kind of interpolation of the momentum representation of the potential on a multi-variate grid. A suitable scheme for the generation of a multi-variate Cartesian grid is described. The method is tested on the Hartree potential for electron-hydrogen scattering in the static no-exchange approximation. Our results show that the Bateman method is capable of producing quite accurate solutions with relatively small number of grid points.
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    Rearrangement and breakup amplitudes from the solution of Faddeev-AGS equations by pseudo-state discretization of the two-particle continuum
    (Elsevier BV, 2024-08-08) Kuruoğlu, Zeki Cemal
    The AGS equations for rearrangement transition operators in the three-particle problem are turned into a set of effective multi-channel two-body equations using the pseudo-state discretization of the two-particle resolvent. The resulting effective equations are LS-type integral equations in the spectator degrees of freedom, much like the LS equations of multichannel inelastic scattering. In particular, the effective potential matrix is real, energy-independent and non-singular, while the propagator matrix has only simple poles. Difficulties associated with the moving singularities of the effective potential matrix in the usual separable-T approach to AGS equations are avoided. After regularization of the kernel via subtraction procedures well known from two-particle scattering, the set of coupled LS-type equations in the spectator momenta are solved rather straightforwardly by the Nyström method. Solutions of effective two-body equations are then used to calculate the breakup amplitudes using the well-known relationship between rearrangement and breakup amplitudes. Calculations using a local momentum-space basis on a benchmark model of the n+d collision show that rather accurate results for elastic and breakup amplitudes can be obtained with rather small bases.