Darmstadt 2008 – wissenschaftliches Programm

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HK: Fachverband Physik der Hadronen und Kerne

HK 34: Postersitzung

HK 34.78: Poster

Donnerstag, 13. März 2008, 14:00–16:00, Poster C3

Quantum scattering theory on a lattice in momentum space — •Vladimir Pomerantsev, Olga Rubtsova, and Vladimir Kukulin — Institut für Theoretische Physik, Universität Tübingen

It is well known that the few-body quantum scattering theory leads to multidimensional integral equations with highly complicated singular kernels above three- and more particle breakup thresholds. This complexity of resulted equations makes their practical solution to be highly nontrivial numerical task [1]. To avoid these complicated singularities, some time ago we proposed [2,3] a new wave-packet approach in which the exact scattering wavefunctions (which are not vectors in Hilbert space) are replaced with normalized stationary wave packets. This approximation leads to replacement of complicated integral equations by matrix equations, the corresponding matrix elements (in an analytical form) having singularities much smoothed as compared to the original integral kernels. In the moment space this approach leads to some lattice approximation for the multidimensional integral equations. Thus, the highly singular integral kernels, being averaged over the lattice cells, results in a rather smooth matrices. The authors present in the talk numerous illustration for three-nucleon scattering above breakup threshold demonstrating the high efficiency of the lattice discretization for solution of the scattering equations.

1. W. Gloeckle et al., Phys. Rep. 274, 107 (1996).

2. V.I. Kukulin, V.N. Pomerantsev, O.A. Rubtsova, Theor. Math. Phys. 150, 474 (2007).

3. V.I. Kukulin, O.A. Rubtsova, Phys. Rev. C 76, 047601 (2007).