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HK: Hadronen und Kerne
HK 55: Structure of Baryons, Mesons VIII, Theory
HK 55.3: Vortrag
Mittwoch, 18. März 1998, 15:00–15:15, J
Convergence of the Algebraic Method for scattering — •W Vanroose, V Vasilevski, F Arickx, and J Broeckhove — Universiteit Antwerpen Groenenborgerlaan 171, 2020 Antwerpen, Belgium
In the algebraic method for scattering, continuum states are expanded in L2 eigenstates of a bound state problem. The most commonly used eigenbasis is the oscillator basis [1]. Traditionaly there exist two regions for the expansion coefficients cn: an internal region where they satisfy the Schrödinger matrix equation and an asymptotic region where they are a combination of the regular and the irregular solution. The two regions are matched at n=N [2].
We investigate a new approach [3] that features three regions: an internal and asymptotic region as before, and an intermediate region where a three-term recurrence relation, modified by asymptotic contribution of the scattering potential, determines the cn. The advantage is a reduction in numerical effort corresponding to a reduction in the size of the internal region. The convergence depends critically on the ranges of the bound and scattering potentials. We investigate this aspect for a number of model potentials. For example, with the gaussian, we are able to reduce the number of oscillator basis states with an order of magnitude.
[1] Vasilevsky V, Filippov G, Arickx F, Broeckhove J, Van Leuven P, J. Phys G: nuclear physics, 18, 1227 (1992)
[2] Heller E J, Yamani H A, Phys. Rev. A 9, 1201 (1974)
[3] Vasilevsky V S and Arickx F, Phys. Rev. A 55, 265 (1997)