The three-body bound state problem is considered using configuration-space Faddeev equations within the framework of the total-angular-momentum representation. Different
three-body systems are considered, the main concern of the investigation being the
i) calculation of binding energies for weakly bounded trimers, ii) handling of systems
with a plethora of states, iii) importance of three-body forces in trimers, and iv) the
development of a numerical technique for reliably handling three-dimensional integrodifferential
equations. In this respect we considered the three-body nuclear problem, the
4He trimer, and the Ozone (16 0 3 3) system.
In practice, we solve the three-dimensional equations using the orthogonal collocation
method with triquintic Hermite splines. The resulting eigenvalue equation is handled
using the explicitly Restarted Arnoldi Method in conjunction with the Chebyshev polynomials to improve convergence. To further facilitate convergence, the grid knots are distributed quadratically, such that there are more grid points in regions where the potential is stronger. The so-called tensor-trick technique is also employed to handle
the large matrices involved. The computation of the many and dense states for the Ozone case is best implemented using the global minimization program PANMIN based
on the well known MERLIN optimization program. Stable results comparable to those of other methods were obtained for both nucleonic and molecular systems considered. / Physics / D.Phil. (Physics)
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:unisa/oai:umkn-dsp01.int.unisa.ac.za:10500/1145 |
| Date | 30 November 2004 |
| Creators | Lekala, Mantile Leslie |
| Contributors | Braun, M., Sofianos, S.A. |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | 1 online resource (vii, 91 leaves) |
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