The role of three-body forces in few-body systems
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Authors
Masita, Dithlase Frans
Issue Date
2006-11-30
Type
Dissertation
Language
en
Keywords
Three-body forces , Differential Faddeev equations , Eigenvalue equations , Restarted Arnoldi algorithm , Orthogonal collocation procedure
Alternative Title
Abstract
Bound state systems consisting of three nonrelativistic particles are numerically
studied. Calculations are performed employing two-body and three-body forces as
input in the Hamiltonian in order to study the role or contribution of three-body
forces to the binding in these systems. The resulting differential Faddeev equations
are solved as three-dimensional equations in the two Jacobi coordinates and the
angle between them, as opposed to the usual partial wave expansion approach. By
expanding the wave function as a sum of the products of spline functions in each of
the three coordinates, and using the orthogonal collocation procedure, the equations
are transformed into an eigenvalue problem.
The matrices in the aforementioned eigenvalue equations are generally of large order.
In order to solve these matrix equations with modest and optimal computer memory
and storage, we employ the iterative Restarted Arnoldi Algorithm in conjunction
with the so-called tensor trick method. Furthermore, we incorporate a polynomial
accelerator in the algorithm to obtain rapid convergence. We applied the method
to obtain the binding energies of Triton, Carbon-12, and Ozone molecule.
Description
Citation
Masita, Dithlase Frans (2006) The role of three-body forces in few-body systems, University of South Africa, Pretoria, <http://hdl.handle.net/10500/1402>