The effect of antisymmetrization in diquark models of baryons.
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Date
1997
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Abstract
In this thesis the effect of antisymmetrization in diquark models of baryons composed of light
(u and d) quarks is investigated. The diquark in this study is considered alternately as a pointlike
and as a composite particle. The wave functions for both diquark and diquark-quark
systems have been determined in a non-relativistic approximation by using the radial
Schrodinger equation and a range ofcentral potentials. The ground state masses ofthe diquarkquark
system have been calculated in three distinct ways:
(1) The ground state energy eigenvalues and the wave functions for thediquark and diquarkquark,
each being treated as a two-body system, have been calculated by using the generalized
Runge-Kutta and search methods.
(2) The expectation values for the potential energy and kinetic energy have been calculated
by using the wave functions derived in (1) for the two-body system without antisymmetrization.
These results have been checked by applying the virial theorem in parallel calculations.
(3) The potential and kinetic energy expectation values have also been determined by taking
antisymmetrization into account via operator kernels namely, norm, potential and kinetic energy
which have been derived by using the non-local Generator Coordinate Method (GCM). The
expectation values of these operator kernels have been calculated with respect to the wave
functions produced in (1). For the purpose of performing the integrations the wave functions
, expanded in terms of cubic splines, and Gaussian quadrature have been employed.
Lastly the diquark and diquark-quark ground state masses were calculated for each
approach, (1) - (3), and compared with
(a) each other,
(b) the results for a two-body system,
(c) the results for a full three-body treatment and,
(d) the average mass of N- b:. .
The form factors and root mean square radii ofthe baryon for the four central potentials have
been calculated with antisymmetrization for each approach (1) - (3) and compared with
(a) each other,
(b) the results for the baryon without antisymmetrization
(c) the results for the baryon with antisymmetrization including the meson cloud
(d) the experimental data.
The trends found are striking and it can be concluded that there is a strong dynamical effect
due to the presence of antisymmetrization in diquark models of baryons.
Description
Thesis (M.Sc.)-University of Natal, Pietermaritzburg, 1997.
Keywords
Baryons., Theses--Physics.