Quantum Monte Carlo Calculations of Three and Six -Quark States
Paris, Mark Wayne
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https://hdl.handle.net/2142/80697
Description
Title
Quantum Monte Carlo Calculations of Three and Six -Quark States
Author(s)
Paris, Mark Wayne
Issue Date
2001
Doctoral Committee Chair(s)
Vijay R. Pandharipande
Department of Study
Physics
Discipline
Physics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Physics, Nuclear
Language
eng
Abstract
Quantum Monte Carlo techniques are applied to quark descriptions of single baryon and nuclear systems using a non-relativistic constituent quark model Hamiltonian. The assumed interaction includes a three-body term arising due to flux-tube confinement, and two-body interactions arising from one-gluon and one-pion exchange. It is strongly dependent on the spin and isospin of the quarks. We solve for single baryon S and P-wave spectra by solving the Schrodinger equation variationally for the ground state of three interacting light-flavored valence quarks. The variational Monte Carlo method is then used to find the ground state of six quarks confined to a cavity of diameter Rc. The variational wave function is written as a product of three-quark nucleon states with correlations between quarks in different nucleons. We study the role of quark exchange effects by allowing flux-tube configuration mixing. An accurate six-body variational wave function is obtained. It has only ~13% rms fluctuation in the total energy and yields a standard deviation of ≤.1%; small enough to be useful in discerning nuclear interaction effects from the large rest mass of the two nucleons. Results are presented for three values of the cavity diameter, R c = 2, 4, and 6 fm. They indicate that the flux-tube model Hamiltonian with gluon and pion exchange requires revisions in order to obtain agreement with the energies estimated from realistic two-nucleon interactions. We calculate the two-quark density, spin, isospin, and color distribution functions and show how they may be used to study and adjust the model Hamiltonian.
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