| A new state of strongly interacting matter, known as the Quark Gluon Plasma, is believed to be created when heavy ion nuclei collide at relativistic energies.; The number of charged-particles produced in the collisions is a direct measure of the produced energy density. This Thesis presents results for the charged particle multiplicity at mid-rapidity at three center-of-mass energies: 19.6, 62.4 and 200 GeV. The energy density, derived from the measured multiplicity in Au+Au collisions, far exceeds the energy density of nuclear matter and the theoretical limit for creation of the QGP. The data were collected with the PHOBOS detector using a vertex tracklet analysis technique to make the measurement.; The energy density, as a function of center-of-mass energy, exhibits a steady (logarithmic) growth. The yield of charged particles per participant pair, in Au+Au collisions, is higher by approximately 40% than that found in corresponding p+p collisions. The centrality dependence reveals that the mulitplicity in Au+Au is larger from the mulitplicity produced in p+p and d+Au systems and shows an increase with centrality.; Ratios of the 200 GeV data with respect to 19.6 and 62.4 GeV provide a precise experimental measurement to distinguish between different models of particle production. The expected rise in multiplicity from pQCD processes (minijets) is not observed in data. The KLN Saturation model is found to describe the trend of the data.; The absence of a rise in the ratios as a function of centrality for energies different by an order of magnitude is a remarkable observation. The data appears to exhibit simple scaling properties for all measured energies. |