Journal of Modern Physics, 2013, 4, 1105-1109 http://dx.doi.org/10.4236/jmp.2013.48148 Published Online August 2013 (http://www.scirp.org/journal/jmp) Study of 12 CC Collisions at 4.5 A GeV to Define Centrality Z. Wazir 1* , A. Rauf 2 , Z. Hussain 1 , M. A. Rafih Amer 1 , S. Ullah 2 , R. Nawaz 2 , K. Ullah 2 , G. Sughra 1 , W. A. Syed 2 , M. Tufail 1 1 Department of Basic Sciences, Riphah International University, Islamabad, Pakistan 2 Department of Physics, International Islamic University, Islamabad, Pakistan Email: * zafar_wazir@yahoo.com Received April 24, 2013; revised May 30, 2013; accepted July 4, 2013 Copyright © 2013 Z. Wazir et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. ABSTRACT Using a statistical method which is based on random matrix theory, the results for the nearest-neighbor energy spacing distributions E(S) obtained from experimental as well as from computational data have been selected for review study. The obtained results confirm that the energy spacing correlation between secondary charged particles depends upon the charged particles multiplicity and central collisions are also associated with charged particles multiplicity. Keywords: Random Matrix Theory; Nearest-Neighbor Energy Spacing Distributions; Spacing Correlations; Central Collisions; Charged Particles Multiplicity 1. Introduction The creation of new phases of strongly interacting matter is the most interesting area of research for physicist for last many years. Physicists are interested in studying characteristics of newly formatting matter under extreme conditions [1-7]. One way to create these new phases is the heavy ion collision at relativistic and ultra relativistic energies. We are interested in centrally dependence of hadron—nucleus and nucleus—nucleus collisions. These experiments indicate the regime change at some values of the centrality as some critical phenomena. If the re- gime change observed in the different experiments takes place unambiguously twice, this would be the most direct experimental evidence to a phase transition from had- ronic matter to a phase of deconfined quarks and gluons [1-7]. After point of regime change the saturation is ob- served. The simple models cannot explain the effect. To trace anticipated order of the phase evolution, for example, with increase of the baryon density, one analy- ses various characteristics of particle production at nu- clear-nuclear collisions depending on the centrality of collisions [8-13]. However, there is an ongoing discus- sion about how to define the centrality experimentally [1-13]. For instance, in various experiments the centrality is defined as a number of protons, projectile and target fragments, slow particles, all particles, as the energy flow of the particles with emission angles equal 0˚ or 90˚, etc. [1-10]. Among the most popular approaches, based on geometrical picture, is a Glauber modeling which con- tains some theoretical approximations [14]. This ap- proach enables one to establish approximately the cen- trality with the aid of the impact parameter b and the multiplicity of identified secondary charged particles in experiments. Note, in this case, however, there is a model dependent definition of the centrality. Evidently, the ab- sence of an unambiguous criterion for the centrality may significantly affect the interpretation of experimental results and, therefore, hide a true signal on the onset of a new phase of the hadronic matter. In a preliminary report [15] it is suggested that tools from Random Matrix The- ory (RMT) [16-22] might be useful in illuminating the presence of correlations in the spectral (momentum) dis- tribution of secondary particles produced in nucleus- nucleus collisions at high energy [18-22]. It is notewor- thy that during the last twenty years the RMT grew into the powerful new statistical theory of fluctuations in a variety of physical problems [19-22]. In various fields, the Dyson-Mehta statistical measures are most often used to quantify a system’s correlations and to determine what information the fluctuations contain. These measures do not depend on the background of measurements and used in the context of RMT give universal forms depending only on the fundamental symmetries preserved [19-22]. Their only requirement is that local mean densities (or secular behaviors) be understood and their effects be removed. Furthermore, a change of fluctuation properties * Corresponding author. Copyright © 2013 SciRes. JMP