Indian Journal of Pure & Applied Physics Vol. 47, December 2009, pp. 839-843 Levy index analysis in relativistic and ultrarelativistic nuclear collision – Evidence of non-thermal phase transition Dipak Ghosh, Argha Deb, Subrata Biswas, Pasupati Mandal & Rittika Sarkar Nuclear and Particle Physics Research Centre, Department of Physics, Jadavpur University, Kolkata 700 032 E-mail: deegee111@gmail.com & dipakghosh_in@yahoo.com Received 10 July 2009; revised 21 August 2009; accepted 31 August 2009 An analysis on Levy index of compound hadrons (pions + protons) emitted from 12 C-AgBr and 24 Mg-AgBr interactions both at 4.5 AGeV/c and 32 S-AgBr interactions at 200 AGeV/c using the results of Takagi moment methodology in emission angle (cosθ) space and azimuthal angle (φ) space has been presented. The results of our study reveal non-thermal phase transition at both relativistic and ultrarelativistic energy. Keywords: Relativistic heavy ion interactions, Compound hadrons, Anomalous fractal dimensions, Levy index 1 Introduction During the last few decades, various experiments have been performed with lepton-lepton, lepton- nucleus, hadron-hadron, hadron-nucleus and nucleus- nucleus interactions at relativistic and ultrarelativistic energies in order to reveal the underlying dynamics of multiparticle production process. The study of the production of relativistic particles (pions) has always been emphasized with the common belief that these particles are the most frequently produced particles and that the knowledge of pion production mechanism is essential for the understanding of main features of high energy interactions. Bialas and Peschanski 1 introduced a new methodology to find out the non- statistical fluctuation in pseudorapidity space in place of analyzing the average features of multiparticle production. The idea of studying the intermittent pattern of particle production was introduced to explain the statistical significance of unusual events having sharp spikes in pseudorapidity interval. The statistical counting variable called the scaled factorial moment (SFM) F q is the main tool for studying intermittency. Scaled factorial moments are designed for extraction of non-statistical fluctuation after eliminating the statistical part. The concept of intermittency was first propounded by Bialas and Peschanski 1 in high energy physics. It has been shown that the average SFM is equal to the moment of a true probability distribution of particle density without any statistical bias. The pioneers suggested that a growth of factorial moment F q following a power law with decreasing phase space interval size signals the onset of intermittency in the context of high energy interactions. The existence of self-similar nature in particle production process directly implies a connection between intermittency and fractality. The word fractality was first introduced by Mandelbrot 2 in widely varying fields from galaxy distributions to coast line analysis. A fractal consists of a system in which more and more structure appears at smaller and smaller scales similar to the one at large scales. The theory of multifractals was developed in order to handle non-uniform fractals. For investigating the fractal structure in multiparticle data, various methods have been suggested. Hwa 3 proposed the G q moment approach which has enriched the study of multifractality in multiparticle production. Hwa and Pan 4 modified the old form of the G q moment by introducing a step function which can act as a filter for the low multiplicity events. Takagi 5 proposed a novel method, T q moment for studying the fractal structure where the difficulties faced in the conventional method were overcome. Takagi 5 pointed out that the experimental data do not show the expected linear behaviour in a log-log plot and this is partially due to the fact that most methods are unable to give the required mathematical limit: the number of points tends to infinity. T q moment approach is different from both F q moment and G q moment approach. One of the properties of universal multifractals is that they can be classified by a parameter μ(0<μ<2) called the Levy index, that indicates the degree of multifractality as well as estimates the cascading rate in self-similar branching process. The Levy index (μ) can also be utilized to decipher possible mechanism