ISSN 1063-7788, Physics of Atomic Nuclei, 2014, Vol. 77, No. 10, pp. 1216–1222. c  Pleiades Publishing, Ltd., 2014. ELEMENTARY PARTICLES AND FIELDS Theory Target Excitation Dependence of Self-Similar Cascading Rate in Multihadron Production Process at 350 GeV ∗ D. Ghosh 1) , A. Deb 1) , Sitaram Pal 2)** , and N. Alam 1) Received April 15, 2014 Abstract—In the present work target excitation dependence of the self-similar cascading rate has been studied in detail in the framework of Levy stable law using the experimental data of pions obtained from π - –AgBr interactions at 350 GeV/c. The Levy indices μ measured from the analysis fulfill the requirement of the Levy stable region 0  μ  2. The study gives an evidence of self-similar cascading mechanism responsible for multiparticle production. The different values of μ indicate different rates of cascading for different degrees of target excitation. Moreover, the values of universal scaling exponent (ν ) obtained from Ginzburg–Landau theory indicate that no clear evidence of second-order phase transition has been found in the interaction. DOI: 10.1134/S1063778814100044 INTRODUCTION Since Bialas and Peschansky proposed to study nonstatistical fluctuation in multiparticle production by the method of factorial moments F q (M ) [1], a large variety of experiments have been performed to search for the anomalous scaling behavior [2] of Scaled Fac- torial Moments (SFM) F q (δ) ∝ (δ) −αq , δ → 0. The anomalous scaling of SFMs or intermittency has been studied extensively with the aim of exploring the possible existence of dynamical fluctuations [1]. The power-law dependence of the SFMs on the bin size is now well established. However, a single mech- anism that could explain intermittency has not been found. To arrive at a definite conclusion about the origin of intermittency, more and more data analysis is necessary. A possible mechanism for the intermittency phe- nomena is the random cascading process [1, 3]. For self-similar cascade mechanism the probability den- sity distribution is obtained by using the Levy stable law and it is characterized by the Levy stability index μ. This index is considered as a measure of the degree of multifractality corresponding to the physically al- lowed limit. Within the region of stability 0  μ  2, ∗ The text was submitted by the authors in English. 1) Nuclear and Particle Physics Research Centre, Department of Physics, Jadavpur University, Kolkata, India. 2) Kanchrapara College, West Bengal, India. ** E-mail: sitaram_ju@yahoo.co.in; palsitaram2012@gmail.com μ has a continuous spectrum. The index μ also allows the estimation of the cascading rate [4]. The two boundaries of the Levy index correspond to different degrees of fluctuation in the particle production: μ = 2 corresponds to the minimum fluctuation from self- similar branching process, μ =0 corresponds to the maximum fluctuation that characterizes the interact- ing system as monofractal [5, 6]. According to cas- cading rate [4], when μ< 1, there is a thermal phase transition. On the other hand, μ> 1 corresponds to nonthermal phase transition during the cascading process [4]. Thus, the index μ gives an evaluation of the cascading rate. It is believed that produced pions (shower par- ticles) are most informative about the fundamental dynamics of the relativistic interactions. The knocked out target protons are also supposed to carry informa- tion about the interaction dynamics, since the time scale of emission of these particles is the same as that of the produced shower particles. These target protons, which are also known as grey particles in nuclear emulsions, are the low-energy part of the intra-nuclear cascade formed in high-energy inter- actions. Here, the number of grey particles n g can serve as a measure of the number of collisions in nuclei and the mean number of collisions is likely to be monotonically rising function of n g eventually saturating at high n g . In general, it is to be noted that n g together with the number of pions may be used as a measure of violence of the target fragmentation [7, 8]. To get more information about the inner dynamics of particle production in high-energy interactions the target excitation dependence of Levy stable law has been analyzed thoroughly. To do this, we have divided 1216