The relationship between fragment multiplicity N IMF and total transverse energy E t in nuclear fragmentation is studied with help of simple analytical considerations. It is suggested that the recent claim about reducibility and thermal scaling is due to an auto-correlation between E t and p the elementary probability deduced from the binomial-like behaviour of N IMF . 25.70.-z; 25.70.Lm Multifragmentation of nuclear species, i.e. the emission of several intermediate mass fragments on a very short time scales has been claimed to be reducible to an elementary process exhibiting a binomial-like behaviour (the so-called 'reducibility'). The two parameters, the elementary probability p for emitting an inert Intermediate Mass Fragment (IMF) and the number of attempts m undertaken by the system to emit such a fragment govern the fragment multiplicity N IMF distribution. Moreover, the dependence of log(1/p) vs 1/ √ E t , where E t is the total transverse energy of Light Charged Particles (LCP's) and IMF's was found to be linear suggesting thermal scaling [1, 2, 3]. There is no clear consensus in the literature about such a statement [4,5,6,7].
PACS:As the characteristics of IMF's enter both in the determination of E t and p, there is a question to which extent auto-correlation effects could play a role. In this short note, we investigate this problem by simple analytical considerations, taking into account some basic experimental facts such as mean transverse energy of LCP's and IMF's as well as the gaussian-like distribution of LCP's multiplicity n as a function of N IMF .For a sake of simplicity, we assume that n has a gaussian shape for a given N IMF [8]. Each gaussian has a constant width, σ n = 6.0, and the same amplitude. Centroids of the gaussians corresponding to a given number of IMF's have a value A N IMF = N IMF as illustrated in Fig. 1. Next we define total transverse energy of LCP's and charged fragments, E t , as:on leave