Chaos and Complexity Letters, 4, 87–142p. (2008)

New Possible Properties of Atomic Nuclei Investigated by Non Linear Methods, Fractal and Recurrence Quantification Analysis

E. Conte, A. Khrennikov, J. P. Zbilut

For the first time we apply the methodologies of non linear analysis to investigate atomic matter. The sense is that we use such methods in analysis of Atomic Weights and of Mass Number of atomic nuclei. Using Auto Correlation Function and Mutual Infomation we establish the presence of non linear effects in the mechanism of increasing mass of atomic nuclei considered as function of the Z atomic number. We also operate reconstruction in phase space and we obtain values for Lyapunov spectrum and D2 - correlation dimension. We find that such mechanism of increasing mass is divergent, possibly chaotic. Non integer values of D2 are found. According to previous studies of V. Paar et al. [5] we also investigate the possible existence of a Power Law for atomic nuclei and, using also the technique of the variogram, we arrive to conclude that a fractal regime could superintend to the mechanism of increasing mass for nuclei. Finally, using Hurst exponent, evidence is obtained that the mechanism of increasing mass in atomic nuclei is fractional Brwonian regime with long range correlations. The most interesting results are obtained by using the Recurrence Quantification Analysis (RQA). We estimate % Recurrences, %Determinism, Entropy and Max Line one time in an embedded phase space with dimension D=2 and the other time in embedding dimension D=l. New recurrences, pseudoperiodicities, self-resemblance and class of self-similarities are identified with values of determinism showing oscillating values indicating the presence of more or less stability during the process of increasing mass of atomic nuclei. All the data were analyzed using shuffled data for comparison. In brief, new regimes of regularities are identified for atomic nuclei that deserve to be deepened by future researches. In particular an accurate analysis of binding energy values by non linear methods is further required.

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