Autocorrelation studies for the first 2+nuclear energy levels

Abstract

The autocorrelation function, and the correlation time are calculated for a series of the first 2 + states of 466 even-even nuclei classified by different parameters related to nuclear structure. The results indicate enhanced values for the P factor compared with other classifying parameters to cumulate nuclei having similar properties nearby each other.Introduction. The introduction of random matrix theory (RMT) to describe the fluctuation properties of nuclear energy states has gained a considerable interest with many physicists [1,2]. Bohigas et al. [3] conjectured that RMT could be used to model the fluctuation properties of quantum systems which are fully chaotic in the classical limit. RMT provides analytical results for the spacing distributions, the level number variance, and the spectral rigidity of quantum systems. Comparing these expressions with the corresponding experimental results has been used as a signature of chaotic dynamics [4][5][6]. It has been realized that the nuclear dynamics interpolates between the Poisson (integrable) and Wigner (chaotic) distributions. The analysis of spectra of nuclei in the ground-state domain shows intermediate behavior [7][8][9][10][11][12][13][14][15][16][17].Parameterizing isotopes of the nuclear chart according to their collective behavior in a single control parameter is an interesting field of research. Many parameters are introduced to take such a role, for example, the number of protons Z, number of neutrons N , mass number A, quadrupole deformation parameter β 2 , R 4/2 ratio, and P factor.The aim of the present work is to answer the following question: which of the previously mentioned parameters can be used to describe the collective behavior of nuclei best? In other words, we search for the parameter that is capable of arranging nuclei of similar collective behavior nearby each other.In order to achieve this aim, we select even-even nuclei for their abundance and simplicity to be described by nuclear models. For each nucleus the first 2 + energy state is takenmost even-even nuclei have 2 + levels as the first excited state. In this way, we collect a series of 466 even-even nuclei ranging between 10 A 256, are taken from National Nuclear Data Center [18] up to August 2010.It is well known that-neglecting the shell closure effectlight nuclei having higher excitation energies of the first 2 + levels on the order of a few MeV. On the other hand, as the mass number A increases, the 2 + excitation energies decrease to be on the order of several tenths of a KeV. Consequently, in general the first 2 + level energy of each nucleus can be used as an indicator of collective behavior.A recent approach proposed by Relaño et al. [19] considers the spectrum of any quantum system as a set of discrete eigenvalues placed along the real energy axis. This set is ordered as any sequence of events occurring at different