Autocorrelation of First 4+ Nuclear Energy States

Objectives To investigate autocorrelation patterns in the first 4 + excitation energies of 466 even-even nuclei (A = 10–256) classified by multiple nuclear structure parameters (P-factor, Np·Nn product, R₄/₂ ratio, β₂ deformation, and neutron number N). Material and Methods Autocorrelation function (ACF) analysis applied to 466 even-even nuclei from the NNDC database. Nuclei sorted by five structural classifiers; ACF and correlation time τ n computed for each classification scheme using the Sprott (2003) time-series methodology. Results The P-factor classification yields the highest ACF value (0.432) and the longest correlation time (τ n = 74), significantly outperforming all other classifiers. The Np·Nn product, R₄/₂ ratio, β₂ deformation, and neutron number N produce progressively lower ACF values and shorter correlation times. Conclusion The P-factor is the most effective single parameter for grouping nuclei with similar 4 + excitation energies, reflecting its superior sensitivity to proton-neutron valence interactions. This result extends the utility of P-factor systematics from the 2 + state to the 4 + state in even-even nuclei.