Understanding the Relationship Between Electric Dipole Polarizability and Photonuclear (-2) Moment in Odd-A Actinide Nuclei

The nuclear electric dipole ( E 1) polarizability ( α E 1 ) is mainly dominated by the dynamics of the giant dipole resonance (GDR). α E 1 is proportional to the (-2) moment of the total photo nuclear cross-section ( σ −2 ). This research investigates the relationship between α E 1 and σ −2 , along with the effects of the Pygmy Dipole Resonance (PDR) and GDR in odd-mass actinide nuclei. For the first time, α E 1 and σ −2 values have been calculated using the Translational and Galilean Invariant Quasiparticle Phonon Nuclear Model (TGI-QPNM) approach for odd-A actinide nuclei. According to TGI-QPNM results, E 1 dipole transitions in the GDR region significantly contribute to σ −2 due to the energy weighting factor. Below the neutron separation threshold, the PDR in neutron-rich nuclei shows a contribution of about 5% to σ −2 values. In this region, E 1 polarizability can reach values of 20%–25%. The α E 1 values indicate the presence of PDR in these nuclei. Additionally, the Adaptive Neuro-Fuzzy Inference System (ANFIS), a new machine learning method, has been performed to analyze the relationship between α E 1 and σ −2 . The ANFIS results have been compared with those from the TGI-QPNM and experimental data. The TGI-QPNM model achieves an R 2 of 0.85–0.95, while the ANFIS model achieves an R 2 of 0.99. Moreover, the study suggests that the ANFIS model, consistent with TGI-QPNM results, could be an effective tool for estimating σ −2 in odd-A actinide nuclei.