Understanding the relationship between electric dipole polarizability and photonuclear (-2) moment in odd-A actinide nuclei

The nuclear electric dipole (E1) polarizability (alpha E1) is mainly dominated by the dynamics of the giant dipole resonance (GDR). alpha E1 is proportional to the (-2) moment of the total photo nuclear cross-section (sigma -2). This research investigates the relationship between alpha E1 and sigma -2, along with the effects of the Pygmy Dipole Resonance (PDR) and GDR in odd-mass actinide nuclei. For the first time, alpha E1 and sigma -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, E1 dipole transitions in the GDR region significantly contribute to sigma -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 sigma -2 values. In this region, E1 polarizability can reach values of 20%-25%. The alpha E1 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 alpha E1 and sigma -2. The ANFIS results have been compared with those from the TGI-QPNM and experimental data. The TGI-QPNM model achieves an R2 of 0.85-0.95, while the ANFIS model achieves an R2 of 0.99. Moreover, the study suggests that the ANFIS model, consistent with TGI-QPNM results, could be an effective tool for estimating sigma -2 in odd-A actinide nuclei.