Odd-Even Staggering in Gamma Vibrational Bands of Deformed Nuclei Insights from Collective Models and Machine Learning Approaches

Authors

  • Pooja Sharma Department of Physics, School of Chemical Engineering and Physical Science, Lovely Professional University, Jalandhar 144 411, India
  • Amit Bindra Department of Physics, School of Chemical Engineering and Physical Science, Lovely Professional University, Jalandhar 144 411, India

DOI:

https://doi.org/10.56042/ijpap.v64i9.22036

Keywords:

Light GBM, Machine learning, Odd-even staggering, Gamma band, Asymmetry parameter, Gd isotopes, Collective models

Abstract

The odd-even spin staggering of gamma-vibrational bands is examined for even-even Gd isotopes in the rare-earth region. The work uses experimental gamma-band energies, the empirical staggering index S(J), the energy ratio R4/2, and the asymmetry parameter gamma0 to follow the evolution from gamma-soft behaviour toward more axially deformed rotational structures. The analysis is framed by collective-model ideas, especially the interacting boson model and the triaxial rotor picture, because both connect gamma-band level splitting with the softness or rigidity of the nuclear shape. A LightGBM regression procedure is further used only as a data-support tool for the missing S(7) and S(8) entries at N = 94. The imputed values are inserted with uncertainty estimates so that the observed trend of the Gd chain can be discussed without leaving artificial gaps in the systematics. The results show strong staggering near the transitional neutron numbers and a close relation between S(J), R4/2 and asymmetry parameter. These observations support the view that gamma-band staggering is a sensitive indicator of triaxial effects, shape evolution and symmetry changes in deformed nuclei.

Author Biography

  • Amit Bindra, Department of Physics, School of Chemical Engineering and Physical Science, Lovely Professional University, Jalandhar 144 411, India

    Light GBM and machine learning techniques are employed in this study to address the odd-even staggering observed in rotational bands associated with gamma vibrations in deformed nuclei. Specifically, we investigate the γ-band for Gd isotopes, using experimental data and theoretical predictions to explore deviations in energy level spacing. The study focuses on the relationship between energy staggering patterns, nuclear deformation parameters, and angular momentum, distinguishing between axial γ-rigid and γ-soft asymmetric configurations in deformed atomic nuclei. To quantify staggering effects, we propose a parameter S(J), linking it to the asymmetry parameter and the ratio R4/2=E(41+) / E(21+)  in deformed nuclei. To enhance data reliability, we integrate a machine learning framework utilizing Light GBM to handle missing data (AI) in experimental datasets. Light GBM models are trained to predict missingness in specific columns using other dataset features as inputs, ensuring robust data handling and preparation. This hybrid approach not only addresses existing gaps in experimental tables but also anticipates similar challenges in future datasets, enhancing the precision of both theoretical and experimental results. Our findings contribute to a deeper understanding of shape coexistence, phase transitions, and symmetry-breaking phenomena in nuclear systems, providing new insights into the mechanisms underlying energy staggering in deformed nuclei.

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Published

2026-09-10

Issue

Vol. 64 No. 9 (2026): Indian Journal of Pure & Applied Physics

Section

Article

License

Copyright (c) 2026 Indian Journal of Pure & Applied Physics (IJPAP)

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Odd-Even Staggering in Gamma Vibrational Bands of Deformed Nuclei Insights from Collective Models and Machine Learning Approaches. (2026). Indian Journal of Pure & Applied Physics (IJPAP), 64(9). https://doi.org/10.56042/ijpap.v64i9.22036

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