Examining potential energy surface through Chebyshev shape parametrization

Abstract: The present study introduce a novel approach, the Chebyshev shape parametrization, to describe the geometric configurations of atomic nuclei, with a particular emphasis on fission dynamics. In this framework, the nuclear surface is represented by a profile function expanded in a Chebyshev polynomial series, with deformation parameters derived analytically under volume conservation and centre-of-mass constraints. The proposed parametrization is shown to be universal robust, and we establish transformation equations that connect it to other widely used shape parametrizations. In the macroscopic approach, the potential energy surface (PES) is computed using the Lublin-Strasbourg Drop (LSD) model, incorporating deformation-dependent energy coefficients expressed in terms of Chebyshev parameters. This enables a detailed investigation of the structural evolution and fission pathways of the nucleus Pa-227 across various deformations, depicting the influence of shape parameters on elongation, asymmetry, and neck formation. Complementing this, microscopic analysis is carried out by calculating single-particle energy levels through diagonalization of the Yukawa-folded mean-field Hamiltonian in a deformed harmonic oscillator basis. The nuclear shape parameters are provided by the Chebyshev parametrization, allowing us to examine shell structure effects at specific deformations. Together, these macroscopic and microscopic studies provide comprehensive insight into the nuclear energy landscape and shape evolution during fission.