Elastic differential neutron-scattering cross section on even Neodymium isotopes

In this paper, we present an analytical formula for the neutron scattering cross section on even-even heavy nuclei, employing the rotational model and making certain assumptions, such as the use of the Yukawa potential shape for the neutron-nucleon interaction, the rigid rotor approximation, and the assumption of a uniformly distributed nuclear matter within the nucleus. Notably, a significant aspect of this study is the avoidance of any approximation of a central potential, in contrast to the commonly employed methods of expanding the potential based on the power of , utilizing the Legendre polynomial basis, or employing Fourier-Bessel analysis. Despite the simplicity of the chosen model (rigid rotor model and the two-parameter potential), our results yield satisfying and encouraging outcomes. This suggests the effectiveness of our approach in analyzing neutron scattering on even-even heavy nuclei. It is important to note that further investigations are warranted to deepen our understanding and refine the assumptions utilized in this study. Future research should explore the applicability of the proposed analytical formula to diverse nuclei and consider more complex models to expand our comprehension of neutron-nucleus interactions.