Genetic Algorithm Approach to Study Low Energy Alpha-Deuteron Elastic Scattering using Phase Function Method

The present study focuses on the analysis of elastic scattering in the α − d system for low-energy data up to 14 MeV. This system holds particular significance due to its direct connection to the 6Li production reaction, which is an important process in nuclear astrophysics and light nuclei synthesis. The primary objective of this investigation is to explore the low-lying excited states of positive parity with iso-spin T = 0, which are crucial for accurately describing the resonance behavior and underlying nuclear dynamics of the system. Central idea: To obtain the interaction potential using the inverse scattering method, we have employed the Genetic Algorithm approach. In this framework, the Genetic algorithm is guided by the underlying physical laws, enabling the accurate extraction of the inverse scattering potential from the elastic scattering data. Methodology: As a reference potential, a combination of three smoothly joined Morse functions has been utilized, characterized by ten model parameters. These parameters are optimized in an iterative fashion to ensure the best fit to the phase shifts extracted from the experimental scattering data. The process of optimization is guided by the computed scattering phase shifts by solving the phase equation using 5th order Runge Kutta method for the reference potential in each iteration. Results: Our approach yields inverse potentials for both single and multi channel scattering. Using the Scattering Phase Shifts obtained from these inverse potentials, we calculate the partial cross-section to determine the resonance energies and decay width. The obtained values of resonance energies and decay width for 3D1, 3D2, and 3D3 states of α − d are in correspondence with the experimental results.