$n\alpha$ Elastic Scattering: An Application of Variable Phase Approach to Local Potential

Distance-dependent phase shifts, amplitude functions, and radial wave functions for neutron-alpha elastic scattering are studied using the Variable Phase Approach. The microscopic KKNN potential is employed to calculate scattering properties for the $S_{1/2}$, $P_{3/2}$, and $P_{1/2}$ partial waves over a range of laboratory energies. The variable phase equations are solved numerically using a fifth-order Runge-Kutta method, allowing a direct examination of how the nuclear interaction generates the scattering phase within the finite interaction region. The results exhibit physically consistent behavior of the phase shifts and yield well-behaved amplitude and wave functions. This study demonstrates that the Variable Phase Approach provides a physically transparent and reliable framework for describing neutron-alpha elastic scattering and for applications in inverse scattering problems.