Background: The nucleon-nucleus scattering has been studied using Gaussain potential withspin-orbit term of Thomas type to fit the experimental scattering phase shifts (SPS). Recently,Hulthen potential without spin-orbit term has been utilised for studying α–nucleon scattering with phase function method (PFM).Purpose: The main objectives of this paper are:1. To obtain the best possible interaction potentials that best describe the neutron-α elasticSPS in various channels.2. To compute the partial cross-sections for scattering p-states and the total cross-section forthe reaction.Methods: The local interaction potential is modeled using Gaussian function. The non-localspin orbit term is chosen to be proportional to derivative of local potential. The phase function method has been numerically solved using 5th order Runge-Kutta method to compute the SPS. The model parameters are varied in an iterative fashion to minimise the mean absolute percentage error (MAPE) w.r.t. the experimental SPS.Results:1. The SPS for S, P and D channels have been obtained with MAPE values less than 3%.2. The partial cross-sections for p 1/2 and p 3/2 have been plotted and the respective resonance energies and FWHM have been found to be in reasonable agreement with values in literature.3. The total cross-section for the reaction has been determined and found to be matching well with experimental findings.Conclusions: Gaussian potential with associated spin-orbit term has been shown to be areasonably good choice for explaining the n-α scattering reaction.