Study of Single Particle Energy Levels by Using Woods-Saxon Potential and its Approximate Solution in Harmonic Oscillator Basis

In this investigation, the approximate solution of Schrodinger equation with mean field Woods-Saxon potential in harmonic oscillator basis has been given. The eigen value energy and corresponding eigen function of bound single particle neutron and proton energy levels for some light, medium weight, and heavy nuclei were determined. Obtained results were compared with numerical solution of Schrodinger equation and good agreements were observed between two methods. By using Nikiforov-Uvarov (NU) method and considering boundary conditions the analytics and accurate solution of Schrodinger equation with Woods-Saxon potential have been represented for S-state neutron single particle. The energy levels for some light, medium weight, and heavy nuclei were calculated. Obtained results showed that the value of energy levels is strictly dependent to the adjustable parameters of Woods-Saxon potential and method of calculation. Such that by increase of atomic number and principle quantum number the discrepancy between calculated data by using numerical solution and analytic solution with different set of adjustable parameters is increased.