The neutron single-particle bound states as solutions of radial Schr¨odinger equation for the central Woods–Saxon potential together with spin-orbit interaction and centrifugal terms have been obtained analytically. By introducing new variable and using Taylor expansion, the differential equation has been transformed to solvable hypergeometric type. This differential equation has also been solved using Nikiforov–Uvarov (NU) method. Neutron single-particle states have been derived as self-adjoint form of hypergeometric series. By means of boundary conditions, which implies eigenvalue condition as complicated relation between energy eigenvalues and parameters of nuclear potential, the neutron single-particle energy eigenvalues have been derived using graphical method. To examine method, numerical results in special cases of S states are evaluated. Results obtained using this method are in satisfactory agreements with available numerical solutions.
