Through the nuclear shell model and single nuclear independence movement in the average self-consistent field model

Yukawa-Wood-Saxon-potential was established

combined with the liquid drop model to set up a comprehensive model potential and the corresponding potential time-independent Schrodinger equation. Applying Taylor perturbation method and radial matrix elements of hydrogen

we got the analytical solution of the nuclear energy level. Several bound state energy level structures of the nucleus were calculated. The results are comparable with the experimental value.