the radial, the angular
and the spin part
$$\psi(r,\theta,\phi,\sigma ) = {1\over r} P_{n\ell}(r)Y_{\ell m_{\ell}} (\theta,\phi) \chi_{m_{s}}(\sigma).$$%%                                                  %   10
The $Y_{\ell m_{\ell}}$'s are spherical harmonics