In the code `HFBRAD` the solutions are restricted
to have a spherical symmetry and do not mix proton
and neutron states. In this situation the
wave functions have the good quantum numbers
( is a good quantum number since the spectrum is discretized
inside a spherical box)
and all the solutions inside an
-block are
degenerated. Furthermore, the radial part of the wave functions
can be chosen to be real. Thus we use the ansatz

for the wave functions. The local densities can be written using the radial functions (omitting the isospin quantum number)

(10) | |||

(11) |

For the kinetic densities we have

(12) | |||

(13) |

Finally the spin current vector densities have only one non vanishing component given by

(14) | |||

(15) |