Polarised neutron diffraction experiments conducted at 4.2 K on Cs$_3$CoCl$_5$ crystals have been analysed by using a $4$-dimensional model Hilbert space made of \abin $n$-electron wave functions of the CoCl$_4^{2-}$ molecular ion. Two spin-orbit mixing coefficients and several configuration interaction coefficients have been optimized by fitting calculated magnetic structure factors to experimental ones, to obtain the best ensemble density operator that is representable in the model space. A goodness of fit, $\chi^2$, less then $1$ has been obtained for the first time for the two experimental data sets available. In the present article, the optimized density operators are used to calculate the magnetic field densities that are the genuine observables probed in neutron diffraction experiments. Density maps of such observables are presented for the first time and numerical details are provided. The respective contributions of spin density and orbital current to the magnetic field density are analyzed