A semiclassical description of Fermions with spin-dependent forces

It is shown how to generalize the semiclassical treatment of dense Fermi gases in the presence of spin-dependent forces. One constructs the Wigner transform of the singlet density matrix in that representation in which the position operator and thez component of the spin operator are diagonal. This way one obtains a matrix in the spin indices which is a function of the semiclassicalp andq variables. Rules are then given how to calculate with this matrix, theμ-matrix. Next, this matrix is explicitly evaluated for independent Fermions in a spherically symmetrical potential, subject to spin-orbit forces. Finally a brief discussion is given about the nature of this matrix and possible uses are proposed.