  Thomas-Fermi theory is developed to evaluate nuclear matrix elements averaged
on the energy shell, on the basis of independent particle Hamiltonians. One-
and two-body matrix elements are compared with the quantal results and it is
demonstrated that the semiclassical matrix elements, as function of energy,
well pass through the average of the scattered quantum values. For the one-body
matrix elements it is shown how the Thomas-Fermi approach can be projected on
good parity and also on good angular momentum. For the two-body case the
pairing matrix elements are considered explicitly.
