  The momentum dependence of the medium modifications on nucleon-nucleon
elastic cross sections is discussed with microscopic transport theories and
numerically investigated with an updated UrQMD microscopic transport model. The
semi-peripheral Au+Au reaction at beam energy $E_b=400A$ MeV is adopted as an
example. It is found that the uncertainties of the momentum dependence on
medium modifications of cross sections influence the yields of free nucleons
and their collective flows as functions of their transverse momentum and
rapidity. Among these observables, the elliptic flow is sensitively dependent
on detailed forms of the momentum dependence and more attention should be paid.
The elliptic flow is hardly influenced by the probable splitting effect of the
neutron-neutron and proton-proton cross sections so that one might pin down the
mass splitting effect of the mean-field level at high beam energies and high
nuclear densities by exploring the elliptic flow of nucleons or light clusters.
