  We study the transition from hydrodynamic to collisionless behavior in
collective modes of ultracold trapped Fermi gases. To that end, we solve the
Boltzmann equation for the trapped Fermi gas via the moments method. We showed
previously that it is necessary to go beyond second-order moments if one wants
to reproduce the results of a numerical solution of the Boltzmann equation.
Here, we will give the detailed description of the method including
fourth-order moments. We apply this method to the case of realistic parameters,
and compare the results for the radial quadrupole and scissors modes at
unitarity to experimental data obtained by the Innsbruck group. It turns out
that the inclusion of fourth-order moments clearly improves the agreement with
the experimental data. In particular, the fourth-order moments reduce the
effect of collisions and therefore partially compensate the effect of the
enhanced in-medium cross section at low temperatures.
