  Angular momentum dependence of nuclear level densities at finite temperatures
are investigated in the static path approximation(SPA) to the partition
function using a cranked quadrupole interaction Hamiltonian in the following
three schemes: (i) cranking about x-axis, (ii) cranking about z-axis and (iii)
cranking about z-axis but correcting for the orientation fluctuation of the
axis. Performing numerical computations for an $sd$ and a $pf$ shell nucleus,
we find that the x-axis cranking results are satisfactory for reasonably heavy
nuclei and this offers a computationally faster method to include the angular
momentum dependence at high temperatures in the SPA approach. It also appears
that at high spins inclusion of orientation fluctuation correction would be
important.
