  It has been debated whether the experimentally-identified superdeformed
rotational band in $^{40}$Ar [E. Ideguchi, et al., Phys. Lett. B 686 (2010) 18]
has an axially or triaxially deformed shape. Projected shell model calculations
with angular-momentum-projection using an axially-deformed basis are performed
up to high spins. Our calculated energy levels indicate a perfect
collective-rotor behavior for the superdeformed yrast band. However, detailed
analysis of the wave functions reveals that the high-spin structure is
dominated by mixed 0-, 2-, and 4-quasiparticle configurations. The calculated
electric quadrupole transition probabilities reproduce well the known
experimental data and suggest a reduced, but still significant, collectivity in
the high spin region. The deduced triaxial deformation parameters are small
throughout the entire band, suggesting that triaxiality is not very important
for this superdeformed band.
