Backbendings of Superdeformed bands in $^{36,40}$Ar

Experimentally observed superdeformed (SD) rotational bands in $^{36}$Ar and $^{40}$Ar are studied by the cranked shell model (CSM) with the paring correlations treated by a particle-number-conserving (PNC) method. This is the first time the PNC-CSM calculations are performed on the light nuclear mass region around $A=40$. The experimental kinematic moments of inertia $J^{(1)}$ versus rotational frequency are reproduced well. The backbending of the SD band at frequency around $\hbar\omega=1.5$ MeV in $^{36}$Ar is attributed to the sharp rise of the simultaneous alignments of the neutron and proton $1d_{5/2}[202]5/2$ pairs and $1f_{7/2}[321]3/2$ pairs, which is the consequence of the band crossing between the $1d_{5/2}[202]5/2$ and $1f_{7/2}[321]3/2$ configuration states. The gentle upbending at the low frequency of the SD band in $^{40}$Ar is mainly effected by the alignments of the neutron $1f_{7/2}[321]3/2$ pairs and proton $1d_{5/2}[202]5/2$ pairs. The PNC-CSM calculations show that besides the diagonal parts, the off-diagonal parts of the alignments play an important role in the rotational behavior of the SD bands.