Abstract
The chiral doublet bands in 135Nd and 136Nd are investigated systematically within the supersymmetry scheme including many-body interactions and possessing the SO(5)(or SU(5)) symmetry on the rotational symmetry. Quantitatively good results of the energy spectra, the energy staggering parameter as a function of the spin and the spin assignment are obtained. The calculation shows that the stronger competition between the pairing and anti-pairing effects exists in these chiral doublet bands and the SU(3) symmetry breaking more seriously exists in the stable chiral structure.