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One new pair of positive-parity chiral doublet bands have been identified inthe odd-$A$ nucleus $^{135}$Nd which together with the previously reportednegative-parity chiral doublet bands constitute a third case of multiple chiraldoublet (M$\chi$D) bands in the $A\approx130$ mass region. The properties ofthe M$\chi$D bands are well reproduced by constrained covariant densityfunctional theory and particle rotor model calculations. The newly observedM$\chi$D bands in $^{135}$Nd represents an important milestone in supportingthe existence of M$\chi$D in nuclei.

Chirality of $^{135}$Nd reexamined: Evidence for multiple chiral doublet bands