A superdeformed (SD) band has been identified in a non - alpha - conjugate nucleus 35Cl. It crosses the negative parity ground band above 11/2- and becomes the yrast at 15/2-. Lifetimes of all relevant states have been measured to follow the evolution of collectivity. Enhanced B(E2), B(E1) values as well as energetics provide evidences for superdeformation and existence of parity doublet cluster structure in an odd-A nucleus for the first time in A = 40 region. Large scale shell model calculations assign (sd)16(pf)3 as the origin of these states. Calculated spectroscopic factors correlate the SD states in 35Cl to those in 36Ar.
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