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A superdeformed (SD) band has been identified in a non -alpha -conjugate nucleus 35 Cl. 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 ( The superdeformed bands observed in the even-even nuclei in upper sd shell have provided favourable condition to describe the collective rotation microscopically involving the cross-shell correlations [1,2]. Complementary descriptions in terms of particle-hole excitations in the shell model [2,3], and α-clustering configurations within various cluster models [4][5][6] have been utilised to interpret the data. Till now no such band has been observed in non -alpha -conjugate odd-A, N =Z isotopes in this region [7]. If a nucleus clusterizes into fragments of different charge to mass ratios, the center of mass does not coincide with its center of charge. As a result a sizeable static E1 moment may arise in the intrinsic frame [8], resulting in several distinctive features in the spectra. Two adjacent opposite parity deformed ∆I = 2 bands connected by strong E2 intra-band transitions in turn are connected by strong E1 inter-band transitions [8] forming an apparent ∆I = 1 rotational band with alternating parity states. Since early seventies [9][10][11], a number of similar alpha-cluster bands have been studied extensively. In the spectrum of 19 F , cluster-model calculations have shown that coupling of a proton hole in the p shell coupled with four nucleons in the sd shell (a proton hole coupled to 20 N e) gives rise to alpha-cluster bands. The lowest alpha + 15 N parity partner bands built on K π = 1/2 + ground-state band, lowest lying famous K π = 1/2 − at 110 keV and some other bands lying above 5 MeV have been observed. So far no similar clustering have been observed in odd A nuclei in the A≃ 40 region, where evidences of clustering have been manifested in even-even nuclei through superdeformation.According to Ikeda [12], in the spectra of light nuclei, cluster like configurations would appear near the threshold energy needed for breakup into proper sub-nuclei. For the nucleus of our interest 35 Cl, the threshold energy [13] to appear as a composite of 32 S and a triton (t) ( 32 S + t) is around 18 MeV. On the other hand, threshold for the decay of the composite system 35 Cl into ( 31 P + α) clusters is around 6.5 MeV. The SD rotational band observed in 36 Ar has been shown to have cluster structure. So one may expect to find deformed cluster bands in the excitation spectra of 35 Cl also generated by coupling a proton hole to SD states in 36 Ar. In this letter, we report the observation of a superdeformed band for the first time in the odd A 35 Cl isotope. The reduced transition probabilities for all...

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