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A simple collective rotational model has been constructed to investigate the identical bands in odd-odd nucleus 194Tl and its neighbor odd-A nuclei 193Tl and 195Tl, to describe the ∆I = 1 staggering effect in signature partner pairs of odd-A superdeformed bands 193Tl (SD1, SD2) and 195Tl (SD1, SD2) and to describe also the ∆I = 2 staggering observed in 194Tl (SD3). The model parameters and the bandhead spin ware obtained by adopted best fit method. The systematic variation of the kinematic and dynamic moments of inertia are studied as a function of the rotational frequency, it is found that the blocking effect of the high-j intruder orbital plays an important role. To describe the ∆I = 1 staggering we extracted the differences between the average transitions I + 2 → I → I 2 energies in one band and the transition I + 1 → I 1 energies in its signature partner. To describe ∆I = 2 staggering we calculated the deviation of transition energies from a smooth reference representing the finite difference approximation to the fourth derivative of the transition energies. We noticed transition energies in the nucleus 193Tl is identical to their N + 1, N + 2 neighbors. Also the analysis done allows us to confirm ∆I = 1 staggering in signature partners of 193Tl, 195Tl and ∆I = 2 staggering in SD3 band in 194Tl by performing a staggering parameter analysis. Introduction Nuclei are considered to be superdeformed (SD) when the nucleus is very far from spherical shape and acquires an elongated shape that can be represented as an approximate ellipsoid with axes in ratio of approximately 2:1:1. Now more than 350 settled superdeformed rotational bands (SDRB'S) in more then 100 nuclei have been well established in several mass regions of nuclear chart [1, 2]. Spin assignment is one of the most difficult and unsolved problems in the study of nuclear superdeformation. Several theoretical approaches to predict the spin of SDRB'S have been suggested [3-9]. Two of the most interesting phenomena observed in SDRB'S are identical bands (IB'S) and staggering effects. The IB phenomenon [10-12] involves SD bands in different nuclei whose moment of inertia and sometimes even γ-ray transition energies, are nearly identical over a significant fraction of the bands. Some SDRB'S show an unexpected anomalous ∆I = 2 staggering effects in the γ-ray energies (a zigzag behavior as a function of rotational frequency or spin) [13-16]. Two ∆I = 4 A. M. KHALAF, et al., 2 rotational sequences are consequently separated into two spin sequences with spin values I + 4n and I + 4n + 2 (n = 1, 2, 3 ...) respectively. Several theoretical attempts have been made to understand the ∆I = 2 staggering in SD nuclei [17-20]. There is another kind of staggering in SD odd-A nuclei, the ∆I = 1 staggering in signature partner pairs [21-23]. In this paper a three parameter formula for SDRB'S is suggested. The model is applied to investigate the IB'S and the staggering effects in Tl nuclei. The model In our model, the excitation energy E(I) for each state with angular momentum I is given by : ( ) [ 1 ( 1) 1] E I Eo a bI I      (1) where Eo is the bandhead energy, a rotational parameter and b characterizes the nuclear softness. In this expression the rigid rotor limit corresponds to b = 0 and ab keeping finite. Taking the bandhead energy Eo as constant we can modify the above energy to contain three parameters as the third term describe the effect of anhermenicty: ( ) [ 1 ( 1) 1] ( 1) E I a bI I cI I       (2) which leads to form the transition energy: ( ) ( ) ( 2) [ 1 ( 1) 1 ( 2)( 1)] 2 (2 1) E I E I E I a bI I b I I c I              (3) Theoretical Aspects Spin assignment is one of the most difficult problems in SD nuclei. This is due to the difficulty of establishing the de-excitation of the SD band into known yrast states. Several related fitting procedure for assigning spins have been proposed [39]. The nuclear rotational frequency is defined as the first derivative of the energy E(I) with respect to the angular momentum Î, ( ) ˆ , ( 1) ˆ dE I I I I dI      (4) The behavior of moment of inertia in SDRB'S is a strong indicator of their nuclear structure. Two possible types of nuclear moments of inertia have been suggested which reflect two different aspects of nuclear dynamics. The kinematic moment of inertia J(1) is defined as the inverse of the slope of the curve of energy E(I) versus Î: IDENTICAL BANDS AND STAGGERING IN SUPERDEFORMED  3 (1) 1 2 ( ) ˆ( ) ˆ ˆ J dE I I dI I

IDENTICAL BANDS AND STAGGERING IN SUPERDEFORMED ROTATIONAL BANDS FOR 193,194,195TL NUCLEI