Determination of Backbending in 122-130Ba Even-Even Isotopes

The γ-unstable O(6) limit of the interacting boson model IBM-1 has been applied successfully to determine the backbending in weakly deformed 122-130 Ba even-even isotope. The application of this limit has showed successes in determining the backbending in the energy levels of the isotopes under consideration through the good coincidence with the experimental results. Determination of Backbending in Ba Even-Even Isotopes. 68 Introduction: The backbending phenomenon occurs due to the rapid increase of the moment of inertia with rotational frequency toward the rigid value [1]. When the rotational energy exceeds the energy needed to break a pair of nucleon, the unpaired nucleon goes into a different orbit causing a change in the moment of inertia [2], other proposed explanation such as rotational alignment [3], and centri-fugal stretching, [4] along with the former, could be described in terms of band crossing [5]. The main purpose of the present work is to investigate the backbending effect in 122-130 Ba even-even isotopes, using γ-unstable O(6) limit of the interacting boson model IBM-1 [6]. Several studies have been performed to investigate the backbending effect in some even-even Ba isotopes [ 7 and 8 ] . Theory: Yrast levels and backbending The lower energy level for each spin is called yrast level [9]. One of the interesting observations made on yrast bands is the presence of small and sudden changes in the moment of inertia on a plot of EJ as a function of J(J+1). The sudden change are usually too insignificant to be noticeable. However if the moment of inertia is plotted against the square of the frequency of the rotation, a local variation in the moment of inertia around a significant high spin would be occured. The rotational energies are given by [2]: ) 1 .( ) 1 ( 2 2 + I = J J EJ h I Is the moment of inertia and J is the spin of the state . where The energy of a transition from state J to the next lower state J-2 is given by [9]: ) 2 ( ) 2 4 ( 2 2 2 − I = − − J E E J J h and the local value of the moment of inertia will be: ) 3 ...( 2 4 2