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Summary: Interacting boson model (IBM-1) was used in the present work to study some of nuclear structures for selected Dysprosium isotope of even mass number Dy( A=154-158). The energy levels and energy ratios of these isotopes were investigated for there are experimental. The calculated results were compared with the available experimental data, the results were in general good agreement. I. Introduction The Interacting Boson Model (IBM), initially introduced by Arima and Iachello has been rather successful in describing the collective properties of several medium and heavy nuclei .We note that in the interacting boson model-1 (IBM-1)one describes an even-even nucleus as a system of N bosons able to occupy two levels, one with angular momentum re- stricted to zero (s boson) and one with angular momentum 2 (d boson). )1( II. The interacting Boson model In the simplest version of the interacting boson model (IBM-1), its assumed that low-lying collective states in even-even nuclei away from closed shells are dominated by excitation of the valence protons and the valence neutrons (particles outside the major closed shell) while the closed shell core is inert. Furthermore, its assumed that the particle configurations which are most important in shaping the properties of the low-lying states are these in which identical particles are coupled together forming pairs of angular momentum 0 and 2.(1) The interacting Boson model (IBM-1) is used in the present work, this model represents very important step formed in the description of collective nuclear excitations. The underlying U(6) group structure of model basis leads to a simple Hamiltonian which is capable of describing the three specific limits of collective structure vibrational U(5), rotational SU(3) and gamma unstable O(6). (2) The interacting boson model offers a simple Hamiltonian, capable of describing collective nuclear properties across a wide range of nuclei, based on general algebraic group theoretical techniques which have also recently found application in problems in atomic, molecular, and high- energy physics )3,4(.

Calculation the Energy Levels and Energy Bands and Energy Ratios for even-even154, 156,158Dy Isotopes