study of nuclear structure of even-even Dy isotopes

(E(8_1^+))/(E(2_1^+)),(E(6_1^+))/(E(2_1^+)) , ( E(4_1^+))/(E(2_1^+)) and the ratios of In this study, the energy of the first exited 21+ for 152-156DY even-even isotopes are compared with the standard values for the three limits, the vibration U(5), gamma-soft O(6) and the rotational SU(3). The back-bending curve and the relation between E/ I as a function of I ( E-GOS), the ratio E(J_1^+)/E(2_1^+) and the ratio r (I+2/I) as a function of spin (I) are drawn for these isotopes to have more information about their properties. Calculation of the energy of different states along the yrast region has been done using the standard relations for each limit, U(5), O(6) and SU(3) and a comparison with the experimental data show that they the isotopes 152-154DY possess vibration U(5) properties and isotope 156DY possess gamma-soft O(6) properties. The interacting boson model IBM-1,BM and IVBM has been used to calculate the energy of different states along the yrast region applying a suitable limit for each isotopes. A program with MATLAB 10 has been built for this purpose. Agood agreement with the experimental data was obtained