Investigation of Mixed Symmetry States in 170-178Yb isotopes

low-lying positive parity states, dynamic symmetries, mixed symmetry states (MSS), reducing electric quadrupole transition probabilities B(E2), branching ratio, reducing magnetic dipole transition probabilities B(M1), and mixing ratios δ(E2/M1) for 170-178 Yb have been investigated by applied IBM-1 and IBM-2 program package. The software package IBM-1 and IBMT computer code for IBM-1 and Neutron Proton Boson NPBOS and Neutron Proton Boson Electromagnetic NPBEM software package have been used. The Ytterbium nuclei with the (170 − 178) mass number considered as rotational nuclei after applying the first and second interacting boson model with studying dynamic symmetry and energy ratios ( E 4 1 + / E 2 1 + ) , ( E 6 1 + / E 2 1 + ) and ( E 8 1 + / E 2 1 + ) that approximated to (3.33,7 and 12). The reducing transition probability for electric quadruple B ( E 2) and branching ratios that state the small values of the ratios R′ and R″ as having rotational characteristics. A study of the mixed symmetry state of these nuclei shows that the lower energy mixing level is the first 1 + level, which distinguishes the rotational determination nuclei. The energy levels values for the states 2 2 + , 3 1 + , 5 1 + , 1 1 + have a clear mixed symmetry state (MSS) directly proportional with Majorana parameters ζ 2 , while 2 3 + , and 2 4 + , tend to be approximately more conservative.