Investigation of Shape Phase Transition in theU(5)-SO(6)Transitional Region by Catastrophe Theory and Critical Exponents of some Quantities

In the present paper, by employing the formation of the Catastrophe Theory, the phase transition points for U(5)-SO(6) transitional Hamiltonian, which is defined according to the affineSU(1,1)algebra are investigated. The energy surfaces of the even-even isotopes of Ru and Pd nuclei are considered and special isotopes which are the best candidates for theE(5) critical point are identified. Also, the analogy between the critical exponents of ground-state quantum phase transition and Landau values for the critical exponents of thermodynamic phase transition are described.