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In the present paper, by employing the formation of the Catastrophe Theory,the phase transition points for U(5)-SO(6) transitional Hamiltonian, which isdefined according to the affineSU(1,1)algebra are investigated. The energysurfaces of the even-even isotopes of Ru and Pd nuclei are considered andspecial isotopes which are the best candidates for theE(5) critical point areidentified. Also, the analogy between the critical exponents of ground-statequantum phase transition and Landau values for the critical exponents ofthermodynamic phase transition are described.

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