  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.
