Solvababe supersymmetric algebraic model for descriptions of transitional even and odd mass nuclei near the critical point of the spherical to unstable shapes

Exactly solvable solution for the spherical to gamma - unstable transition in transitional nuclei based on dual algebraic structure and nuclear supersymmetry concept is proposed. The duality relations between the unitary and quasispin algebraic structures for the boson and fermion systems are extended to mixed boson-fermion system. It is shown that the relation between the even-even and odd-A neighbors implied by nuclear supersymmetry in addition to dynamical symmetry limits can be also used for transitional regions. The experimental evidences are presented for even- even [E(5)] and odd-mass [E(5/4)] nuclei near the critical point symmetry.