Solvable models for the gamma deformation having X(5) as limiting symmetry. Removing some drawbacks of the existing descriptions

Two solvable Hamiltonians for describing the dynamic gamma deformation are proposed. The limiting case of each of them is the X(5) Hamiltonian. Analytical solutions for both energies and wave functions, which are periodic in γ, are presented in terms of spheroidal and Mathieu functions, respectively. For illustration, the case of 152Sm is treated with the spheroidal function method.