Starting from the original collective Hamiltonian of Bohr and separating the beta and gamma variables as in the X(5) model of Iachello, an exactly soluble model corresponding to a harmonic oscillator potential in the beta-variable (to be called X(5)-β^2) is constructed. Furthermore, it is proved that the potentials of the form β^2n (with n being integer) provide a "bridge" between this new X(5)-β^2 model (occuring for n=1) and the X(5) model (corresponding to an infinite well potential in the

more »

... ta-variable, materialized for n going to infinity. Parameter-free (up to overall scale factors) predictions for spectra and B(E2) transition rates are given for the potentials β^2, β^4, β^6, β^8, corresponding to E(4)/E(2) ratios of 2.646, 2.769, 2.824, and 2.852 respectively, compared to the E(4)/E(2) ratios of 2.000 for U(5) and 2.904 for X(5). Hints about nuclei showing this behaviour, as well as about potentials "bridging" the X(5) symmetry with SU(3) are briefly discussed.