Exactly separable version of X(5) and related models

One-parameter exactly separable versions of the X(5) and X(5)-β2 models, labelled as ES-X(5) and ES-X(5)-β2 respectively, are derived by using in the Bohr Hamiltonian potentials of the form u(β)+u(γ)/β2. Unlike X(5), in these models the β1 and γ1 bands are treated on equal footing. Spacings within the γ1 band are well reproduced by both models, while spacings within the β1 band are well reproduced only by ES-X(5)-β2, for which several nuclei with R4/2=E(41+)/E(21+) ratios and [normalized to E(21+)] β1 and γ1 bandheads corresponding to the model predictions have been found.