Exactly separable version of X(5) and related models

Abstract One-parameter exactly separable versions of the X(5) and X(5)- β 2 models, labelled as ES-X(5) and ES-X(5)- β 2 respectively, are derived by using in the Bohr Hamiltonian potentials of the form u ( β ) + u ( γ ) / β 2 . Unlike X(5), in these models the β 1 and γ 1 bands are treated on equal footing. Spacings within the γ 1 band are well reproduced by both models, while spacings within the β 1 band are well reproduced only by ES-X(5)- β 2 , for which several nuclei with R 4 / 2 = E ( 4 1 + ) / E ( 2 1 + ) ratios and [normalized to E ( 2 1 + ) ] β 1 and γ 1 bandheads corresponding to the model predictions have been found.