X(3): an exactly separable γ-rigid version of the X(5) critical point symmetry

A γ -rigid version (with γ = 0) of the X(5) critical point sy mm etry is constructed. The m odel, to be called X(3) since it is proved to contain three degrees of freedo m , utilizes an infinite well potential, is based on exact separation of variables, and leads to para m eter free (up to overall scale factors) predictions for spectra and B ( E 2) transition rates, which are in good agree m ent with existing experi m ental data for 172 Os and 186 Pt. An unexpected si m ilarity of the β 1 -bands of the X(5) nuclei 150 Nd, 152 S m , 154 Gd, and 156 Dy to the X(3) predictions is observed.