Parameter - free solution of the Bohr Hamiltonian for actinides critical in the octupole mode

An analytic, parameter-free (up to overall scale factors) solution of the Bohr Hamiltonian involving axially symmetric quadrupole and octupole deformations, as well as an infinite well potential, is obtained, after separating variables in a way reminiscent of the Variable Moment of Inertia (VMI) concept. Normalized spectra and B(EL) ratios are found to agree with experimental data for Ra and Th, the nuclei known to lie closest to the border between octupole deformation and octupole vibrations in the light actinide region.