Giant resonances are collective excitation modes for many-body systems of fermions governed by a mean field, such as the atomic nuclei. The microscopic origin of such modes is the coherence among elementary particle-hole excitations, where a particle is promoted from an occupied state below the Fermi level (hole) to an empty one above the Fermi level (particle). The same coherence is also predicted for the particle–particle and the hole–hole excitations, because of the basic quantum symmetry between particles and holes. In nuclear physics, the giant modes have been widely reported for the particle–hole sector but, despite several attempts, there is no precedent in the particle–particle and hole–hole ones, thus making questionable the aforementioned symmetry assumption. Here we provide experimental indications of the Giant Pairing Vibration, which is the leading particle–particle giant mode. An immediate implication of it is the validation of the particle–hole symmetry.

New analytic solutions of the quadrupole collective Bohr Hamiltonian are proposed, exploiting an approximate separation of the β and γ variables to describe γ-soft prolate axial rotors. The model potential is a sum of two terms: a β-dependent term taken either with a Coulomb-like or a Kratzer-like form, and a γ-dependent term taken as a harmonic oscillator. In particular, it is possible to give a one-parameter paradigm for a β-soft, γ-soft axial rotor that can be applied, with considerable agreement, to the spectrum of 234U.

A solution of the Bohr collective Hamiltonian for the $\beta$-soft, $\gamma$-soft triaxial rotor with $\gamma \sim \pi ∕6$ is presented making use of a harmonic potential in $\gamma$ and Coulomb-like and Kratzer-like potentials in $\beta$. It is shown that, while the $\gamma$-angular part in the present case gives rise to a straightforward extension of the rigid triaxial rotor energy in which an additive harmonic term appears, the inclusion of the $\beta$ part results instead in a nontrivial expression for the spectrum. The negative anharmonicities of the energy levels with respect to a simple rigid model are in qualitative agreement with general trends in the experimental data.