Pairing rotations are the low-energy excitations of finite superfluid systems, connecting systems that differ in their number of Cooper pairs. This paper presents a model-independent derivation of pairing rotations within an effective theory that exploits the emergent breaking of $\text{U}\left(1\right)$ phase symmetries. The symmetries are realized nonlinearly and the Nambu-Goldstone modes depend only on time because the system is finite. Semimagic nuclei exhibit pairing rotational bands while the pairing spectrum becomes an elliptical paraboloid for open-shell nuclei. Model-independent relations between double charge-exchange reactions and $\alpha$ particle capture or knockout in open-shell nuclei are in analogy to the pair transfer reactions in a single superfluid. Odd semimagic nuclei are described by coupling a fermion to the superfluid. The leading-order theories reproduce data for pairing rotational bands within uncertainty estimates.

• Received 26 February 2022
• Accepted 6 April 2022

DOI:https://doi.org/10.1103/PhysRevC.105.044322