Higgs response and pair condensation energy in superfluid nuclei

The pairing correlation in nuclei causes a characteristic excitation, known as the pair vibration, which is populated by the pair transfer reactions. Here we introduce a new method of characterizing the pair vibration by employing an analogy to the Higgs mode, which emerges in infinite superconducting/superfluid systems as a collective vibrational mode associated with the amplitude oscillation of the Cooper pair condensate. The idea is formulated by defining a pair-transfer probe, the Higgs operator, and then describing the linear response and the strength function to this probe. We will show that the pair condensation energy in nuclei can be extracted with use of the strength sum and the static polarizability of the Higgs response. In order to demonstrate and validate the method, we perform for Sn isotopes numerical analysis based the quasi-particle random phase approximation to the Skyrme-Hartree-Fock-Bogoliubov model. We discuss a possibility to apply this new scheme to pair transfer experiment.