The nuclear incompressibility is a key parameter of the nuclear equation of state that can be extracted from the measurements of the so-called “breathing mode” of finite nuclei. The most serious discrepancy so far is between values extracted from Pb and Sn, that has provoked the longstanding question “Why is tin so soft?”. To solve this puzzle, a fully self-consistent quasiparticle random-phase approximation plus quasiparticle-vibration coupling approach based on Skyrme-Hartree-Fock-Bogoliubov is developed. We show that the many-body correlations introduced by quasiparticle-vibration coupling, which shift the isoscalar giant monopole resonance energy in Sn isotopes by about 0.4 MeV more than the energy in ${}^{208}\mathrm{Pb}$, play a crucial role in providing a unified description of the isoscalar giant monopole resonance in Sn and Pb isotopes. The best description of the experimental strength functions is given by SV-K226 and KDE0, which are characterized by incompressibility values $K_{\infty }=226\mathrm{MeV}$ and 229 MeV, respectively, at mean field level.

• Received 3 November 2022
• Revised 20 February 2023
• Accepted 7 July 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.082501