Testing the Mutually Enhanced Magicity Effect in Nuclear Incompressibility via the Giant Monopole Resonance in the $^{204,206,208}$Pb Isotopes

Using inelastic $\alpha$-scattering at extremely forward angles, including $0^\circ$, the strength distributions of the isoscalar giant monopole resonance (ISGMR) have been measured in the $^{204,206,208}$Pb isotopes in order to examine the proposed mutually enhanced magicity (MEM) effect on the nuclear incompressibility. The MEM effect had been suggested as a likely explanation of the "softness" of nuclear incompressibility observed in the ISGMR measurements in the Sn and Cd isotopes. Our experimental results rule out any manifestation of the MEM effect in nuclear incompressibility and leave the question of the softness of the open-shell nuclei unresolved still.