Nuclear Excitation Energies
One of the ways to measure the stability of nuclear ground states is to measure the energy necessary to raise it to its first excited state. The excitation energies for the even-A isotopes of lead are shown, and the required energy is dramatically larger for the isotope which has a magic number of neutrons. This is strong evidence for a shell model of the nucleus.
The isotope lead-208 is particularly unique in being "doubly magic" with Z=82 and N=126.
Nuclear Structure Concepts
Booth & Combley