What does this equation mean?

Superimposed on the smooth topography the semi-empirical mass formula describes is a set of sharp local peaks that the liquid-drop picture cannot produce at all. In 1949, Maria Goeppert Mayer published a systematic case, built from the accumulated evidence of unusually low neutron-capture cross-sections, higher first-excited-state energies, and anomalously large numbers of stable isotopes and isotones, that nuclei with 50 or 82 protons, or 50, 82, or 126 neutrons, are unusually stable — closed shells, by direct analogy with the closed electron shells that make noble gases chemically inert [ 5 ] . In the same year and independently, Otto Haxel, J. Hans D. Jensen, and Hans Suess published the same conclusion, and the pair of papers, arriving at an explanation resting on strong spin-orbit coupling in the nuclear potential, jointly established the nuclear shell model; Mayer and Jensen shared the 1963 Nobel Prize in Physics for the work [ 6 ] . The magic numbers — 2, 8, 20, 28, 50, 82, and 126 — are the landscape’s genuine local peaks in a sense the liquid-drop terms alone do not supply: a nucleus with a closed shell sits measurably higher in binding energy per nucleon than smooth interpolation between its neighbors would predict, exactly as an adaptive peak sits above the surrounding fitness surface by more than the local gradient alone would account for. The signature is sharpest in the neutron (or proton) separation energy — the cost of removing one more nucleon from an otherwise identical isotope — which drops abruptly immediately after a magic number is crossed, the nuclear analogue of a fitness cliff rather than a gentle slope; a doubly magic nucleus, closed in both N and Z simultaneously, sits at the intersection of two such cliffs and is correspondingly the most sharply peaked point in its neighborhood on the whole chart.