The liquid-drop mass formula treats the dominant binding term as
PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · The nuclear force and nuclear models · The nuclear force and nuclear models
The Nucleus Resolved, Ch The deuteron and what two nucleons do to each other
Problem
The liquid-drop mass formula treats the dominant binding term as aVA, proportional to the number of nucleons, and electron-scattering form factors show the central nuclear density ρ0≈0.16nucleonfm−3 to be essentially the same from oxygen to lead.
((a)) If every pair of nucleons contributed the same attractive energy independent of A, use oxygen-16's measured binding energy B=127.6MeV, spread evenly over its 120 nucleon pairs, to predict the binding energy of iron-56 (which has 56×55/2=1540 nucleon pairs) on this pairwise assumption.
((b)) The measured binding energy of iron-56 is 492.3MeV. Give the ratio of the pairwise prediction to this measured value, and explain, using the exchange character of the nucleon-nucleon force (attractive mainly in even relative orbital states, weak or repulsive in odd ones) together with its short-range repulsive core, why binding energy grows only in proportion to A and why the same two features are needed to keep ρ0 constant, as required by the volume term aVA.