Suppose, counter to the actual nuclear force, that every nucleon in a nucleus…
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
Suppose, counter to the actual nuclear force, that every nucleon in a nucleus attracted every other nucleon with the same energy, regardless of distance or of how many other nucleons are present (no saturation, no exchange character, no repulsive core). The measured total binding energy of carbon-12 is B(12C)=92.16MeV, and the measured total binding energy of gold-197 is B(197Au)=1559.4MeV.
((a)) Using carbon-12 as the calibration nucleus, find the binding energy that this pairwise model assigns to a single nucleon-nucleon pair.
((b)) How many distinct pairs of nucleons are there in gold-197?
((c)) Use the answers to parts (a) and (b) to predict the total binding energy of gold-197 on the pairwise model, and state the ratio of predicted to measured binding energy.
((d)) Give the two features of the nucleon-nucleon force, established from the two-nucleon evidence on scattering and on the deuteron, that between them explain why the pairwise model fails so badly, and state which observation about heavy nuclei generally this failure is consistent with.