Someone argues: "The central nucleon density of every nucleus above comes out the same
PHYSICS · Multi-part · Fermi University Physics · Nuclear Physics · The nuclear force and nuclear models · The nuclear force and nuclear models
The Nucleus Resolved, Ch How big a nucleus is, and what the mass surface knows
Problem
Someone argues: "The central nucleon density of every nucleus above A≈16 comes out the same, about 0.160 nucleons per fm3, simply because nucleons behave as hard spheres of a fixed radius, equal to the proton's rms charge radius 0.841fm, packed as tightly as geometry allows. On this view the constant central density is a geometrical fact about packing spheres and says nothing about the nuclear force."
((a)) Take the volume of a nucleon as that of a hard sphere of radius 0.841fm. Using the central nucleon density 0.160fm−3 inferred from the measured charge density, work out the fraction of the nuclear volume actually occupied by nucleon spheres (the packing fraction).
((b)) The densest possible arrangement of identical hard spheres (close packing) fills about 0.74 of the available volume. Compare this with your answer to part (a) and say what it shows about the claim above.