Nuclear radius constant

Fit the measured radii of nuclei against mass number and they land on R = r₀A^(1/3) with r₀ ≈ 1.2 fm. The cube root is the whole story: radius growing as A^(1/3) means volume growing as A, so every nucleus has essentially the same density — about 2.3 × 10¹⁷ kg/m³, a teaspoon of which weighs a billion tonnes. Nucleons behave like an incompressible liquid drop, which is the premise of the semi-empirical mass formula and of Bohr and Wheeler's 1939 theory of fission.

Treat the number as approximate. Values between 1.2 and 1.25 fm appear in the literature depending on whether the fit is to charge radii from electron scattering or to matter radii from hadron scattering, and light nuclei deviate badly — this is a systematics, not a CODATA constant. Still, it is enough to get a nuclear Coulomb barrier or an alpha-decay tunnelling estimate right to a factor of two.