Nuclear density

Nuclear density is the density of the nucleus of an atom, averaging about 4×10¹⁷ kg/m³. The descriptive term nuclear density is also applied to situations where similarly high densities occur, such as within neutron stars.

The nuclear density in a typical nucleus can be approximately calculated from the size of the nucleus. The radius of a typical nucleus is R = A^{1 / 3}r₀ where A is the mass number and r₀ is 1.25 fm, with deviations of 0.2 fm from this value. The nucleon's density n satisfies

${4\over 3} \pi n R^3 = A$

Therefore $n = {3\over 4\pi {r_0}^3} = 0.122 \ \mathrm{fm}^{-3} = 1.22 \cdot 10^{44} \ \mathrm{m}^{-3} (= 2.026 \cdot 10^{17} kg\cdot \mathrm{m}^{-3})$.
Experimentally determined value is $n = 0.16 \ \mathrm{fm}^{-3}$. The mass density given above is the product of this by the nucleon mass 1.67×10⁻²⁷ kg.

The components of an atom and of an atomic nucleus have varying densities. The proton is not a fundamental particle, being composed of quark-gluon matter. Its size is approximately 10⁻¹⁵ meters and its density 10¹⁸ kg/m³. Using deep inelastic scattering, it has been estimated that the "size" of an electron, if it is not a point particle, must be less than 10⁻¹⁷ meters. This would correspond to a density of roughly 10²¹ kg/m³.

Probing deeper within particles, one finds quarks which appear to be very dense and very hard. There are possibilities for still higher densities when it comes to quark matter, gluon matter, or neutrino matter. In the immediate future, the highest experimentally measurable densities will likely be limited to leptons and quarks.

See also

• Nuclear equation of state
• Nuclear matter
• Quark-gluon plasma
• Nuclear compressibility