PX262 - I1 - nuclear matter and the liquid drop model

in realistic models of metals and other materials, the properties are determined by the electrons interacting with each other an the nuclei, where the nuclei are assumed to be stable (or slowly moving) point charges
the relevant length scale $\sim 10^{- 10}$ m
the nuclei are comprised of many protons and neutrons $(10^{2} - 10^{3})$ interacting over length scales of $10^{- 15}$ m
nuclei contain most of the mass of the atoms, but much smaller
ie: $m_{e} ≃ 9 \times 10^{31}$ kg ; $m_{p}, m_{n} ≃ 1.7 \times 10^{- 27}$ kg
some facts for models to consider:
- unstable nuclei decay, transforming spontaneously to other nuclei
- when nuclei collide with enough force, there is fission and fusion (+ energy)
scattering experiments show that a nucleus can be modelled roughly as a sphere with radius, $R$ , which depends on the number of nucleons:

R = R_{0} A^{1 / 3}

where, $R_{0} ≃ 1.2 \times 10^{- 15}$ , and $A = Z + N$ is the mass number $\propto$ volume of the nucleus

masses of nuclei are measured in units of the 'unified atomic mass unit', u $= 1.6605 \dots \times 10^{- 27} kg$
$m_{p} ≃ m_{n} ≃ 1$ u, so the mass of a nucleus $≃ A$ u
the relation $R \propto A^{1 / 3}$ means that all nuclei have approximately the same density:

ρ = \frac{A u}{4 π / 3 R^{3}} = \frac{3}{4 π} \frac{1.6605 \dots 10^{- 27} A}{R_{0} A} ≃ 2.3 \times 10^{17} {kg m}^{- 3}

cf. density of iron $\sim 7000 {kg m}^{- 3}$
neutrons and protons, like electrons, are fermions, and have spin- $1 / 2 ℏ$
they adhere to the pauli exclusion principle, and have magnetic moments that interact with magnetic fields
nuclear binding energy is the energy required to separate nucleus into its protons and neutrons, $E_{B} :$

E_{B} = (Z m_{p} + N m_{n}) c^{2} - (_{Z}^{A} M c^{2})

where, $_{Z}^{A} M$ is the mass of a nucleus of an element $M$ , and is les than $(Z m_{p} + N m_{n})$

nearly all stable nuclei have binding energies in the range $7 - 9$ MeV per nucleon