= Solution
A <Wigner crystal> is an ordered electron arrangement favored when repulsion overwhelms the kinetic cost of localization. In a three-dimensional <electron gas> with a neutralizing background, define a mean spacing $a=(3/4\pi n)^{1/3}$ and effective Bohr radius $a_B^*=4\pi\varepsilon\hbar^2/(m^*e^2)$. The <Coulomb-to-kinetic energy ratio of an electron gas> scales as
$$
E_C\sim\frac{e^2}{4\pi\varepsilon a}\propto n^{1/3},\qquad E_F\sim\frac{\hbar^2}{m^*a^2}\propto n^{2/3},\qquad\boxed{\frac{E_C}{E_F}\sim\frac a{a_B^*}=r_s.}
$$
Thus \b[low density favors the crystal in the degenerate quantum model]. Translational symmetry is broken, and excitations include collective lattice vibrations. The melting criterion depends on dimension, screening, disorder and quantum fluctuations, so this scaling argument does not supply a universal numerical transition density.
The <electron crystallization on liquid helium> experiment provides an important related observation: a dilute two-dimensional electron sheet above liquid helium crystallized on cooling. It was a classical electron system, with thermal rather than Fermi motion competing with Coulomb energy; its coupling parameter is $\Gamma=E_C/(k_BT)$. It therefore illustrates Coulomb ordering without being a direct measurement of the zero-temperature three-dimensional quantum transition.<Evidence for a Liquid-to-Crystal Phase Transition in a Classical, Two-Dimensional Sheet of Electrons by C. C. Grimes and others>[Physical Review Letters 42, 795–798 (1979), abstract: classical sheet, density range and melting temperatures]{ref}
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