= Solution
The <radial distribution function> is the conditional <number density> of neighbors at separation $r$, divided by the bulk <number density> $n$. In an isotropic three-dimensional liquid, the mean number in a thin spherical shell is $dN=4\pi nr^2g(r)dr$. Strong short-range repulsion makes $g(r)$ very small inside the effective particle core. A first maximum marks the nearest-neighbor coordination shell. More distant shells give weaker oscillations, which decay toward $g(r)=1$ as long-range positional correlations disappear. A typical simple liquid has no indefinitely repeated sharp lattice peaks.
\Image[/past-exam-of-the-quantum-condensed-matter-course-of-the-university-of-cambridge/2004-liquid-radial-distribution.png]
{title=Excluded core and damped coordination shells in a schematic liquid pair distribution}
{description=An original illustrative hard-core liquid profile, not experimental data. The horizontal limit is one; the neighbor count additionally contains the spherical-shell factor $4\pi nr^2$.}
The <static structure factor> measured by diffraction is related to the Fourier transform of $g(r)-1$. Thus the broad diffraction maxima of a liquid and the damped real-space coordination shells describe the same short-range organization.
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