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  "body": "\n## Example\n\nConsider a homogeneous and isotropic classical fluid in $\\R^3$ with number density $\\rho \u003e 0$.\nLet $g(r)$ be its radial distribution function and $h(r) = g(r) - 1$ the total correlation function, where $r$ is the distance between two particles.\nThe Ornstein–Zernike equation defines the direct correlation function $c$ by\n$$h(\\abs{x - y}) = c(\\abs{x - y}) + \\rho \\int_{\\R^3} c(\\abs{x - z}) \\, h(\\abs{z - y}) \\, dz, \\quad x, y \\in \\R^3.$$\nFor known $h$ it is a [[convolution integral equation|EY75YD988Z]] of the second kind for $c$ on $\\R^3$, and for known $c$ one for $h$.\n\nCheck by the Fourier transform: the integral is the convolution $c * h$, so the equation becomes $\\hat h(q) = \\hat c(q) + \\rho \\, \\hat c(q) \\hat h(q)$.\nHence $\\hat h = \\frac{\\hat c}{1 - \\rho \\hat c}$ and $\\hat c = \\frac{\\hat h}{1 + \\rho \\hat h}$, wherever the denominators do not vanish.\n\n## Remarks\n\nThe equation splits the correlation between two particles into a direct part $c$ and an indirect part carried through a chain of other particles.\nBy itself it has two unknown functions, so it needs a second relation, a closure, such as the [[Percus–Yevick approximation|K3E536PSRJ]] or the [[hypernetted-chain equation|MRJ2FHX6K1]].\n\n## Explanations\n\n### L1 human\n\nIn a liquid, the position of one molecule influences where its neighbours are likely to be.\nThe equation says that this influence is the sum of a direct effect and of effects passed on through a third molecule, then a fourth, and so on.\nBecause the indirect part is a convolution, it is simple in Fourier space.\n",
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