  We explicitly describe all Hilbert function spaces that are interpolation
spaces with respect to a given couple of Sobolev inner product spaces
considered over $\mathbb{R}^{n}$ or a half-space in $\mathbb{R}^{n}$ or a
bounded Euclidean domain with Lipschitz boundary. We prove that these
interpolation spaces form a subclass of isotropic H\"ormander spaces. They are
parametrized with a radial function parameter which is OR-varying at $+\infty$
and satisfies some additional conditions. We give explicit examples of
intermediate but not interpolation spaces.
