  We discuss the spatial structure of the Cooper pair in dilute neutron matter
and neutron-rich nuclei by means of the BCS theory and the
Skyrme-Hartree-Fock-Bogioliubov model, respectively. The neutron pairing in
dilute neutron matter is close to the region of the BCS-BEC crossover in a wide
density range, giving rise to spatially compact Cooper pair whose size is
smaller than the average interaparticle distance. This behavior extends to
moderate low density ($\sim 10^{-1}$ of the saturation density) where the
Cooper pair size becomes smallerst ($\sim 5$ fm). The Cooper pair in finite
nuclei also exhibits the spatial correlation favoring the coupling of neutrons
at small relative distances $r \lesim 3$ fm with large probability.
Neutron-rich nuclei having small neutron separation energy may provide us
opportunity to probe the spatial correlation since the neutron pairing and the
spatial correlation persists also in an area of low-density neutron
distribution extending from the surface to far outside the nucleus.
