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We investigate the spatial structure of the two-neutron wave function in theBorromean nucleus $^{11}$Li, using a three-body model of $^9$Li $+n+n$, whichincludes many-body correlations stemming from the Pauli principle. The behaviorof the neutron pair at different densities is simulated by calculating thetwo-neutron wave function at several distances between the core nucleus $^9$Liand the center of mass of the two neutrons. With this representation, a strongconcentration of the neutron pair on the nuclear surface is for the first timequantitatively established for neutron-rich nuclei. That is, the neutron pairwave function in $^{11}$Li has an oscillatory behavior at normal density, whileit becomes a well localized single peak in the dilute density region around thenuclear surface. We point out that these features qualitatively correspond tothe BCS and BEC-like structures of the pair wave function found in infinitenuclear matter.Comment: 4 pages, 3 eps figures. The version to appear in PR

Coexistence of BCS- and BEC-Like Pair Structures in Halo Nuclei