We propose a new framework by means of the dineutron condensate (DC) wave function to describe the dineutron correlation, which is characterized by the spatially strong correlation of a spin-zero neutron-neutron pair, in neutron-rich nuclei with an active deformed core surrounded by valence neutrons. Using the DC wave function for a 2α+2n system, which corresponds to a toy model for the 10 Be system, we investigate the neutron-neutron correlation around the 2α core and discuss the mechanism of the dineutron formation at the surface of finite nuclei. To investigate dineutron correlations in realistic nuclear systems, we superpose the antisymmetrized molecular dynamics (AMD) wave functions and the DC wave functions. Applying the AMD+DC method to 10 Be, we show effects of the DC wave functions in the ground and excited 0 + states of 10 Be and discuss the dineutron correlation in them.Subject Index: 210, 211, 213 §1. IntroductionRecently, neutron-rich unstable nuclei are investigated intensively and various exotic phenomena have been discovered. The dineutron correlation is one of the key issues attracting a great interest in the physics of unstable nuclei. The dineutron correlation means the strong spatial correlation between two neutrons in the spinzero channel. Even though two neutrons do not form a bound state in free space, they attract each other rather strongly. It was suggested that the spatial correlations between two neutrons are enhanced, such as in a low-density region of an infinite nuclear matter, 1)-7) in the surface region of neutron-skin nuclei 8)-11) and that of neutron-halo nuclei. 12)-25) In such nuclear systems, the strongly correlated neutronpair with a rather compact size can be regarded as a semi-bound or a virtually bound state called a dineutron. The dineutron correlation is considered to be an important aspect to understand the structures of unstable nuclei.In studies of the symmetric and asymmetric nuclear matter, it was shown that the strength of the two-neutron correlation changes as a function of the matter density. 1)-7) Matsuo suggested a continuous transitions from a weak BCS-like coupling to a strong boson-like coupling in accordance with a decrease of the matter density 5) (the BCS-BEC crossover, such as in a superfluid Fermi gas 26) ). The bosonic behavior of dineutrons is often discussed in relation to the α condensation suggested in a low-density symmetric nuclear matter. 27) In finite nuclear systems, the importance of the pairing correlation in spherical and deformed nuclei has been discussed well so far. In the medium-heavy nuclei, Matsuo et al. have investigated the neutron-neutron correlation and collective modes