The particle unbound 26 O nucleus is located outside the neutron drip line, and spontaneously decays by emitting two neutrons with a relatively long life time due to the centrifugal barrier. We study the decay of this nucleus with a three-body model assuming an inert 24 O core and two valence neutrons. We first point out the importance of the neutron-neutron final state interaction in the observed decay energy spectrum. We also show that the energy and and angular distributions for the two emitted neutrons manifest a clear evidence for the strong neutron-neutron correlation in the three-body resonance state. In particular, we find an enhancement of two-neutron emission in back-to-back directions. This is interpreted as a consequence of dineutron correlation, with which the two neutrons are spatially localized before the emission.PACS numbers: 21.10. Tg,23.90.+w, Correlations among particles lead to a variety of rich phenomena in many-fermion systems, such as superconductivity and superfluidity. The spatial distribution of particles is also affected by the correlations. For manyelectron systems, the Coulomb repulsion between electrons yields the so called Coulomb hole, in which the distribution of the second electron is largely suppressed in the vicinity of the first electron [1,2]. In atomic nuclei, in contrast, an attractive nuclear force leads to the dineutron and diproton correlations, with which two nucleons are spatially localized in the surface region of nuclei [3,4]. These nuclear correlations have attracted lots of attention recently [5][6][7][8][9], in connection to physics of weakly bound nuclei.In order to probe the inter-particle correlation, it has been a standard way in atomic physics to measure a double ionization with strong laser fields [10][11][12][13]. It has been observed that the ionization rate is significantly enhanced due to the electronic correlation, and moreover, there is a strong momentum correlation between the two emitted electrons. The corresponding experiment in nuclear physics is the Coulomb breakup of the Borromean nuclei 11 Li and 6 He, in which those nuclei are broken up to the core nuclei, 9 Li and 4 He, and two neutrons in the Coulomb field of a target nucleus [14][15][16]. The observed breakup probabilities, especially those for the 11 Li nucleus, show a sharp peak in the low-energy region, which can be accounted for only by taking into account the neutron-neutron correlations. Furthermore, from the observed strength distribution, the opening angle between the valence neutrons in the ground state of the Borromean nuclei has been inferred employing the cluster sum rule [14,17,18]. For both 11 Li and 6 He, the extracted opening angles were significantly smaller than the value for the independent neutrons, that is, 90 degrees, and clearly indicate the existence of the dineutron correlation.A small drawback with the cluster sum rule approach is that it yields only an expectation value of the opening angle and a detailed angular distribution cannot be studied with this method. F...