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The quasi-persistent neutron star X-ray transient and eclipsing binary EXO 0748-676 recently started the transition to quiescence following an accretion outburst that lasted more than 24 years. We report on two Chandra and twelve Swift observations p erformed within five months after the end of the outburst. The Chandra spectrum is composed of a soft, thermal component that fits to a neutron star atmosphere model with kT^inf~0.12 keV, joined by a hard powerlaw tail that contributes ~20% of the total 0.5-10 keV unabsorbed flux. The combined Chandra/Swift data set reveals a relatively hot and luminous quiescent system with a temperature of kT^inf~0.11-0.13 keV and a bolometric thermal luminosity of ~8.1E33-1.6E34 (d/7.4 kpc)^2 erg/s. We discuss our results in the context of cooling neutron star models.
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