We perform a search for dormant comets, asteroidal objects of cometary origin, in the near-Earth asteroid (NEA) population based on dynamical and physical considerations. Our study is based on albedos derived within the ExploreNEOs program and is extended by adding data from NEOWISE and the Akari asteroid catalog. We use a statistical approach to identify asteroids on orbits that resemble those of short-period near-Earth comets using the Tisserand parameter with respect to Jupiter, the aphelion distance, and the minimum orbital intersection distance with respect to Jupiter. From the sample of NEAs on comet-like orbits, we select those with a geometric albedo $p_V leq 0.064$ as dormant comet candidates, and find that only $sim$50% of NEAs on comet-like orbits also have comet-like albedos. We identify a total of 23 NEAs from our sample that are likely to be dormant short-period near-Earth comets and, based on a de-biasing procedure applied to the cryogenic NEOWISE survey, estimate both magnitude-limited and size-limited fractions of the NEA population that are dormant short-period comets. We find that 0.3-3.3% of the NEA population with $H leq 21$, and $9^{+2}_{-5}$% of the population with diameters $d geq 1$ km, are dormant short-period near-Earth comets.
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