Reflected starlight measurements will open a new path in the characterization of directly imaged exoplanets. However, we still lack a population study of known targets amenable to this technique. Here, we investigate which of the about 4300 exoplanets confirmed to date are accessible to the Roman Space Telescopes coronagraph (CGI) in reflected starlight at reference wavelengths $lambda$=575, 730 and 825 nm. We carry out a population study and also address the prospects for phase-curve measurements. We used the NASA Exoplanet Archive as a reference for planet and star properties, and explored the impact of their uncertainties on the exoplanets detectability by applying statistical arguments. We define a planet as Roman-accessible on the basis of the instrument inner and outer working angles and its minimum planet-to-star constrast (IWA, OWA, $C_{min}$). We adopt for these technical specifications three plausible configurations labeled as pessimistic, intermediate and optimistic. Our key outputs for each exoplanet are its probability of being Roman-accessible ($P_{access}$), the range of observable phase angles, the evolution of its equilibrium temperature, the number of days per orbit that it is accessible and its transit probability. In the optimistic scenario, we find 26 Roman-accessible exoplanets with $P_{access}$>25% and host stars brighter than $V$=7 mag. This population is biased towards planets more massive than Jupiter but also includes the super-Earths tau Cet e and f which orbit near their stars habitable zone. A total of 13 planets are part of multiplanet systems, 3 of them with known transiting companions, offering opportunities for contemporaneous characterization. The intermediate and pessimistic scenarios yield 10 and 3 Roman-accessible exoplanets, respectively. We find that inclination estimates (e.g. with astrometry) are key for refining the detectability prospects.
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