Due to its proximity, youth, and solar-like characteristics with a spectral type of K2V, Eps Eri is one of the most extensively studied systems in an extrasolar planet context. Based on radial velocity, astrometry, and studies of the structure of its circumstellar debris disk, at least two planetary companion candidates to Eps Eri have been inferred in the literature (Eps Eri b, Eps Eri c). Some of these methods also hint at additional companions residing in the system. Here we present a new adaptive optics assisted high-contrast imaging approach that takes advantage of the favourable planet spectral energy distribution at 4 microns, using narrow-band angular differential imaging to provide an improved contrast at small and intermediate separations from the star. We use this method to search for planets at orbits intermediate between Eps Eri b (3.4 AU) and Eps Eri c (40 AU). The method is described in detail, and important issues related to the detectability of planets such as the age of Eps Eri and constraints from indirect measurements are discussed. The non-detection of companion candidates provides stringent upper limits for the masses of additional planets. Using a combination of the existing dynamic and imaging data, we exclude the presence of any planetary companion more massive than 3 Mjup anywhere in the Eps Eri system. Specifically, with regards to the possible residual linear radial velocity trend, we find that it is unlikely to correspond to a real physical companion if the system is as young as 200 Myr, whereas if it is as old as 800 Myr, there is an allowed semi-major axis range between about 8.5 and 25 AU.
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