  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.
