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A receiving antenna with a matched load will always scatter some power. This paper sets an upper and a lower bound on the absorption efficiency (absorbed power over sum of absorbed and scattered powers), which lies between 0 and 100% depending on the directivities of the antenna and scatter patterns. It can approach 100% as closely as desired, although in practice this may not be an attractive solution. An example with a small endfire array of dipoles shows an efficiency of 93%. Several examples of small conical horn antennas are also given, and they all have absorption efficiencies less than 50%.