The Oxford dictionary has ataraxia (ataraxy) as a valid word but not ataraxis. however, I've seen and heard the ataraxis being used once in while. But it happens that the guys at Oxford do not recognize it (ataraxis) as a word. You can search ataraxis and many sites, along with Google itself, will define it. Now the question is whether I can use the word ataraxis and ataraxy (ataraxia) in place of each other and will any examiner such as those at GRE and GMAT consider and approve it.