Ataraxis or/and ataraxia, a quandary. A question over their existence and usage?

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.

Ataraxia is a central term in Epicurean philosophy, and this is the way it is normally spelled.

Greek tarattô means "to perturb", and a-tarax-ia is a regularly formed derivation meaning a state of "unperturbedness", mainly of the mind, when one manages to remain unworried. It is similar to the Stoic ideal of apatheia "unfeelingness", which is stronger and more rigid, being unmoved by any emotion at all.

Most Greek and Latin words on -ia become -y in English. But for some reason the Latin spelling ataraxia is the one in common use in modern academic literature.

Ataraxis could be a perfectly valid derivation in Greek, "[the action of] being unperturbed", though perhaps it could mean "the action of non-perturbing". For whatever reason, this is not the form Epicurus and Lucretius chose, as far as I know, and it never came into common use.

Google Ngrams bears this out: