The mention of ataraxia in the letter to Herodotus is noteworthy, too:
Quote from Epicurus, Letter to Herodotus[82] ἡ δὲ ἀταραξία τὸ τούτων πάντων ἀπολελύσθαι καὶ συνεχῆ μνήμην ἔχειν τῶν ὅλων καὶ κυριωτάτων.
[82] But mental tranquillity (ataraxia) means being released from all these troubles and cherishing a continual remembrance of the highest and most important truths. (Hicks)
And the real freedom from this kind of trouble consists in being emancipated from all these things, and in preserving the recollection of all the principles which we have established, especially of the most essential of them. (Yonge)
The troubles one is released from have to be fear and anxiety of gods, death, etc., since the section directly preceding this about the importance of atarxia is:
QuoteWe must also recollect that that which principally contributes to trouble the spirit of men is the persuasion which they cherish that the stars are beings imperishable and perfectly happy, and that then one’s thoughts and actions are in contradiction to the will of these superior beings; they also,[454] being deluded by these fables, apprehend an eternity of evils, they fear the insensibility of death, as that could affect them. What do I say? It is not even belief, but inconsiderateness and blindness which govern them in every thing, to such a degree that, not calculating these fears, they are just as much troubled as if they had really faith in these vain phantoms. (Yonge)