Greek ψυχή (psychē); Latin anima (spirit) and animus (mind), in Lucretius
The soul is a body made of very fine atoms, spread throughout the whole body, with its ruling part, the mind, seated in the chest. It can neither exist nor feel apart from the body, and when the body dies its atoms disperse. See Death Is Nothing To Us.
1. Key Texts
(1) Next one must observe, by reference to our sensations and feelings (for these will provide the most secure conviction), that the soul is a body of fine texture, distributed throughout the whole aggregate, most closely resembling breath with a certain admixture of heat, and in some respects resembling the one, in some respects the other. (2) But there is also a part which differs greatly from even these in fineness of texture, and because of this is more closely in harmony with the rest of the aggregate. (3) All this is made evident by the powers of the soul, its feelings, its ease of movement, its thought processes, and those things whose removal brings death to us. (4) Next one must observe that the soul is mainly responsible for sensation. (5) Yet it would not have acquired this, had it not been somehow enclosed by the rest of the aggregate. (6) But the rest of the aggregate, while providing this cause for the soul, itself acquires a share of this property from the soul; yet it does not acquire all that the soul acquires. (7) Hence on the departure of the soul it does not have sensation. For it did not have this power in itself, but provided for another thing - the thing which had come into being along with it - the conditions for it to have it; and this thing, through the power now perfected in it as a result of motion, was at once producing for itself the property of sensation, and giving it back to the aggregate as well, by virtue of closeness and reciprocity of motion, as I have said. (tr. Long & Sedley)