should I cite with (Smith et. al 2000, ch 6) or (Jeff et. al 2000) and then add a citation for each chapter in the cited literature section?

I've checked The Chicago Manual of Style and the New Oxford Style Manual and it seems that the second style is preferable. I don't know if there is a standard way to abbreviate if you have to cite many different chapters.

However, if you're writing for a journal, there might be a preferred style, which can be described in the journal style guide or applied directly by the typesetter.

should I cite with (Smith et. al 2000, ch 6) or (Jeff et. al 2000) and then add a citation for each chapter in the cited literature section?

I've checked The Chicago Manual of Style and the New Oxford Style Manual and it seems that the second style is preferable. I don't know if there is a standard way to abbreviate if one has to cite many different chapters.

However, if you're writing for a journal, there might be a preferred style, which can be described in the journal style guide or applied directly by the typesetter.