We can assume to act morally is what is right. So if not acting morally you are not doing what is right.

Are you familiar with the Prisoner's Dilemma? Now personally, I take it to be a demonstration that self-interest is not rational. But supposing that self-interest prevailed universally, whenever such situations arose, and they arise very frequently, we would end up with the worst outcome instead of the best.

So if you are willing to think of moral behaviour as that which promotes the best solution for the community, rather than the individual, with a bit of hand-waving as to what the limits of 'community' are, then I think you have a basis for the motivation moral action in identification with others rather than with an isolated 'self'. I have an old essay about it if you want to pursue this line.

What does this mean though? What is right is what has to be done? Is it about rules? — Πετροκότσυφας

It is about what ought to be done (or avoided). I doubt that "ought" can be adequately reduced to something that is more basic.

So if you are willing to think of moral behaviour as that which promotes the best solution for the community — unenlightened

But that is not what moral behavior is in reality.

Are you familiar with the Prisoner's Dilemma? Now personally, I take it to be a demonstration that self-interest is not rational. — unenlightened

Then you understand it incorrectly. Prisoner's dilemma is not a demonstration of irrationality, it is the demonstration that rational behaviour can be sub-optimal, especially regarding maximising self-interest.

It is an inaccurate description of human nature, Dawkins dealt with this in his book The Selfish Gene.

Dawkins admits at the beginning of that book that genes are not selfish, and that they have no interests; the whole notion is an analogy. It's a shame he forgets it in what follows.

But if you think self interest is rational, then give me the rationale as to why your interests are more interesting than another's? I have never seen it done, but only assumed. To say that it is human nature is not to say that it is rational, obviously. The prisoner's dilemma demonstrates what follows from rational implementation of self interest, not that self interest is rational.

Incidentally, I remember you had an interesting essay about this on your blog! (Y)

Linked in my first reply. Curiously, I also just came across this, which might be relevant to the op, though I haven't read even the available extract yet.