# How does binding energy change as more fermions interact?

The subject is few-body quantum mechanics. Given a system of $$N$$ identical fermions (spin 1/2) interacting through pairwise potentials $$V_{ij}$$, how does the binding energy change between $$N$$ and $$N+1$$? Obviously this depends on the potential, so say it is the attractive Coulomb case:

$$V_{ij} = -\frac{1}{r_{ij}}$$

Both intuitive and analytical explanations are welcome.

Where I am at regarding this:

An estimate on the binding energy can be found using the variational principle, but this method gives only a lower bound on the binding energy. In general, this lower bound seems to decrease as $$N$$ increases (the system may be less bound). As the bound may be decreasing due to insufficiency in the variational wave function approximating the system, I cannot conclude that the binding energy is decreasing, let alone by how much.

Classically, I am thinking that, if a system of $$N$$ particles is bound, then adding another particle to the mix (increasing the total energy) increases the likelihood that one particle may gain energy enough to escape. I would expect this effect to diminish as $$N$$ increases. Although, the virial theorem states that $$KE \approx -1/2 PE$$, which may counteract this effect as $$N$$ increases. However, I am not sure how far any of this this extends to the quantum case.

• What is the application? Identical fermions repel each other. – my2cts Feb 6 at 8:33
• The application is in particle physics theory. Identical fermions would attract if interacting via a scalar mediator, I think, so I'm not sure if they have to repel each other. – alefs Feb 6 at 15:37
• this is rather vague. Superconductivity, perhaps? – my2cts Feb 6 at 22:11