So the way I understand binding energy is that if I have two nucleons and I let the come together, they’ll decrease their potential energy as they move closer and this will speed them up as they’re flying towards eachother. Therefore, binding energy is the energy that you must remove from the nucleons so that they stay together and don’t fly past eachother rather than a energy you put in to hold them together. But by that logic, wouldn’t adding nucleons always increase the binding energy then? For example, if I have nickel-62 and I want to add a nucelon to it, then as the nucleon and nickel atom move closer together with a certain kinetic energy, I have to remove that kinetic energy for them to stay together which would be the binding energy. Therefore, binding energy should continuously increase but the curve decreases at nickel-62, so is my understanding that binding energy is the amount of energy you take out wrong?
A qualitative argument is : because there are two forces entering into the binding of individual nucleons into ensembles: the strong force (attractive), the electromagnetic (repulsive) and neutrons can act as a |"shield" for an electromagnetic repulsion, it is not strange that there exists a maximum in the curve.
Because the strong nuclear force is short range, the Coulomb repulsion between protons has infinite range, and because neutrons are more massive than protons.
The binding energy due to extra nucleons (whether protons or neutrons) increases rapidly at small atomic masses but slowly at large masses, because only the nearest neighbours of added nucleons are bound to them. On the contrary, added protons feel repulsion from all the protons in a nucleus, so this repulsive potential grows slowly to begin with when there are few protons, but grows as the square of the number of protons divided by the radius of the nucleus (which only increases as the cube root of the number of nucleons).
But you can't just add neutrons instead, because if the n/p ratio becomes too high, the higher mass neutrons will beta decay into protons.
The equilibrium between these effects essentially sets the binding energy per nucleon for a nucleus of a given atomic mass and results in the peak around iron and nickel.