If EC is "endothermic", what is the mechanism?
Typically, an energy gradient is associated with some kind of force. Is there an identified repulsive nuclear force at these scales, that is counteracting the electromagnetic attraction? Electro-Weak force? Strong force?
Please explain in more detail if you have the time.
Also, why is a lepton able to interact with a quark like this? Why is it able to change an "up" quark to a "down" quark at all?
First question, what I mean by endothermic is the overall energy of the combined nucleus (proton rich) plus electron system is lower after EC than before, EC is effectively converting the excess energy of a nuclear excited state (excess energy which in this case due to EM force from the excess protons) into the higher rest mass of a neutron relative to a proton plus electron. Since the end state is at a lower energy than the start, the potential barrier that is between the electron's wave function before (barrier due to the prohibited intermediate states of an electron "between" an innermost orbital and being part of the nucleus) can be tunneled through--that is where the probabilistic nature of radioactive decay is from, in this case, it's the probability of the electron tunneling from its stable inner orbital state into the merged state with a proton. so the reaction in this case is governed by three forces, EM and weak force (the electron-proton interaction) and EM and strong force (which creates the high energy initial state due to EM force larger than strong force in the excess proton nucleus and low energy final state due to strong force over EM force in the balanced nucleus afterwards with the new neutron replacing the proton)
For the second question, I don't know how to explain the exact mechanism, but the most analogous example is the reverse reaction of beta decay where a down (-1/3 charge) quark is changed into an up (+2/3) to change a neutron into a proton--in at case (effectively the reverse reaction) e charge is conserved intrinsically and the spin is balanced by the emission of a neutrino.
In both cases, it's the weak force that is governing the electron reaction that is occurring IIRC
The neutrinos are the key in these reactions as they are the spin-balancers of the nuclear world, and being uncharged leptons (the uncharged counterparts to electrons), allow the reactions to balance--the spin of the emitted neutrino is the opposite of the electron involved in the reaction.
Apologies if this is partially incorrect or muddy, it's been 14 years since my quantum classes. I'll think about it more and see if I can come up with a better explanation, but the fundamental basis is, as stated before, the electron has specific states that are energy minima (the "orbitals" the innermost of which is the lowest allowed potential energy state, so it can't move any further inward via normal (radiative emission of a photon, ie a pure EM interaction) modes, so there is a potential barrier to it moving into the nucleus. In a normal nucleus, the electron present there would be at a higher energy state than in the orbital, so it's transition there is prohibited. In a proton rich nucleus, that state is now a lower energy state, so there becomes a finite probability it will tunnel through the barrier and undergo capture.
In my previous example of degenerate matter and neutron stars, the electron states are modified by gravity to collapse inward, basically reducing the "radius" of the orbitals and allowing energy level degeneracy (gravity overcomes the exclusion forces preventing multiple electrons from occupying similar states), and when that gravitational force is high enough (again, think about it from an energy basis, the higher the density, the lower the energy state, so when there is enough gravitational force to overcome the exclusion forces, the defer ate states become allowed) the collapse goes further, and forces the electrons through the barrier to combine with the remaining protons and form all neutrons--a neutron star, which is, in effect, one big nucleus, where gravity (usually the weakest force, at least when it comes to nuclear interactions) is sufficient to dominate over the others and not only keep it together, but prevent neutron decay--a beta decay would require an neutron to form a proton and electron, and that would be a higher energy state, and thus prohibited.
Ugh.
