What "changes" in the quantum state of bound nucleons that cause that system to have mass defect?

Question

The electric field in an excited hydrogen atom is non-zero over a bigger volume than the electric field in a ground-state hydrogen atom. The energy associated with this extra electric field must be provided to excite the ground-state atom.

Intuitively, it is clear that in a system where the potential energy of the electron is lower, the overall mass is also lower. There's less energy here.

When two nucleons bind together. Their masses decrease. Is there a similar analog change in wave function between them akin to a reduction in the volume of the electric field of the electron? Is it possible to conceptualize this loss of mass through the change of component wave functions/behavior?

Does the exchange of pions/residual strong force alter the probability densities in a way where it is clear that the wave function of the bound systems possess less energy than unbound?

I would like to know if it's possible to explain mass defect without using the phrase "binding energy" or "Minus the energy it takes to separate the components"

Answer 1

An under-appreciated fact about electromagnetism is that the Lorentz follows from Maxwell's equations (see user4552's answer to this question). You can derive the potential energy between two charges by simply computing the energy of the electromagnetic charges via

$$Energy = \int \left[\frac{\epsilon_0}{2}|\vec{E}|^2 + \frac{1}{2\mu_0}|\vec{B}|^2\right] dV$$

So there is not actually a fundamental distinction between binding energy and energy stored in the electromagnetic field, and you can think of it however you like.

The weak and strong nuclear forces are much more complicated than the electromagnetic force, but the same conclusion carries over. In fact it's common to understand the binding energy of the strong force by thinking about the energy stored in the field; the potential energy due to the strong nuclear force scales linearly with distance, as long as the distance is small. This arises because two particles with charge under the strong force (such as quarks) develop strings of gluons connecting them, called flux tubes. The length of the flux tube scales linearly with distance, and therefore the energy grows linearly as well. I assume the story is the same when you consider pion exchange at larger scales than individual quarks.

Answer 2

Does the exchange of pions/residual strong force alter the probability densities in a way where it is clear that the wave function of the bound systems possess less energy than unbound?

It is better to be consistent and use the same mental picture when comparing coupling in atoms and nuclei (Indeed, there are parallels.) Thus, if we speak of nuclear forces as an exchange of pions, we should also visualize the electromagnetic forces as an exchange of photons. The difference is that pions are massive, that is they are described by Klein-Gordon equation, whereas photons are described by wave equation (i.e., a Klein-Gordon equation with zero mass.) This means that nucleon potential exhibits a Yukawa-like behavior rather than a more simple Coulomb one. (This is further complicated by the Coulomb repulsion between protons.)

When two nucleons bind together. Their masses decrease. Is there a similar analog change in wave function between them akin to a reduction in the volume of the electric field of the electron? Is it possible to conceptualize this loss of mass through the change of component wave functions/behavior?

One we have agreed that the nucleon interaction can be approximately described by a potential, the same reasoning applies as in the case of a hydrogen atom, although with correction for the shape of the potential and the fact that the nucleons have approximately equal masses - whereas in an atom the center-of-mass can be safely assumed to coincide with the nucleus. Here is a figure taken from these notes:

What might be confusing is that realistic nuclear potentials are quite sharp, and often depicted as nearly square potential wells:

This is however only a convenient approximation.