# How can photons interact with nuclei?

How can photons such as X-rays or gamma rays interact with the nuclei of atoms given that, as I understand it, the length scale of a nucleus is around a couple of femtometers? So, shouldn’t the size of a nucleus be smaller than the wavelengths of most gamma rays by a significant degree? As an extreme example, how can photons interact with a proton (such as by reflecting off of it or imparting momentum to it)?

• I’m not really sure what the problem is? You can have an infinitely large conductive wall and photons would still interact with it by reflecting off of it. Where exactly is the problem?
– Y2H
Commented Jun 14 at 23:42
• Atoms are also much smaller than the typical wavelengths of light emitted. E.g. Balmer alpha emission comes from an atom three orders of magnitude smaller than the wavelength of the photon emitted. Commented Jun 16 at 8:02

While it is true that being small relative to wavelength tends to reduce an objects interaction with waves, there's no absolute restriction. You can, for example, buy a wristwatch that sets itself from low frequency radio signals of ~5 km wavelength. It interacts enough to decode the time.

Resonance can make an object behave as if it is much larger than its physical size. This is important in the Mössbauer effect. You should also consider that a macroscopic object contains many nuclei. Even if the probability of a photon interacting with an individual nucleus may be small, the probability of interaction with one of the many nuclei is much larger.

It is better to think of this in terms of the characteristic energy scales involved. The outermost electron orbitals of for example a transition metal have energies of order ~several electron volts, and can be "talked to" with an ultraviolet photon. The innermost orbitals have energies of order several tens of kiloelectron volts and can be talked to with x-ray photons. Nuclear processes have energies of order ~several million electron volts and communicate their presence with gamma ray photons.

In general, this means that a UV photon can't penetrate beyond the outermost orbitals; an x-ray photon can penetrate to the innermost orbitals, and to penetrate the nucleus you need a gamma ray.

• In other words, the way it is produced is the way it works. Commented Jun 17 at 4:07

This is the same question as: "How can visible light interact with atoms?" And it has the same answer: Quantum mechanics.

Your nucleons/electrons are charged particles bound in some field. Quantum mechanics tells us, that such particles can be described as a sum of certain wave functions called Eigenstates. Each Eigenstate is associated with an exact energy value that the particle has in that state. As such, these Eigenstates are constant in time because either energy and/or time must be undetermined (Heisenbergs uncertainty principle: if the particle is localized in time, its energy is unknown, and vice versa). So far, so good.

However, when you look at a superposition (sum) of two Eigenstates with different energy values, the resulting probability cloud of the particle is not constant in time anymore. Instead, the probability cloud of the particle oscillates with a frequency proportional to the energy difference between the states.

Now, when you have an electron or a proton oscillating in probable location, the oscillating particle acts like an electromagnetic antenna that either emits or absorbs a photon of its oscillating frequency. In the process, the particle changes over from one of the two Eigenstates to the other, either supplying or absorbing the energy of the photon.

Of course, the electromagnetic field is also a quantum field of photons which can be in a superposition of being emitted and not, but I guess that goes beyond the scope of this question.

There are three main types of interactions a photon can have with an atom:

1. elastic scattering
2. inelastic scattering
3. absorption and re-emission

I am only going to talk about the first one, as the third one was already mentioned by @nielsnielsen.

Why is the sky blue? The answer is the same to your answer, it is probabilities, and quantum mechanics. It is because the visible light coming from the Sun (white, not yellow) interacts with the atoms in the atmosphere. This light from the Sun is made up of a wide range of wavelengths including visible.

This interaction (as you correctly suspected) is wavelength dependent. This is one of the first lessons to learn about QFT, it is rather better to think of waves of every particle we know of, the atoms, and the photons are all just waves of energy. Photons propagate freely, while energy in the atoms of the atmosphere is captured and bound.

Now if you give up the misconception of thinking of atoms as some kind of balls, and rather think of them as a excitation of a field, a wave of energy and do the same for photons, then you can realize that the probability of their interaction depends on their energy content (or wavelength) or spatial extent.

So you have one type of wave of energy (atoms) bound into some structure, and these have some spatial extent, and photons have frequency (and corresponding wavelength). Now if these spatial extensions are closer, the interaction has a higher probability.

For example, the atoms in the atmosphere are very small (relative to the wavelength of visible light which is 400-700nm), so the light that has smaller wavelength, will have a higher probability (because its "size" is closer to the atoms' spatial extent) of interacting with it. That light is the blue part of the spectrum, shorter wavelength, so the blue light will scatter with higher probability, hence the sky looks blue.

This type of interaction, elastic scattering not only works for gases, but for liquids:

https://physics.stackexchange.com/a/120080/132371

Ever wondered why a long tube of water looks blue? An it works for certain solids (ever wondered why really the prism brakes light into different paths, same reason).

The answer to your question is quantum mechanics and the wavelength dependent nature of interaction between light and atoms.