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I found this question on Quora: https://www.quora.com/Can-you-theoretically-shoot-an-atom-fast-enough-to-kill-its-target

I think the Quora answer is good but incomplete, and it got me wondering what would actually happen.

In theory, a nearly infinite amount of energy could be imparted into a molecule as you keep adding 9's after the decimal point, but lets put a limit on it, say oh my god particle velocity, but a much heavier object, like a gold atom, not a proton. (oh my god particle has roughly the energy of a baseball, 5 OZ at 94 mph, so an atomic mass of 197 means equivalent energy of a 61 lb object traveling at 94 mph - more than enough to knock an average person off their feet pretty easily.

Two scenarios

1. Shooting someone at point-blank range, the atom hits them directly at very high velocity, would the atom pass through them leaving a slightly larger than atom size hole or would it interact with the atoms it hits to the extent where most of the energy would radiate throughout the body.




2. Shooting them from a distance where the atom would interact with air molecules and in the process, sending radiation in all directions, perhaps doing almost as much damage to the person holding the gun than the target, a little bit like the relativistic baseball, only much smaller.

I know about Anatoli Petrovich Bugorski and I think that stream of particles passed through him, and obviously didn't kill him. So, I'm thinking, the atom would pass through the person and not kill them, but I'm mostly guessing.

So this is actually the sort of question covered in my Master's courses at Delft! I will try to see if I remember the basics well enough, but I went into condensed-matter physics and not particle physics.

So you've got a particle that enters a non-vacuum, what does it do? The answer is that it starts to interact with the atoms that it's passing by. But mostly these interactions are just tiny little nudges of the electrons in those atoms, and the problem is that it is moving so fast that it doesn't get very much time to interact with them. But each interaction slows down the particle, and as it goes slower it potentially deposits more radiation and slows down even further. This leads to charged particles giving their biggest radiometric dose at a certain distance inside the medium they're penetrating, and this peak is called the "Bragg peak." It is hugely important when you are trying to irradiate a tumor. So for example we have always had a mechanism to irradiate nearby tissues less than tumor tissues and that is "rotate the subject or beam about the tumor," so that non-tumor tissues are simply exposed to the beam for less time. But with proton and heavy-ion radiotherapy, you have these more pronounced Bragg peaks that can be centered directly on the cancer, so they kill those cells much more effectively than the other ones in the path of the beam.

The basic problem that you are going to have is that as you move to higher energies, the Bragg peak moves further and further into the body. By the time you're in the TeV scale, I wouldn't be surprised if it had moved so far that you could no longer reliably hit someone with that Bragg peak even if you were going through them from the foot first trying to attenuate it through their leg so as to lodge the main payload in their brain.

Now it's possible that you can get enough dose in their head to kill some brain cells with a single particle, and that becomes a medical question that becomes off-topic for this particular issue. But if you're expecting a bullet hole type wound, then the answer is "probably there is no way to do that."

I am replying to the original title of the OP before the edit by David Z:

Is it possible to kill someone with a single atom and a particle accelerator?

The answer is no, and there is experimental evidence in the case of Anatoli Burgoski that you mention:

Bugorski survived longer than just a few days. In fact, the dude is alive and pretty well in 2018 at 75 years old. The accelerator incident didn't leave him entirely unscathed, however; he's human, after all. The beam burned a path through his skull and brain tissue, and, for the next couple of days after the event, the spots on his head where the beam entered and exited experienced some skin peeling. Bugorski lost the hearing in his left ear and now experiences constant tinnitus. The left side of Bugorski's face gradually became paralyzed, making it look oddly frozen in time. (Who needs Botox?) He has also suffered at least six tonic-clonic (aka grand mal) seizures and also experiences absence (aka petit mal) seizures.

You are asking about one high energy particle being able to kill.

The intensity of the proton beam that passed through Anatoli's head was $10^13$ protons per pulse. The energy of each proton 76 GeV, and he is still alive.

One particle is trivial compared to $10^13$ and, as another answer states we are all bombarded with high energy cosmics during our life.

The reason is that a charged particle will have a path with small interactions through matter, as discussed in other answers. Here is a bubble chamber picture of protons in a beam ( the number of protons in the beam is reduced for bubble chamber beams, for clarity in the pictures)

This worksheet is based on images recorded by the 2 m bubble chamber at CERN on 10 August 1972. The bubble chamber was exposed to a beam of protons from CERN ’ s proton synchrotron PS with a momentum of 24 GeV/c.

The electromagnetic interactions are those that generate the ionisation of the tracks, the width is less than a micron. Passing through the head the disturbance is minimal , similar to what is seen in the picture above. More damage happens with strong interactions, but those have to hit a nucleus, where two of the five protons entering have managed to do in the two meter chamber. ( the picture was picked because there was an interaction, the real probability has to count all the empty of interactions frames) . These strong interactions are the ones that can destroy cells by cascading through living matter.

The higher the energy of a particle the smaller the deBroglie wavelength

so the probability of hitting anything on its path is smaller with higher energy, a particle has to hit head on a nucleus which has dimensions of a fermi, for a strong interaction to happen.

Thus the answer is no, a single particle no matter of how high the energy it carries is, cannot kill. As we deal with quantum mechanics the correct framing is : "the probability of a very high energy particle to kill a human is infinitesimally small"

Now on some statements in your question:

but a much heavier object, like a gold atom, not a proton. (oh my god particle has roughly the energy of a baseball, 5 OZ at 94 mph, so an atomic mass of 197 means equivalent energy of a 61 lb object traveling at 94 mph - more than enough to knock an average person off their feet pretty easily.

An atom as it enters a body will immediately shed its electrons with electromagnetic interactions and will just be like 197 protons out of the $10^13$ in the beam hitting Anatoli's head. There is a probability that some of those $10^13$ protons have hit and interacted with the strong interaction, as in the picture above, in the head. What happens as far as interactions go, the end products will leave just ionizing, no cascade, as there is no cascade in the picture above. The velocity near light velocity means in a very small interval of time the particles near velocity c traverse the head and are out.

For a high momentum beam particle to transfer its energy to the body , the body should act as a rigid body. Instead it is a quantum mechanical system held together by electromagnetic interactions. A nucleus in the body hit and interacting directly with the projectile cannot transfer any momentum to the body, as far as the strong interactions go it is as if it is free, everything happens much faster than the electromagnetic bonds keeping the body in shape can respond to. The hit nucleus will react as the interactions in the picture, generating secondary particles which again will have a small probability of interacting strongly before they leave the head volume.

Shooting them from a distance where the atom would interact

It would interact as the tracks in the picture, just ionisation, and keep its course. The probability of a strong interaction with air is very very small.

The beam entering the bubble chamber in the picture above, was sent through air, because it was so few protons at a time, and when we had a glitch in picture taking we would joke that the cat crossed the beam!

We are all struck by cosmic rays in the form of relativistic ions, many times in our lives. See, for example, this paper. There is a phenomenon called the "Bragg peak" that seems to limit the energy deposition rate when an ion beam is passing through material, resulting in a large fraction of net energy being deposited in the last relatively small fraction of the beam path. So, if the ion energy is high enough, most of the beam energy ends up somewhere on the far side of a finite-thickness target like a human being.

Interaction of a single particle with a human body, of course, is probabilistic. There's a finite chance the particle will interact with an atom near the start of its path through the body, and the same goes for its chances of interacting at any interval along its path. So, your question really asks whether or not destruction of everything along any specific very thin path through the body can kill. I doubt it, but am not sure. It seems very unlikely that destruction of, e.g., all the nerves along a sub-millimeter long straight path would kill. There's a lot of redundancy in our neural circuitry (for good Darwinian reasons, considering that we're constantly bombarded with cosmic rays!).