A particle beam weapon would be good for shooting something where you did not want to burn a hole in it, but rather wanted to deliver energy to something inside - perhaps a lifeform, or some element of a spaceship. The precision (in 3 dimensions) would minimize damage to the rest of the target which might be desirable for various reasons. It might be less likely to blow up. Or you could salvage it. Or you could disable a ship without punching a hole in the side and killing the crew.
As background consider what real particle beams are used for. Conventional radiotherapy uses photons which is electromagnetic radiation. Particle radiation has the benefit that a moving charged particle unloads its energy mostly at the point where it slows down.
So a particle beam is good for depositing energy at a specified distance into an object, and that energy deposit site (here a tumor) can be governed by adjusting the amount of energy put on a proton.
Other ions are used for particle beam radiation. One hears about carbon ion radiation and I see that other particles (neon, krypton) have been tried.
from The Emerging Role of Carbon-Ion Radiotherapy
While conventional radiation generally passes continually through a
biological target, with dose delivered roughly equivalently throughout
the beam path, particle beams release energy at the inverse of their
velocity. Particle beams thus deliver a lower entry dose, depositing
the majority of their energy at the flight path terminus, yielding an
asymptotic dose peak (the “Bragg Peak”) (15). This allows for a dose
concentration distribution impossible with conventional irradiation
Today, proton dominates particle therapy. However, the larger mass of
carbon results in decreased beam scattering, yielding a sharper dose
distribution border with minimal penumbra (16). Radiobiologically,
carbon-ion beams result in two to three times the relative biological
effect (RBE; the biological effectiveness of one type of ionized
radiation relative to another, given the same amount of absorbed
energy) of proton and conventional irradiation methods
So the more massive the particle, the more kinetic energy and the more precise the beam? Apparently not.
is an excellent reference on Bragg curves, which depict energy deposition at given depths for a charged particle with a given energy.
From that site
When the primary ion of high-Z breaks up, it results in several low-Z
fragments, each of which deposits small amounts of energy in the
material. The sum total of all the energy deposited by all fragments
can never add up to the energy deposited by the primary ion. This
causes the Bragg Curve for fragmenting high-Z ions like Iron to drop
So heavy ions like titanium and iron and gold which fragment do not cleanly bring their energy to a given depth and drop it off - they fragment and deposit energy along the way sort of like electromagnetic radiation. Sloppy.
Carbon must not fragment like that and neither do xenon or krypton. I presume xenon and krypton do not because they are noble gases but why that should be true (or what governs the tendency to fragment in a given ion) is beyond my ken.
So: more massive = more punch, and noble gases are less fragment prone and more likely to deliver the energy at the depth you want. Radon is the heaviest noble gas and so that is my answer.
Addition in case you want to use this in an atmosphere and the air is in the way.
1: Shoot a dart with a conductive wire.
2: Turn the wire into plasma with a huge electrical charge. It will in essence be a horizontal lightning bolt.
3: The expanding plasma will leave a low density core of near vacuum. It will be where the wire was.
4: Discharge your particles down this transient vacuum path.