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Comment by mppm | Hacker News Reader

This is somewhat inaccurate from a physical perspective. What you say would be applicable to the attenuation of gamma rays, which is governed by low-probability interactions and is therefore exponential. But alpha particles, being charged an heavy, lose energy continuously through electron interactions and have a relatively fixed range in matter, beyond which the incidence is practically zero.

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No, that is just plain wrong. All attenuation is exponential (except very special stuff like energy resonances at certain particle energies). You just get very different exponents for rarely vs. frequently interacting particles. The charge of an alpha particle is also only twice the charge of a beta particle with a far higher (orders of magnitude, not just a factor of 2) penetration depth. The relevant difference is actually the mass and size (i.e. cross-section) of an alpha particle that makes it far more frequently interacting.

There are some more differences that govern the cross-section like conservation of momentum and angular momentum in certain interactions where there are differences between gamma and alpha particles. Or magic number nuclei that are relevant for neutron absorption.

But in general, for a given material and particle, attenuation is always always always exponential over the penetration depth vs number of particles, until you hit a low enough energy that some other mechanism for energy transfer can come into play or become unavailable, where the exponent will change and you will see a change in slope.

Please take a look at slide 11 of this presentation [1]. Stopping power and Bragg peak (slide 30) are also relevant concepts. What you are describing applies to photons and neutrons, but not to charged particles.

1. https://indico.cern.ch/event/975141/contributions/4137563/at...

Well then, please read what those slides say. Then read what I wrote.

The Bragg peak is about energy deposition, not the number of particles arriving at some point. When the energy of a particle changes going through the medium, the absorption changes. Still an exponential curve, just piece-wise exponential. Look at slide 11, that cutoff. Look at the logistic formula for it and its limit going right: still an exponential.

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