Quantum physics is @dga471’s specialty, so I think we should listen to him. Here are my two cents: I don’t think radioactive alpha decay is self-caused, because:
Alpha decay is a tunneling problem: first you describe your particle by a wavefunction that is confined by a potential barrier. Given a general potential, the wavefunction can be solved completely in a deterministic way from the Schrödinger equation. If you solve for it with the potential barrier, you get that parts of it leaks out of the potential barrier. Look at this schematic from wikipedia:
The red line is the wavefunction and the rectangle is the potential barrier. Given that the shape of the wavefunction is caused by the potential barrier and the Schrödinger equation
, it is hard to argue that it is self-caused.
Further problematic is the fact that this phenomenon is not constrained to quantum physics. There are many examples of classical waves (such as light, sound waves, etc) that can tunnel through potential barriers. So, if one wants to claim that the wavefunction tunneling through a potential barrier is self-caused in quantum physics, one has to also claim that (for example) water waves tunneling through a potential barrier is also self-caused.
So, at least at the level of wavefunctions, I don’t think that quantum tunneling is self-caused.
Now, there is another issue: Once one has a wavefunction, an observation collapses the wavefunction so that the particle now resides in a particular position (as opposed to being spread out over space). The probability of the particle being in a certain position is non-zero as long as the wavefunction is non-zero at that point. Because the wavefunction is non-zero outside of the barrier, sometimes an observation will find the particle to be outside of the barrier - this is how an alpha particle can escape the confines of a nucleus. Certainly this is not self-caused. Similar to what @dga471 said, obviously an observation caused the wavefunction to collapse. Note that “observations” does not necessarily means “observations by humans”.
This is also not taking into account the various meanings of “caused” in philosophy. For example, one can say that all of this is caused by the rules of physics, and therefore cannot be self-caused.