Interesting you use the term, "catalyzes particle decay, ...." because that term comes from Chemistry, an area in which we all have some practical experience. But it turns out the processes are different.
In Chemistry we have lots of materials at higher energy levels that can and do react with other things to release that energy: for example, burn a piece of coal using the oxygen in the air. And yet, the input materials appear to be very stable over long time periods - like coal! So we talk about the "Activation Energy" for a reaction. That is, to get it started, we must actually add some extra energy - just a little - to push the input materials into a higher-than-normal state so they will react. Once they start that the reaction proceeds to completion releasing not only our little "kick-start" energy but also the energy stored in the original materials. To burn a piece of coal we first have to raise its temperature with a small match flame. Once it ignites, the heat the reaction releases provides a continuing source of Activation Energy for the rest of the carbon atoms in the coal to burn with oxygen. And the net result is release to us of a lot of heat energy and some light. One of the important characteristics of this process is that the rate of the reaction is dependent on temperature, because that is what determines the AVERAGE energy content of the input materials (and hence, how much extra is required to get things going).
In the case of subnuclear particles, however, that does not appear to be the mechanism. All such particles occupy fixed quantized energy states, and many of these are higher energy than some stable lower-energy state. Thus, they decay by releasing energy (as a wave, or as an energetic other subnuclear particle), but it never appears to require an Activation Energy as Chemical reactions do. For example, these processes are completely INDEPENDENT of the temperature. The energy release occurs randomly in time at a rate determined entirely by the subnuclear particle itself and its current quantized energy state. We can measure those rates and, indeed they are unique for all known decay processes, but we can't change them by external manipulation.
The intensity of energy output decays exponentially over time because the number of particles in higher energy states available to decay decreases with every decay event. Based on that we can characterize each process by a "half-life", which is the time it takes for the intensity of energy output to decay from initial value to only half that output. For example, Strontium 90 is an isotope of Strontium created in nuclear fission reactions of Uranium that decays by emission of a gamma ray. Its half-life for this process is about 10,000 years. So if we have 1 gram of Strontium 90 today, 10,000 years from now only 0.5 grams of it in that form will remain, the rest having decayed into other things. Although the process is long, Strontium 90 is still considered an unstable isotope. With an Atomic Weight of 90, 1 gram amounts to 1/90 x 6.023 x 10^23 atoms of this metal, and half of them will decay over 10,000 years. That is 315,567,360,000 seconds, roughly, so gamma rays are emitted at the AVERAGE rate over that time of 10,603,476,580 events per second!
As you say, to some it appears that "more massive particles are more unstable". That is not quite true. Current models of nuclear stability and energy states indicate that, as you climb through the number of atomic particles in a nucleus, there are areas of great stability and, between them, areas of substantial instability. It happens that the heaviest elements we have been able to observe are in an area where models predict that even heavier ones will be more unstable, so it is increasingly difficult to create such atoms synthetically and just as hard to observe them (thus proving the creation) in their rapid decay. But those same models predict also that there is a much higher mass range that will have stable atoms. We just can't make anything like that yet, and no such atoms appear to exist anywhere close to us in the universe. They would have had to be created within a truly massive star, probably during some hugely catastrophic destructive event resulting from the intense gravitational pressures required to force nuclear particles together to make such elements.
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