Of course, power density is inversely proportional to half-life. Low power density BECAUSE the half-life is 432 years.

> power density is inversely proportional to half-life

It's not that simple. The energy per event varies by orders of magnitude depending on the specific transition (even within given particle decays, the energy of the emitted particle varies), also the number of atoms per volume or mass varies depending on material.

Clearly. However it IS a good approximation. For RTGs, we desire primarily alpha emitters as alpha particles are generally the easiest type of decay product to shield (the thin metal casing will stop all alpha particles). And common Alpha emitters such as Po-210, Am-241, Pu-238, and U-232 all have a decay energy of about 5-6MeV even though they differ in half life (and thus power density) by 3 orders of magnitude.

The approximation holds true for the heavy elements, with similar atomic mass. I wonder if the power density of any similar half-life lighter nuclei would be significantly greater, or whether the energy of decay reduces roughly proportionately with their mass.

And, of course, almost all alpha emitters are heavier elements: https://www.researchgate.net/profile/Adam_Woolsey2/publicati...

> that can be used without refining

It has to first be separated from the rest of the actinide waste, which is very challenging, as they're chemically similar elements. Previously this had to be done with a centrifuge (separating by mass), but a lot of research effort has gone into developing more practical chemical refining methods.