Radio Active Halo’s are fairly complex. I will summarize the basic problem that they pose and then link you to an article which will do a much better job than I can of explaining them. Basically, when certain radioactive isotopes decay to the next step in the radioactive chain they give off alpha particles with a certain amount of energy. These alpha particles discolour a ring around the decaying radioactive material. There will be different rings for the different stages. This is all noncontroversial. However, the problem for uniformitarianism is that in some locations a daughter isotope in the Polonium radioactive decay chain with an extremely short half life measured in microseconds for one of them has been found in solid rock without any rings from its parent isotopes. The entire supply of this isotope would decay in seconds (and the radiohalos could only form after the rock cooled.) So their appears to only be three explanations for how this could happen. 1) That the radioactive isotope was created instantly in the rock. 2) that the half life for this isotope was much slower in the past so that the rocks would have had time to cool before all of the material had decayed. Or 3) that somehow the radioactive material was able to find its way into the rock via contamination in cracks.
Obviously evolutionists prefer the third explanation and in some of the locations (where we are dealing with isotopes with halflifes measured in days) this appears to be a viable theory. However, for the isotope with a halflife measured in microseconds there is no time for this and it has been found in locations where there appears to have been no possibility for contamination. Anyway here is a link to a technical article which may help explain this better than I could. Its not the most helpfull article but it should help. http://www.icr.org/index.php?module=articles&action=view&ID=471
I’m not going to ignore your response or the link you provided. I’m just not going to get to it this evening because I have to arise very early during the workweek. I will look at it, and I thank you for providing the link.