My ultimate conclusion is that such radiation surveillance from outside the buildings should be constitutional, because what's an "unreasonable search" when looking for drugs (or even for evidence of murder) becomes reasonable when looking for radiation weapons.
This is an interesting discussion in relation to previous memestreams threads about particle privacy. I strongly reject the notion that you have no expectation of privacy in particles you emit that are not natually detectable by other humans. However, I recall hearing a rumor that the feds were monitoring all inbound roads toward DC for radiation, and I don't recall being concerned about this from a 4th amendment standpoint. Is this a slippery slope? If its effective and has a low false positive rate then I don't really think so.