jimmysnyder said:
Thanks again hamster143. Whether it is considered constant depends on the intents and the purposes. As I am interested in the square of the distance, am I correct that the effect would be on the order of .06 * .06 = .0036?
No, the variation of distance is 0.03 , the variation of flux is (1.03^2 - 1) ~ 0.06.
But the effect on half-lives will likely be many orders of magnitude smaller, because it also depends on cross section.
To give you an idea:
Uranium 238 is a relatively stable isotope, with half-life of several billions of years. In a kilogram of uranium 238, there are 12,000 spontaneous decays per second.
If uranium 238 can capture antineutrinos with the same cross-section as hydrogen in water, you can place that kilogram of uranium within 10 m from a nuclear reactor and it would only induce one additional decay every 10 hours. That effect is obviously so tiny that it's not even measurable.
You seem to be suggesting that maybe the effect of neutrinos is much higher. You can try to verify that by setting shop near the reactor. Part of the problem is, in addition to neutrinos, reactors produce all other kinds of radiation. For example, neutrons.
Instead of measuring half-life, you want to measure decays per second. Set up a system with a quantity of radioactive material, a Geiger counter, and some shielding. Uranium-238 (aka depleted uranium) is relatively easy to obtain. Put the whole system into a lead box to block cosmic rays and such, load it into a car. Find a nearby nuclear reactor. I don't know where you live. Here in Southern California, one can legally get within a couple hundred meters from the San Onofre reactor.