For the purpose of this post, I'll accept that they can convert protons to neutrons as described, although I'm very dubious about this.
Here [wikipedia.org] is a table of nickel isotopes.
Here [llnl.gov] is the first source I found for neutron cross sections of nickel isotopes (pdf). (See figure 12, look at the left hand side of each 'destruction channels for ??Ni' plot for what low energy (thermal) neutrons will do.)
Cross sections are in barns, and are approximate as I'm eyeballing them off a logarithmic scale.
58Ni [stable, 68% abundant] (0.006 barn) -> 59Ni [-> 59Co, 76000 yr half life]
59Ni [unstable but long lived] (0.02b) -> 59Co [stable] or (0.005b) ->56 Fe [stable] or (0.004b) -> 60Ni [stable]
60Ni [stable, 26%] (0.006b) -> 61Ni [stable]
61Ni [stable, 1%] (0.002b) -> 62Ni [stable]
62Ni [stable, 4%] (0.006b) -> 63Ni [->63Cu, 100yr]
63Ni [unstable] (0.001b)-> 64Ni [stable]
64Ni [stable, 1%] (0.004b) -> 65Ni [->65Cu, 2.5 hr]
None of the cross sections are hugely larger than the others, so all these reactions will occur with reasonable frequency. So irradiating nickel with thermal neutrons, you are going to produce radioactive 59Co (76000yr), 63Ni (100yr) and 65Ni (2.5hr). The 65Ni isn't a problem - turn off the reactor, wait a couple of days, and it will all be gone. The 59Co is only a bit of a problem - with such a long half life, it isn't very radioactive. The 63Ni however is nasty. Like 137Cs (30yr) from the Fukashima reactors, the half life is short enough to be quite radioactive but long enough that you can't just wait it out. Finally, the nickel won't be 100% pure, so you have to worry about what neutron irradiation will do to the impurities.
The 65Ni means when you turn off your reactor, it will continue to produce residual heat for hours.
The article gives the impression that weak nuclear reactions aren't dangerous, but this is not so. If it were, nuclear reactor waste wouldn't be dangerous.
This reactor will be producing ionizing radiation when running (mostly gamma rays, some beta rays mostly from 65Ni decay, and a tiny amount of alpha particles from 59Co(n,a)56Fe.) This will require some pretty heavy shielding to stop it. (A good sized water bath should work, every 7cm of water [xkcd.com] halves the radiation and you want hot water anyhow. But concrete is less prone to leak away.) You'd also need to worry about stray neutrons, although I expect that can be fixed with a thin layer of something that has very high thermal neutron cross section and no dangerous daughter products.
In short, I don't think I want this in my basement.
Source: http://rss.slashdot.org/~r/Slashdot/slashdotScience/~3/JanNzUqws9M/story01.htm
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