**Update April 10:**Oh wow; I just discovered http://www.res.kutc.kansai-u.ac.jp/~cook/PDFs/MAN2.pdf (11.2 MB) "Models of the Atomic Nucleus" by Norman Cook. Even though I've only just read a little bit so far it's really awesome! Read it instead of my stabs in the dark (though the +2p+4n trend is still good

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A thought occurred to me the other day, which I've started to flesh out; I think I'm ready to discuss it with people interested in physics to get feedback. I might be completely wrong and/or others may have thought of this before

**You can skip to the numbered points for the summary.**

This all started when I saw a table of nuclides like http://www.nndc.bnl.gov/chart/reColor.jsp?newColor=t12 looking up info on Th-232 & related isotopes. Thorium has the longest HL of any actinide. But I noticed a couple other things too: Th-232 is immediately surrounded by a 'dead zone' of short half-life isotopes; I wondered if this was related to http://en.wikipedia.org/wiki/Mattauch_isobar_rule or such. The second-longest lived actinide is U-238; same dead zone around it too... The longest lived plutonium isotope is Pu-244, which doesn't form in nuclear reactors (Note http://www.world-nuclear.org/info/Nucle ... Plutonium/ table with "Percentage of Pu isotopes at discharge") because of a dead zone around it too...

Th-232

U-238

Pu-244

They are evenly spaced: 2 protons and 4 neutrons apart.

So, ok, is that a coincidence? Keep going: Cm-250. Not the longest lived isotope of Curium, but there's that dead zone around it again. After that the stability of the isotopes decreases to the point where the pattern ends. Note e.g. http://en.wikipedia.org/wiki/Template:Ra_to_Es_by_HL But what if you go backwards 2p4n from Th-232? Radium 226. Longest-lived Radium isotope, with a 1600 year half-life and then there's a gap of three elements where the longest-lived isotope is less than four *days*.

Huh.

But what if we keep going back by 2p4n?

Radium-226

Radon-220 (short HL)

Polonium-214 (short HL)

Lead-208. Woah there. That's the *last* stable isotope.

And so here I find that if you draw a line from Pb-208 to Cm-250 you hit some very long-lived actinides (including the top two) plus Radium-226. And so I've been wondering about this for a while now.

The other day i had some free time and I sat down and thought about alpha and beta decay. It is also extremely curious to note that the 'island chain' Th-232, U-238, etc. forms (BTW, is there a specific name for this group of isotopes?) undergo alpha decay while the dead zone undergoes beta. http://commons.wikimedia.org/wiki/File:NuclideMap.PNG I also started to think about how the protons and neutrons might be arranged in the actinides and I came up with several ideas.

**1) Pb-208 forms a core and then the protons and neutrons are arranged around it.**

I thought about the 2 proton, 4 neutron stepping and it seemed unlikely that it was a 6-nucleon hunk in orbit around the Pb-208. But it was even numbers; divide by 2? A tritium nucleus (pnn) in orbit sounded better, but if there was just one it would be unstable (consider the half-step between Th-232 and U-238). Pairs of neutrons and deuterons? The D binding energy wasn't overly great: http://commons.wikimedia.org/wiki/File: ... otopes.svg and then it dawned on me.

**2) Stable 2 protons and 4 neutron pattern = an alpha particle and a pair of neutrons.**

If this is correct, alpha decay in the actinides is simply the ejection of an alpha already orbiting the Pb-208 core. I quickly did some calculating:

Ra-226 = Pb-208 + 3 (alpha + (2n))

Th-232 = Pb-208 + 4 (alpha + (2n))

U-238 = Pb-208 + 5 (alpha + (2n))

Pu-244 = Pb-208 + 6 (alpha + (2n))

Cm-250 = Pb-208 + 7 (alpha + (2n))

How pretty!

The next thing I wondered about was U-235; why is it SO stable? Looking at the HL chart It's interesting that +2p4n is Pu-241 (relatively unstable) BUT +4p8n is the very stable Cm-247. I thought that that can't be a coincidence. Also U-235 is three neutrons less than U-238 and three nucleons more than Th-232. That looked like a clue. And it dawned on me that the three nucleons more than Th-232 were 2p1n which = a Helium-3 nucleus. Which is stable and as I recall has an affinity for neutrons... Could it be?

**3a) An odd number of neutrons in a stable-ish isotope represents a He-3 nucleus, aka "helion"**http://en.wikipedia.org/wiki/Helion_%28chemistry%29

I then very excitedly did the math for several isotopes; U-235 would be the Th-232 structure plus a helion. U-233 would be just a pair of neutrons less than U-235. Pu-239 would be U-235 plus an alpha. Np-236 would be... Well it has an odd number of protons and so in analogy I guessed:

**3b) An odd number of protons in an isotope represents a H-3 nucleus, aka Tritium.**

This would help explain why the isotopes of odd numbered actinide elements are so few; they are inherently unstable AND tend to decay by beta.

So I'm having fun playing with the numbers and I try to think of what Thorium breeding would look like and I get this:

Pb-208 + 4 (alpha + (2n)) + n = ? (Th-233)

8p + 17n = ?

Does the odd neutron remain temporarily free and directly decay as the HL is short? (in the 'dead zone' around Th-232)

Does it steal from an alpha to make 3 alpha + helion + 5 (2n)?

I considered what the decay product Pa-233 would look like:

4 alpha + tritium + 3(2n)

And its decay product U-233:

4 alpha + helion + 3(2n)

And suddenly the pattern was clear. When Th-232 captures a neutron, it's not the alpha particles:

**4) Pairs of neutrons (dineutrons) in orbit around the Pb-208 core may capture a neutron and become unstable trineutrons that decay like (and to) tritium nuclei.**

(Note http://en.wikipedia.org/wiki/Neutronium )

Immediately it became clear to me that this must partially be what the dead zones are! ALSO it would so help to explain why there are usually TWO beta decays in breeding, for both Th-232 and U-238:

nnn -> pnn -> ppn

So there you have it! Thoughts?