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PostPosted: Jan 29, 2014 2:14 pm 
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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 ;)
---

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! :D

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? :-)


Last edited by Np-236 on Apr 10, 2014 3:44 am, edited 1 time in total.

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PostPosted: Jan 30, 2014 1:06 am 
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So what about Cf-256, with only 12.3min. HL ?


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PostPosted: Jan 30, 2014 6:39 am 
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jaro wrote:
So what about Cf-256, with only 12.3min. HL ?


As I noted, the pattern breaks after Cm-250; it's really a downhill slope after Th-232:

Ra-226 1.6 Ky
Th-232 14 By
U-238 4.5 By
Pu-244 81 My
Cm-250 8.3 Ky

252 is the limit for isotopes with HLs of 1y or more
http://en.wikipedia.org/wiki/Template:Ra_to_Es_by_HL

Cf-252 2.6y
Es-252 1.3y

But really the 'edge of the cliff' looks more like 251, which is the most stable isotope of Californium at 900y or so (Cf-251 appears to be Cm-247 plus an alpha). In my model, the structure would be +7alpha +helion +6(2n)

Perhaps that's a limit of the shell? My model does not explain the downward trend in HLs after Th-232. I note however http://www.sjsu.edu/faculty/watkins/nuclearstruct.htm which has the comment: "The data in the above table suggests that there are structures of the alpha particles. There is no significant increase in binding energy for two alpha particles but for three there is." which would explain why the trend only starts at Radium (3 alpha) and not at e.g. Polonium (1) or Radon (2).

In terms of speculation, Cf-251 would have 14 particles orbiting the lead core, Cf-252 the same (8alpha+6(2n)) and Es-252 the same as well (7alpha+helion+trition+5(2n)). Is 14 the limit? Cm-250 is also 14 (7alpha+7(2n))...


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PostPosted: Jan 30, 2014 11:21 am 
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The island of stability causes problems for this theory I would imagine.

That is if it actually exists (it appears to but we can't make superheavy isotopes neutron rich enough to actually confirm this).


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PostPosted: Jan 30, 2014 2:25 pm 
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E Ireland wrote:
The island of stability causes problems for this theory I would imagine.


How so?

If (as you noted) it does actually exist, I imagine it would be similar in nature to how Radium to Curium exists beyond Lead; there is a gap of instability followed by a new region of stability. This would support the http://en.wikipedia.org/wiki/Nuclear_shell_model (though it does not explain how the nucleons are arranged inside ;). The actinides (plus Radium) appear to be the filling in of a shell. Why it stops here at 7 alphas (or 14 orbiting units) is not explained by my model, but the trend of decreasing stability as the nucleus gets heavier than Thorium is apparent in http://en.wikipedia.org/wiki/Template:Ra_to_Es_by_HL which implies a destabilizing force that increases faster than the alpha additions can increase stability. Repulsion by the dineutrons? Something I haven't considered? *shrug*


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PostPosted: Jan 30, 2014 5:40 pm 
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Quote:
A model derived from the nuclear shell model is the alpha particle model developed by Henry Margenau, Edward Teller, J. K. Pering, T.H. Skyrme.
Maybe this is what you have observed.

_________________
DRJ : Engineer - NAVSEA : (Retired)


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PostPosted: Feb 10, 2014 5:56 am 
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Some additional thoughts:

When, for example, U-238 decays (alpha), its (2n) to alpha ratio goes above 1:1, which is rather unstable. And so I think what's going on in that case is that a dineutron beta decays to a deuteron:

nn -> pn

This is immediately attracted to another dineutron and forms an unstable hydrogen-4:

pn + nn -> pnnn

which in turn beta decays to the nicely stable alpha:

pnnn -> ppnn

5) In excess, a dineutron beta decays to a deuteron, then fuses with another dineutron and beta decays again to an alpha particle

Now, I was looking at the case of U-235, which is basically:

4 alpha
helion
4(2n)

It alpha decays To Th-231 but then beta decays to relatively stable Pa-231 which wants to alpha decay rather than a second beta. This was a bit of a head-scratcher at first, since U-235 minus an alpha would give:

3 alpha
helion
4(2n)

but Pa-231 should be:

4 alpha
trition
2(2n)

and working backwards, before the beta decay, the Th-231 would be:

4 alpha
(nnn)
2(2n)

So, my solution is that in cases where again (2n) > alpha, if a helion is present, you can get:

ppn + 2n + 2n => ppnn + nnn

(possibly by an unstable helium-5 intermediate?)

and then nnn -> pnn

6) If a helion is present in cases of excess dineutrons, an alpha plus a trineutron will result.

The case of U-233 is similar as it alpha decays to Th-229 then again to Ra-225 but then beta decays to 225-Ac before starting to alpha decay again:

U-233
4 alpha
ppn
3(2n)

Th-229
3 alpha
ppn
3(2n)

Ra-225
2 alpha
ppn
3(2n)

ppn + 2n + 2n => alpha + nnn

Ra-225
3 alpha
nnn
(2n)

nnn -> pnn

Ac-225
3 alpha
pnn
(2n)


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PostPosted: Feb 10, 2014 6:03 am 
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Now, i was looking at Pu-241 and it should be relatively stable:

5alpha
ppn
5(2n)

yet it has a short HL and beta decays, which implies something else. Pu-240 capturing a neutron gives a clue:

Pu-240
6alpha
4(2n)

+n ->

Pu-241
6alpha
nnn
3(2n)

But why would that be the case when U-235 isn't like that?

*shrug*


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PostPosted: Feb 10, 2014 6:14 am 
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Further, if Pu-241 is:

6alpha
nnn
3(2n)

and then beta decays to Am-241:

6alpha
pnn
3(2n)

and then captures a neutron, becoming Am-242, is this the structure?

6alpha
pnn
nnn
2(2n)

or is there a rearrangement where an alpha is broken (due to very high alpha to (2n) ratio? also due to presence of nnn?) and it becomes this?

5alpha
pnn
ppn
4(2n)

Is the second one of these Americium-242m?


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PostPosted: Feb 18, 2014 2:44 pm 
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Further thoughts on Am-242/242m

What if the short HL of Am-242 is due to a structure:
6alpha
pnnn
3(2n)

Could the extra energy in Am-242m be keeping a deuteron semi-stable?
6alpha
pn
4(2n)


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PostPosted: Feb 19, 2014 11:50 pm 
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A difficulty emerges when I try to reconcile my simple model with the nuclear spin values. Note:

http://en.wikipedia.org/wiki/Template_t ... clear_spin

Values of e.g. 5/2 for U-233 and 7/2 for U-235 imply a whole bunch of unpaired nuclides (or multiple non-even groupings e.g. ppn). I will have to think on this.


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PostPosted: Apr 10, 2014 3:47 am 
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OK everybody, in case you didn't notice the edit I made at the top, please see "Models of the Atomic Nucleus" by Norman Cook http://www.res.kutc.kansai-u.ac.jp/~cook/PDFs/MAN2.pdf (11.2MB PDF) which is awesome and has taught me a lot even though I've only started reading it :)


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