From: blom@husc15.harvard.edu
Newsgroups: sci.chem
Subject: Re: Technetium
Summary: Nucleon shell model, elementary style
Keywords: nucleon shell model proton electron pairing magic numbers
Date: 21 Jan 93 20:37:56 GMT
Reply-To: blom@husc.harvard.edu
Followup-To: sci.chem
Organization: Harvard University Science Center

In article <C14nyC.Fyp@world.std.com>, moroney@world.std.com (Michael Moroney) writes:
> staff@rabbit.augs.se (Staffan Friberg) writes:
> 
>>In article <C0zK8D.Bu1@world.std.com> moroney@world.std.com (Michael Moroney) writes:
> 
>>> There is some sort of structure to the nucleus, similar to electron shells.
>>> The protons (and neutrons) pair up.  The stable odd-proton elements all have
>>> only one or two stable isotopes, while even-proton elements have as many as
>>> 10 stable isotopes.  It turns out that technecium (and promethium) didn't
>>> even get one stable isotope.
> 
>>What does this structure look like. Do they just pair up two by two or is it
>>more complex than that?
> 
> There is a shell structure of some sort, like electron shells of atoms.
> Some numbers are rather stable, much like the noble gas shells of atoms
> are stable, so like noble gases are stable (don't "want" to gain or lose
> electrons) these nuclei are stable against nuclear processes.  I think
> 3 of these stable shells are helium, tin and lead.  Note that helium nuclei
> are commonly formed by radioactive alpha decay, lead is the end-point of
> the decay of the heavy elements, and tin has 10 stable isotopes.
> I've read a theory that the next number is 114, and element 114, if it
> can be made, might be stable or have an exceptionally long half-life (anyone
> know if any progress has been made recently to make elements near 114?)
> 
> -Mike


OK.  I'll now proceed to tell you all everything I know.  I hope this helps. 
First of all, large nuclei become less stable because the strong force which
bonds the nucleii acts only at short range because its mediators, the pions,
are short-lived.  Photons, the mediators of the electromagnetic force, are
very stable, and although this force is 100x weaker than the strong force.  As
nuclei become very large, the strong force dies off very rapidly and the nuclei
become less stable.

The protons and neutrons are hypothetically assumed to lie in shells because
this explains nuclear stability.  Nucleons have spins which correspond to
half-integer multiples of h bar.  (or, if you like, half integer multiples of
h/2pi, where h is Planck's constant.)  Electrons have spins of 1/2 or -1/2. 
Protons and neutrons have spins of 1/2, -1/2, 3/2, -3/2, 5/2, -5/2, etc. 
Arranging them into shells, we find they fill in a fairly regular pattern:
(I have filled the shells in pairs, which have opposite spin.  By pairing
particles with opposite spin, we greatly increase their stability.  This is the
reason for the even-even rule.)  Oh, and somehow, there are 2 1/2-spin
nucleons, 6 3/2 spin nucleons, and 2n n/2-spin nucleons per shell.  [Insert
favorite hand-waving argument here.]  I guess it has to do with angular
momentum and quantum number, sort like electron shells, but I don't think
anyone REALLY knows.

  2: 1/2

  8: 3/2
 10: 1/2

 20: 5/2
 26: 3/2
 28: 1/2

. . .

2,8,20,28,50,82,and 126 turn out to be "magic" numbers.  Nucleii with this
number of either protons or neutrons are exceptionally stable.  Nucleii with
a magic number of protons and a magic number of neutrons are even more stable.

To previous poster: Element 126 is the one, I believe, which is expected to be
very stable.  (Rather than 114, although that might come pretty close.)  By
really stable people mean "as stable as Radium" or so, although who knows?  It
might not be radioactive...  Ha.

Hope this makes some sense.  I'm actually a bit fuzzy right now about the above
nucleon pairing scheme.  Somehow I can't get it to work properly.  Anyhow,
that's the general idea.  If I figure out what I was doing wrong, I will
repost.  Ciaou, everyone, and have duckie days.

Eric Blom
Harvard U


P.S.  OK.  I figured out my problem.  Somehow there are 2k nucleons with 2k-1/2 
spin.  So there are a total of 12 nucleons in an 11/2-spin shell.  So the 
diagram goes like this:

*2: 1/2

6: 3/2
*8: 1/2

14: 5/2
18: 3/2
*20: 1/2

*28: 7/2
34: 5/2
38: 3/2
40: 1/2

*50: 9/2
58: 7/2
64: 5/2
68: 3/2
70: 1/2

*82: 11/2
92: 9/2
100: 7/2
106: 5/2
110: 3/2
112: 1/2

*126: 13/2
138: 11/2
148: 9/2
...

By this point, it's all speculation.  The shells marked with asterisks show
special stability, and correspond to magic numbers.  Again, both the protons
and the neutrons form these shells, and they seem to do so independantly.  To
be very stable, a nucleus likes to have filled shells of protons and neutrons.

No one to date has tried to synthesize element 126.  Considering it's large
size, I would be extremely surprised if element 126 has a half life over a
fraction of a second.  After all, if it did, there's a good chance we'd see it
on Earth or in star spectra.

Eric Blom
Harvard U