Re: [Phys-l] question on radioactivity of Tc and Pm

[John Denker <jsd@av8n.com>]

Michael E. has already provided some good advice on this
subject when it came up in another form.

Executive summary:
> If you want to understand more about radioactive decay and stability of various nuclides, bite
> the bullet and buy/borrow a nuclear physics or nuclear chemistry book that explains beta decay.
> For the vast majority of nuclides (until we get so massive that alpha decay begins to occur)
> beta-decay is what radioactivity is.  Beta decay does not occur between isotopes.  Beta decay
> occurs between isobars.  Study beta decay.

For the rest of the story, see:
    http://mailer.uwf.edu/listserv/wa.exe?A2=ind0703&L=chemed-l&T=0&F=&S=&P=4329


Now, if you take that advice, you find that it does not fully
answer the question ... but it does allow you to discuss the
question in a more sensible way.

On the usual chart, the isobars run diagonally, which is inconvenient.
Here is the scatter plot for stable nuclides with an odd baryon number,
plotting Z as a function of A, so that the isobars run vertically.
  http://www.av8n.com/physics/img48/isobars.png

     Note: The color code has minimal significance.  It just separates
     one "count-by-two" series from the next.

You immediately see that every isobar has *some* point of stability,
with the famous exception of A=5, until we get into the regime of
alpha decay in the heavy elements.  This is what we would expect from
the fact that "beta decay is what radioactivity is" for most elements.

You can see that the "glitch" near Tc is not unprecedented;  there
are similar glitches near Cl and Pr.  However ... that is not much
of an explanation for Tc, because there are magic-number stories
you can tell about Cl and Pr that do not work for Tc;  55 is not
a magic number.

It is tempting to argue that 99Tc is "very nearly" stable, in the
sense that its beta decay energy is less than 300 keV, whereas
typical beta decays are in excess of 1000 keV.  One then makes a
"Florida recount" argument, to the effect that if you run enough
races you will eventually have one where there is a close and/or
fluky outcome ... and all sorts of second-order and third-order
contributions that you normally neglect suddenly require attention.

However, I'm not impressed by that argument either.  Before you
start blaming something on fluky higher-order effects, you have to
make the case that the first-order contributions come out "close".
But why should Tc come out close?
 -- 97Tc is not the end-member of a series;  it is part of a
  series extending from 81Br to 99Ru, wherein all the other
  members are stable.
 -- Similarly 99Tc is not the end-member of a series;  it is
  part of a series extending from 97Mo to 107Ag, wherein all
  the other members are stable.

==================================

It is OK to offer hand-wavy explanations as hypotheses that
should be checked.  But the ones offered so far do not check
out particularly well.  We stand in need of new hypotheses.