Re: Nuclear topics in physics?

["John S. Denker" <jsd@MONMOUTH.COM>]

> >  2a) why don't light nuclei decay?
> >  2b) why don't heavy nuclei decay any more rapidly than they do?
> >  2c) why is spontaneous fission rare compared to other decay modes?
> >
> > I don't see any way to even approach question (2c) without first
> > spending some quality time running down the various decay modes.
> >
> >   http://www.science.uwaterloo.ca/~cchieh/cact/nuctek/decaytype.html


Ludwik Kowalski wrote:
> The above URL describes all modes of decay. In my opinion
> this is not necessary to deal with 2c question at the very
> elementary level. Here is a possible sequence:
>
>  a) Start from plotting potential energy between two point-like
> fragments versus distance between them; it is proportional to
> to 1/r.
>
> b) But this is correct only as long as short-range nuclear
> attractive forces are negligible with respect to the Coulomb
> force. Thus at very small r the total potential energy starts
> decreasing when r gets smaller. And the point-like V=f(r)
> approximation is no longer applicable.

Lost me there.  I suspect "no longer applicable" isn't what was
intended;  perhaps the intention was "V = f(r) is no longer the
simple 1/r repulsion" or something like that.

> c) Nuclear forces keep pieces together and the system is
> at a potential energy of roughly 200 MeV above what it
> would be at a much large r. I would ask student to assist
> me in populating the V versus r table for r larger than
> about 2e-14 meters and symmetrical fragments (Z=46).
> That is the region in which nuclear forces are negligible.

> d) I would then draw the potential energy diagram with
> a hill (barrier) which "frustrates the tendency to go down."

OK, we're formulating a barrier-penetration problem.

> e) Now comes the time for "hand waving." I could say that,
> according to principles of physics called QM, to be explained
> in a more advanced course, a transition under the barrier is
> not totally forbidden, as in classical physics. The probability
> of transition depends on how thick and how tall the barrier
> is.

OK, so far so good.  We can even do some rough numerical
calculations with this model.  WKB.  Evanescent waves at
the edge of the fish-tank and all that.

> Spontaneous fission would be very fast for Fm nuclei
> (Z=100), for example, but it is very slow for U nuclei
> (Z=92). For Z<80 spontaneous fission is so rare that it can
> not be detected. I would sketch potential barriers for the
> three cases on the blackboard.

Seriously lost me there.  For any potential I can imagine,
the foregoing model predicts that alpha decay will dominate
spontaneous fission by some truly astronomical factor.  That
is, the model predicts that spontaneous fission will be
unobservable.  I don't see any way to escape that prediction,
without going to a significantly more-complicated model.

> That is how I learned
> about fission, more or less. The liquid drop model,

Sorry, the liquid-drop model is something else.  Quite a
bit more complicated.

http://dbhs.wvusd.k12.ca.us/Chem-History/Bohr-Fission-1939.html

> and the tunneling effects came much later.

Huh?  Tunneling was understood long before the liquid-drop
model came along.  For some dates, see
  http://farside.ph.utexas.edu/~rfitzp/teaching/jk1/lectures/node70.html


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

I suppose the real question is how would I salvage the situation.
Answer:  I might use the barrier-penetration argument to discuss
alpha decay, but I wouldn't pretend that it describes fission.  I
would say that it predicts that fission doesn't happen the way
alpha decay happens (which is true) and that if you want to understand
fission you need a more complicated model.

I just can't bring myself to put up a model and then lie about
what the model predicts.