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Re: Nuclear topics in physics?



"John S. Denker" wrote:

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 responded:

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approximation is no longer applicable.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 I suspect "no longer applicable" isn't what was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.

THAT IS CORRECT. ALSO NOTE THAT THE V(r) IS
NO LONGER 1/r, EVEN FOR "SIMPLE REPULSION"
OF RIGID CONDUCTIVE SPHERES (WHEN THE
CENTER OF MASS AND THE CENTER OF CHARGE
NO LONGER COINCIDE).

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.

SEE BELOW.

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.

Nowhere did I bring the alpha decay under consideration;
the ratio of alpha over fission probabilities was not even
mentioned in my outline. Red hearing? I hope not. I did
NOT "LIE ABOUT what the model predicts, " I said that
many questions are left for more advanced courses.

Is it not true that the model predicts a rapid increase of the
fission probability per unit time (lambda) when Z goes up
from 80 to 100? That was the main point of my crude
argumentation based on drawn diagrams of V(r).

If I were asked to calculate lambda for a particular nucleus
I would say, honestly, that I do not know how to do this
without a lot of relerning and learning. I would not pretend
to know more than I do.

As far as I recall, the calculations of that kind, done by
theoretical physicists, often disagree with experimentally
measure lambdas by very large factors. I suspect this is
still true today. But I would be able to explain, if asked,
how fission-lambdas were measured in some favorable
situations.

BY THE WAY, THE FIRST URL PROVIDED BY JOHN,
(PLUS THE PAPERS OF MEITNER AND FRISCH TO
WHICH BOHR REFERS) ARE EXCELLENT RESOURCES
FOR THOSE OF US WHO WANT TO DEAL WITH THE
HISTORY OF FISSION. THE TERM FISSION WAS
INVENTED BY MEITNER AFTER SHE LEARNED
ABOUT THE DISCOVERY OF BARIUM IN URANIUM
BOMBARDED BY NEUTRONS (GERMANY, 1939).
SHE WAS ALSO THE FIRST TO PUBLISH THE
ESTIMATED AMOUNT OF ENERGY PER FISSION
USING THE E=M*C^2 FORMULA. SPONTANEOUS
FISSION WAS DISCOVERED IN MOSCOW, IN 1940.
Ludwik Kowalski