Re: radioactivity

[John Denker <jsd@MONMOUTH.COM>]

At 01:50 PM 10/28/00 -0500, cliff parker wrote:
> I do understand that there are various energy states within the nucleus as
> there are various states with electrons.

OK.

> What would cause a neutron to be ejected at any time regardless of the
> energy state it was found within?

The ejection is not "regardless" of the initial energy.

Tunneling rates depend on how close the initial energy was to the top of
the barrier.  It also depends sensitively on the thickness of the barrier.

> Line spectrum emissions give evidence to the quantum nature of
> energy relating to electrons.

Wow.  I guess that's true in some sense, but I wouldn't have said it that
way.  That focuses attention on the wrong things.

*) Energy _per se_ is not quantized.
*) The energy levels of an undamped harmonic oscillator are nicely
quantized and evenly spaced.
  -- But an anharmonic oscillator has unevenly-spaced levels,
  -- and if the oscillator has damping (which all real oscillators do)
     it can oscillate at any frequency you like.
*) The energy levels of a single mode "A" of the EM field are nicely
quantized and evenly spaced -- but in free space there will be another mode
"B" with energy levels that differ by non-quantized amounts from mode "A".
*) Planck's constant is called "the quantum of action" and it doesn't even
have units of energy.  It has units of energy*time, or equivalently
momentum*distance.  Action is quantized, not energy.
*) Angular momentum has units of action, so it sometimes makes sense to
talk about quantization of angular momentum.
*) Things like baryon number and lepton number are quantized integers (no
hbar involved).


>  What is the evidence that lead to an understanding of the quantum nature
> of energy relating to protons and neutrons?

The line spectra from nuclei are even more line-like than the line spectra
from electrons.
  -- nuclear transitions have energies on the order of MeV
     and lifetimes ranging to days, years, or even billions of years....
     ... and that's a lot of Q!
  -- electronic transitions have energies on the order of eV
     and much shorter lifetimes ...
     ... i.e. vastly less Q.

Evidence for the shell structure within nuclei can be obtained in ways very
closely analogous to the way you would take a fluorescence spectrum of
electronic shell structure.  Using Mössbauer techniques you can achieve
astonishing resolution.
  http://www.nobel.se/physics/laureates/1961/mossbauer-bio.html