Nuclear Physics - Analysis of Stability in Atomic Nuclei
A simplified example can be presented which gives the basic premise.
It will be clear that the concept would apply to all nuclei that are more
complex, although there are some slight variations that will be
discussed. We will consider a standard Helium atom nucleus, which
is described as containing two protons and two neutrons. For the sake
of this discussion, we will consider the nucleons to not move and to be
in a formation of a tetrahedron, where the four nucleons are all
equally distant from each other.
Known parameters of atomic nuclei provide a guideline regarding
how rapid such migration would have to occur. We know that atomic
nuclei are on the order of 10-13 cm in diameter. A proton
has a mass of 1.65 * 10-24 gm. We calculated above the
force of electrostatic repulsion, at 2.3 * 10+7 dynes.
Assuming non-relativistic motions, and for minimal variations in the
distances involved, F = m * a or a = F / m, will give
an approximation of the acceleration of the proton.
This solves to an acceleration of 1.4 * 10+31 cm/sec2.
We might consider an absolute limit of an individual proton's movement
due to Coulomb repulsion from another proton, to be half the nucleus
diameter, or 5 * 10-14 cm, if nuclear stability is
to be maintained. Again assuming non-relativistic velocities, then
d = 1/2 * a * t2 or t2 = 2 * d / a or
t2 = 7 * 10-45 or t = 8.5 * 10-23 seconds.
This value is not particularly precise because we did not consider the
variable force due to the variable distances that exist, but it
is only meant to give a ball-park idea of the time involved for the
repulsion portion of this cycle. The entire cycle would then be
on the order of 1.5 times that long or 1.2 * 10-22 seconds.
This reasoning represents the longest interval that the proton-proton
repulsion could be in effect without the electrostatic repulsion
destroying the integrity of the nucleus. Therefore, it represents
a guide to the longest possible cycle time for the process described
above. As long as the electrons complete their entire migration
pate in a shorter time than this, then the protons would not be
de-stabilized, although they would likely experience a cyclic oscillation
at that rate. If the cycle occurred more rapidly than that, the
movements of the protons would be smaller and stability would
be greater.
This situation suggests that the electrons, if described as moving,
would need to traverse a cycle of three segments, or around 2.5 *
10-13 cm in a period no longer than 1.2 * 10-22
seconds, which implies a minimum velocity of around 2 * 10+9
cm/sec, about 1/15 the speed of light. This is interesting in that,
should it be a higher velocity, then relativistic velocities of
the electrons would increase their mass and possibly affect the
reasoning regarding the mass defect and many other effects.
There are a variety of ways the electrons might actually move
within the nucleus. A more generalized form of the above argument
involves taking the time integral of the attraction between each proton
and the electron during whatever path is followed. For most geometries
of electron movement, the resulting effect is a slight reduction of the
net attractive force. The initial (migrate) argument above would have had
too much attractive force for stability, and effects such as this might
ensure that the time-average of the attraction exactly equals the
time-average of the proton-proton repulsion, in making a stable nucleus.
A discussion below will consider the situations where there are more or
less than an optimal number of electrons within the nucleus, and the effects
on stability, on the half-life and the radioactive decay schemes.
Preference for Beta- or Beta+ or EC Decay in Light Nuclei Isotopes
There has been recognized that the "single atomic weight"
graphs discussed and displayed below tend to have much steeper sloped curves
for lower atomic weights than the same graphs for higher atomic weights.
Since one conclusion of this analysis is that the slope of those curves
represent an indication of stability regarding beta decay, there is the
implication that heavier nuclei would more rarely emit beta- or beta+
particles, which is borne out by experimental evidence.
Regarding beta- and beta+ decay, the graphs displayed below suggest
that the half-life of any isotope might be predicted from the slope
of the appropriate graph, and that the total energy (kinetic and radiation)
might also be predicted for any isotopic beta decay.
Preference for Alpha Decay in Heavy Nuclei Isotopes
A similar analysis of actual atomic weight graphs shows an entirely
different pattern regarding decay involving alpha particles.
For light nuclei, the curve is inverted which suggests that alpha
particle emission is not possible. For the heaviest isotopes, the
slope of such curves exceeds the slope of the curves for beta decay,
which suggests a natural preference for alpha decay for such isotopes.
In addition to this, the universal extreme symmetry preference for
isotopes with even numbers of protons and also even numbers of neutrons
seems to suggest a special stability of 4He nuclei, which
is the alpha particle. This symmetry-based stability might suggest
that such structures exist within heavy nuclei, which might explain
why they leave the nucleus as a bundle as an alpha particle.
This might imply that within heavy nuclei there are distinct organized
structures, the simplest of which would be the alpha particle.
This presentation was first placed on the Internet in November 2003.
Atomic_Nuclei_2