Earlier I made a posting about the addition of a proton or neutron to a stable
isotope and observed that if one of these new compositions is stable then the
other one must not be. This observation holds throughout the entire list of
elements on the chart that I have been referencing. Now I have a hypothesis as
to why this is true.
First of all, it is important to note that the above additions result in a new
element or isotope that has one additional nucleon. After completing a great
deal of research on the subject I see that a group of elements that share the
same number of nucleons have an interesting behavior. They exhibit energy
levels like an electron cloud around a single nucleus. A minimum energy level
(ground level) is always present and adjacent elements are always at a higher
level. It takes one beta plus or minus decay to get between these adjacent
levels and it appears that this will be energetically favored and always occur
at some future time. The time frame for this decay might be quite extensive,
but it will be measurable in the form of radioactivity. I think of this
process as a lot like the decay of electrons from higher energy levels which
eventually get to the ground state.
I constructed an equation that can be used to find the expected number of
nucleons as a function of the number of protons within a nucleus. I restricted
the range of protons so that it eliminates the very few proton case and also
stops at a proton count of 40 so that I can concentrate the research to the
region to which I am interested and to improve the curve fit substantially.
I then transformed the above expected nucleon number verses proton count into
the reverse relationship. In this manner I can enter the nucleon count and
calculate the proton and neutron numbers that ideally support it.
As an example, if I enter a nucleon count of 40 I arrive at an expected proton
count of 19 and an associated neutron count of 21. The element that this
chooses is potassium 40. Now this should be the location of the minimum energy
level or ground state for 40 nucleons. The interesting thing I observed is
that this element is unstable with a very long half life. My explanation is
that the number of protons and the number of neutrons are both odd so they
cannot pair up. The resulting mismatch reduces the binding energy enough that
it actually falls below the adjacent elements of Calcium 40 and Argon 40 which
each have an even count of both types of nucleons. Also, it is apparent that
the fall off rate of binding energy verses error in nucleon ideal distribution
is such that the next element on each side of the two above has less binding
energy than these ideal ones. For this reason I propose that a beta type decay
process will eventually yield one of the two stable levels one step at a time
as each decay takes place.
It should be noted that this odd proton, odd neutron count situation is
virtually always unstable. And likewise the even proton, even neutron case is
similarly always stable when it occurs at the ideal count position. When just
one of these counts is even the elements tend to be stable, but less so.
I have not reviewed the cases where other types of decays are present and that
might yield fertile ground for future research.
The conclusion I draw from my search is that there will not be a case where the
addition of a proton or a neutron from a currently stable element will both
result in a stable new isotope or element. One or the other of these processes
has less binding energy and a beta plus or beta minus decay will point to it.
There are conditions where neither new product is stable, but these are fairly
rare.
I plan to analyze the decay times of the energy steps in these nuclear
configurations and compare them to the time frames for electron energy level
steps. The levels of energy events within the nucleus are enormously larger
than chemical ones but the decay times are likewise much longer. These
characteristics seem to be contradictory.
Dave
