Abstract
Theoretical formulae have been developed for
the energy of a nucleus according to a statistical
model and an expansion has been made.
The results have been applied to the numerical
calculation of energies, radii, the surplus of
neutrons over protons in stable nuclei and finally
to a discussion of the various ni.
As seen from graph III, very good results
have been obtained for the energy agreeing almost
exactly with experimental results even down to
the small nucleus ₇N¹⁴ which really ought to be
outside the scope of a statistical model, owing
to having so few as 14 particles.
Graphs III and IV give good values for the
mid -point between max Δ and min Δ. The breadths
max Δ - min Δ ought to be somewhat larger in
particular for the nuclei with an even number of
particles.
The inclusion of the spin terms in the energy
enables us to consider the stability of nuclei in
greater detail than has been possible in the older
calculations. We can state for any given nucleus,
whether it ought to be stable or not. It is, of
course, in the nature of the statistical model
that local fluctuations are smoothed out, so that
we can only expect statistical agreement with
experimental results.
With this reservation the results are satisfactory
for nuclei with an odd number of particles,
except that the model only gives stable nuclei
the spin one-half, whereas experiments show that
nuclei exist with spins as great as nine-halves.
On the other hand, the region of stability
for nuclei with an even number of particles as
given by the model is too small, as can be seen
from the fact that the total number of isobars
could only just be two. (Or from n₄-n₁~o which
amounts to the same thing).
It is possible that with other interaction
potentials better agreement could be obtained, it
seems more probable that the disagreement is due
to the fact that in the statistical model, the
difference between even and odd particles is not
sufficiently pronounced.
