Environmental Engineering Reference
In-Depth Information
The square well potential that has been useful in explaining alpha particle decay is a
simpli
cation, we know that the only interaction is the short-range attraction between
nearest-neighbor nucleons. The outer edge of the well will be rounded off again on
the scale of
dR
o
and the physical reason for the edge of the well is simply that
outside the boundary there are no more particles to be attracted to. The whole
distribution is spherical in order to maximize the attractive energy, which can be
restated as minimizing a (
(fictitious) repulsive surface energy. While the closest
analogy is to a drop of water, where the intermolecular interactions are also
short range, limited to nearest neighbors, the same argument, maximizing attractive
(long-range) gravitational energy, explains the spherical shape of the sun. The same
approach of Equation 2.35 can be applied to a metal like liquid mercury, where,
however, there is no accumulating Coulomb repulsion, since each electron is
accompanied by a positive ion.
It seems that the motion of the strongly bound alpha particle, within this liquid
sphere of nucleons, is reasonably free, and this situation of free motion of a particle
in a dense medium also occurs in the motion of electrons in solids such as gold or
silicon. We will come back later to reasons for free motion in these cases, such free
motion is bene
cial to the operation of devices including solar cells. Inmany cases in
physics, the motion of a single particle in a many-particle medium can be simpli
ed
by treating the effect of other particles by an effective potential or even as empty
space with a boundary imposed. In physics, it is productive to use the simplest picture
that works.
