1) In electrostatic you might ask students
to estimate the coulomb barrier preventing
positive D ions to fuse at low temperatures.
Here is my suggestion. First tell students
that in addition to repulsive forces the
ions attract each other by very strong
nuclear forces. But these forces do not
obey the 1/r^2 law. They are negligibly
small when r is above a distance R (called
range). For x<R the attractive nuclear
forces are much larger than repulsive
electric forces. That would be a good
justification for defining the coulomb
barrier, CB, as the value of the electric
potential at r=R.
The rest is trivial. Assume that R=3 F,
for example, and calculate CB. Note that F
is the unit of length (femtometer or 10^-15 m).
My answers were 478 kV and 358 kV, at R=3 F
and 4 F, respectively. You may or may not link
this problem with the cold fusion controversy.
2) If you do then consider addressing the
screening effect. Some scientists say that
screening is possible
when D ions are embedded
in metals, such as Pd or Ti. Simply stated,
and without trying to argue about what causes
screening (local clouds of electrons at crystal’s
boundaries?) one can simply declare: screening
consists of lowering of the coulomb barrier by
To illustrate screening do the following.
Place one deuteron at x=0 at treat the other
deuteron, at x>0, as a probe charge. That is what
I did to calculate coulomb barriers. Then place
an electron at some negative value of x, for
example, -2 F. The CB is now V=V1 + V2 (where
V1 is the positive part due to the deuteron
and negative V2 is the negative part due the
electron). You will see that CB approaches
zero when electron is approaching the origin,
as it should be. My answer, for R=4 F, was
CB=120 kV for the electron placed at x=-2 F.
And nothing prevents you from introducing more
than one screening electron.
4) Yes, I know that three or more particles would
usually not be at rest
on the x axis. And I know
that the nuclear potential is not a rectangular
well. My goal is to estimate the orders of
magnitude of CB, and to illustrate the idea
5) By the way, we usually think that the
so-called “free electrons” in metals are
uniformly distributed, like in ionized
gases. What evidence do we have for this?
6) No, I am not trying to poison your mind
with poisonous and heretical pseudo science.