What does the potential barrier energy measure?

[iScience]

The energy of an incident charged particle refers to its kinetic energy. What does the potential barrier energy refer to qualitatively?

EDIT: Is it just in reference to the "potential barrier" in the classical sense? where if the particle has less than the energy V, then it doesn't go through?

Also, how would one go about quantifying the barrier energy of say, the walls of a container?

 

[Simon Bridge]

Potential energy.
The barrier is part of the potential energy function.

The barrier height of the walls of a container would be the minimum work required to leave the container starting from the potential energy at the bottom.
i.e. to get mass m over a hill height h requires at least mgh work, so the potential barrier height of the hill is mgh.

 

[Khashishi]

Usually we design containers that are practically leakproof, so the barrier energy is effectively infinite. But you can quantify the barrier by measuring how many particles tunnel through it and putting it into a tunneling equation.

 

[Simon Bridge]

We usually make containers so it takes a finite amount of work to remove stuff from them.
This translates to a finite barrier height.

The classical picture of a potential well is something like a ball in a bowl... it rolls back and forth to a height depending on it's energy. Plot the bslls gPE vs horizontal position and you will see the barrier is finite even if the bowl sides are leakproof.

 

[Khashishi]

I guess it all depends on the problem at hand. I was picturing a vacuum vessel with gas inside.

 

[Simon Bridge]

OK. A bottle of gas then...
If you were to describe the container in terms of the potentials that were containing the gas, you would still be describing the amount of work needed to get from one place to another ... because that is what "potential energy" means. If the gas had the kinetic energy to punch through the walls, then it's energy level would be higher than the potential barrier describing the walls.
Punching through the walls, in this case, is the same as going over the potential barrier.

There is no decent classical analogy for tunnelling.