How Does the London van der Waals Force Relate to the Casimir Effect?

[Kruger]

The London van der Waals force is approximatly given by F=-c *a^-7 where a is the distance between two neutral atoms and c is something like this:

C=-23*hbar*c/4pi*(alpha1*alpha2)

where alpha1 and alpha2 =(epsilon-1)/(4pi*N)

and N is the atom number density and epsilon the permittivity.

--> Question 1: Does that mean if I have a body with 10^30 atoms the moledule number density is 10^30?

Now from the force between neutral atoms we can get to the Casimir-force. We can then just calclulate how much one atom of Plate A is attracted by the atoms of the other plates. Doing so with all atoms on Plate A we can sum over all the resulting forces and have the Casimir-Force.

Question 2: is this correct?

 

[akhmeteli]

The London van der Waals force is approximatly given by F=-c *a^-7 where a is the distance between two neutral atoms and c is something like this:
C=-23*hbar*c/4pi*(alpha1*alpha2)
where alpha1 and alpha2 =(epsilon-1)/(4pi*N)
and N is the atom number density and epsilon the permittivity.
--> Question 1: Does that mean if I have a body with 10^30 atoms the moledule number density is 10^30?
Now from the force between neutral atoms we can get to the Casimir-force.

The molecule number density cannot be dimensionless, so you have to divide 10^30 by the volume of the body.

 

[Physics Monkey]

The Casimir force is related but not identical to the van der Waals force, a fact which was first explicitly demonstrated by E. M. Lif****z and later J. Schwinger in the 1950's. In particular, the Casimir force is strongly dependent on the geometry of the system and is actually repulsive between two metal hemispheres. This revelation spoiled Schwinger's attempt to explain sonoluminescence using the Casimir force.


Lif****z's Paper:
E. M. Lif****z, Sov. Phys. JETP 2, 73, 1956

A nice experiment and good discussion:
http://prola.aps.org/abstract/PRL/v78/i1/p5_1

Edit: Ha! This is somewhat absurd, I can't write Lif****z's name because it has **** in it.