Exploring the Origin of Born Repulsion of Atoms

[smimth]

hello,

I am curious about born repulsion of atoms, ie short range repulsion energy term proportional to 1/r^n. I find this in many solid state type books and they all call it the born repulsion and give no hints to its derivation or where it comes from. In _Atomic Physics_ 6th ed. by Max Born, I find "a law of the form b/r^n has been tried with good success..." in chap. IX but gives no hints to the origin of this form. Is anyone aware of a reference where the theory behind this form is described? Perhaps it is even in _Atomic Physics_ but my browsing has not found it yet.

Thank you,
smimth

 

[genneth]

There is no theory --- it is purely a functional form for a short-range repulsion that is convenient. It turns out that usually the exact form of the interaction does not matter, so one just picks something which makes the algebra simpler.

 

[charng]

Hello smimth,

That is an interesting question! The concept of born repulsion of atoms refers to the repulsive forces that exist between atoms at a short range, which are commonly observed in solids. This repulsion is a result of the overlapping electron clouds of the atoms, which creates a repulsive force due to the Pauli exclusion principle. This principle states that no two electrons can occupy the same space with the same spin state.

The exact form of the Born repulsion term, b/r^n, is derived from the Born-Mayer potential, which is a mathematical model used to describe the interaction between atoms in a solid. This potential takes into account both the attractive and repulsive forces between atoms, and the repulsive term is proportional to 1/r^n, where r is the distance between the atoms.

The value of n depends on the type of interaction between the atoms, such as ionic, covalent, or metallic bonding. For example, in ionic bonding, n is typically around 8, while in metallic bonding, it is closer to 6. These values have been experimentally determined and are in good agreement with the observed behavior of atoms in solids.

I hope this helps answer your question. If you would like to learn more about the Born-Mayer potential and the theory behind it, I recommend looking into solid state physics textbooks or papers on the topic. Best of luck in your research!