Can anyone offer an explanation for the powers (6 and 12) used in the Lennard Jones potential? (other than simply saying weak attractive and strong repulsion forces)

I am especially looking for short derivation that can be used to argue that the attractive potential falls off with the sixth power of interatomic distance.

Also, I understand that the repulsive part is used as a convenient way to mimic an exponential. How do we go from the Pauli exclusion principle to an exponential barrier?

Thanks

I am especially looking for short derivation that can be used to argue that the attractive potential falls off with the sixth power of interatomic distance.

Also, I understand that the repulsive part is used as a convenient way to mimic an exponential. How do we go from the Pauli exclusion principle to an exponential barrier?

Thanks

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