Range of the interactions: long/short-range

I have seen in Long/short-range interaction that in scattering theory $$𝑟^{−𝑛}$$ is a short range potential for $$n>1$$ and a long range potential for $$n\leq1$$.

Now, why do we say that van-der-Waals and dipole-dipole are long range if they have the form $$𝑟^{−𝑛}$$ with $$n=3,6$$ respectively?

• But $1/r^n$ is long range. It has scale symmetry. Jan 23 '20 at 20:21
• "Short" and "long" are conventional and inexact terms (and different conventions are used in different areas). In this case, the forces are long-range because they (approximately) obey a power law: short-range would be exponentially decreasing forces. Jan 23 '20 at 20:23
• Yes, not very clear. Thanks
– Kio
Jan 23 '20 at 22:46

• One finds many definitions in the literature; usually criteria can be expressed through the 2-body interaction potential $$V(r)$$.
• $$V(r) \propto r^{-\alpha}$$, with $$\alpha \leq$$ dimensions is considered a standard definition for long-range interactions. Dipolar interactions in a Bose-Einstein condensates are long-range by this definition.
• Also, if $$V(r)$$ falls off slower than exponentially, correlations are then qualitatively different and are often considered as long range in some contexts. Van der Waals interactions fall into this category.