Universal physics of bound states of a few charged particles

Abstract

We study few-body bound states of charged particles subject to attractive zero-range/short-range plus repulsive Coulomb interparticle forces. The characteristic length scales of the system at zero energy are set by the Coulomb length scale $D$ and the Coulomb-modified effective range $r_{\mathrm{eff}}$. We study shallow bound states of charged particles with $D\gg r_{\mathrm{eff}}$ and show that these systems obey universal scaling laws different from neutral particles. An accurate description of these states requires both the Coulomb-modified scattering length and the effective range unless the Coulomb interaction is very weak ($D\to \infty$). Our findings are relevant for bound states whose spatial extent is significantly larger than the range of the attractive potential. These states enjoy universality -- their character is independent of the shape of the short-range potential.

arXiv comment8 pages, 6 figures, extended discussion, results unchanged, to appear in Phys. Lett. B

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