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 reff. We study shallow bound states of charged particles with D≫reff 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→∞). 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.
Highlights
Shallow bound states of two neutral particles with zero angular momentum live in a classically forbidden region and retain almost no information about binding interactions [1]
The main finding of our study is that there is a new family of universal few-body bound states for charged systems interacting via a potential VC + VS
In contrast to neutral particles, the zerorange approximation to VS is not guaranteed to be useful for realistic shallow bound states: The Coulomb barrier makes the
Summary
Shallow bound states of two neutral particles with zero angular momentum live in a classically forbidden region and retain almost no information about binding interactions [1]. A celebrated VS is a zero-range potential tuned to reproduce the scattering length [2, 3, 4] It provides a powerful starting point for studying universal bound states (i.e., independent of the shape of VS ) in nuclear and atomic physics [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. The main finding of our study is that there is a new family of universal few-body bound states for charged systems interacting via a potential VC + VS Their properties are fully determined by the Sommerfeld parameter, the Coulomb-modified scattering length and effective range, as well as the three-body parameter. In contrast to neutral particles, the zerorange approximation to VS is not guaranteed to be useful for realistic shallow bound states: The Coulomb barrier makes the
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