Relating Binding Energy and Scattering Length of Weakly Bound Dimers of Strontium

Abstract

The s‐wave scattering length (a) is an important parameter in ultracold collisions and precision tests of fundamental physics, yet its accurate calculation remains a challenge. Solving suitable vibrational Schrödinger equations with scaled interaction potentials and reduced masses, the relationship between the binding energy (D0) of the highest vibrational state and the s‐wave scattering length is derived for a set of ground state Sr2 isotopomers. The resulting “a versus D0” relations are robust even if approximate potentials are used, thus enabling reliable scattering lengths to be determined directly from experimental binding energies. The presented approach will have broad applicability, notably when an accurate potential is unavailable and when the literature (semiclassical) counterparts of the probed “a versus D0” relations become inadequate.

Relating Binding Energy and Scattering Length of Cold Hybrid Ion‐Atom Systems

“…The observed “universality” means that knowledge of only one of the low‐energy atom‐ion scattering properties allows for not only the reliable determination of all these characteristics, but also the reliable determination of their mass sensitivities. [ 4,5,16 ] Having an adequate relationship over the range of the binding energies pertaining to the diverging scattering length, the relations can be confidently used to investigate the mass sensitivity of the probed scattering properties, as well as other properties. As seen in Figure 3 , the proximity of a scattering pole allows the mass sensitivity of the scattering length to be enhanced by quite a few orders of magnitude and may thus be suitable for probing the variability of the electron‐to‐proton mass ratio β.…”

“…The models are capable not only of capturing the global scattering properties, but also of providing reliable predictions. However, in some situations, like in the case of the $$-1/r^6$$ atom‐atom long‐range interaction, [ 4,5 ] the $$-1/r^4$$ models may become limited by the neglect of omnipresent “higher‐order” terms. To probe the role of such terms, we have decided to proceed in the same way as we did in the case of the atom‐atom interaction, namely, to derive the numerical relations between the binding energies ( D last ) of the highest vibrational states and the s ‐wave scattering lengths ( a ) for suitable models by solving appropriate vibrational Schrödinger equations with scaled interaction potentials.…”

“…To probe the role of such terms, we have decided to proceed in the same way as we did in the case of the atom‐atom interaction, namely, to derive the numerical relations between the binding energies ( D last ) of the highest vibrational states and the s ‐wave scattering lengths ( a ) for suitable models by solving appropriate vibrational Schrödinger equations with scaled interaction potentials. [ 4–6 ] Relying on the availability of a set of highly accurate and globally defined theoretical potential energy functions, the actual calculations were performed for the 6 Li$$_2^+$$ and 7 Li$$_2^+$$ dimers in the $$X^2\Sigma _g^+$$ ground electronic state.…”