Asymptotic-bound-state model for Feshbach resonances

Abstract

We present an asymptotic-bound-state model which can be used to accurately describe all Feshbach resonance positions and widths in a two-body system. With this model we determine the coupled bound states of a particular two-body system. The model is based on analytic properties of the two-body Hamiltonian and on asymptotic properties of uncoupled bound states in the interaction potentials. In its most simple version, the only necessary parameters are the least bound state energies and actual potentials are not used. The complexity of the model can be stepwise increased by introducing threshold effects, multiple vibrational levels, and additional potential parameters. The model is extensively tested on the 6 Li-40 K system and additional calculations on the 40 K-87 Rb system are presented.

Feshbach resonances inHe3*-Goosen1, Tiecke2, Vassen3 et al. 2010Phys. Rev. ASelf Cite142320View full textAdd to dashboardCite

“…The free parameters in our model which determine the magnetic field resonance position B 0 and the field width B are the binding energies A S, and the overlap between various molecular states ψ A S, |ψ A S , [20]. Next we discuss how we can obtain these quantities by utilizing known molecular potentials.…”

“…To predict the magnetic field position and width of Feshbach resonances, we use the ABM [20,22,23]. We recapitulate the basic principles of the ABM and show how this model can be applied to metastable helium.…”

“…This scattering matrix S = S P S Q (of the effective problem in P space) is a product of the S P matrix and a resonant part, S Q , which involves coupling of a Q space bound state to P space [27]. The S P matrix, which describes the scattering process in P space in the absence of coupling to the Q space, is determined by considering only the dominant bound state in P space [20]. Here we neglect the other nearby resonance poles in P space [28], which is a valid approximation if the background scattering length (a bg ) is larger than the typical range of the interaction potential [20].…”

“…The S P matrix, which describes the scattering process in P space in the absence of coupling to the Q space, is determined by considering only the dominant bound state in P space [20]. Here we neglect the other nearby resonance poles in P space [28], which is a valid approximation if the background scattering length (a bg ) is larger than the typical range of the interaction potential [20]. By determining the total S matrix, we are able to deduce the (magnetic field) position and width of the Feshbach resonance.…”

“…In addition, we also will consider homonuclear 3 He * -3 He * and 4 He * -4 He * collisions. We will work with the asymptoticbound-state model (ABM) [20], which will be reviewed in Sec. II.…”