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International Journal of Quantum Chemistry

The calculation of feshbach resonances using coupled propagator equations

Hongbin Zhan, Yinchun Zhang, Peter M. Winkler

Published Feb 12, 1994• 6 citations
Publisher

Abstract

A coupled channel theory of resonances has been formulated within the propagator approach of many-body theory and applied to the 1s3s2 resonance of e-helium scattering. This system has previously been studied both experimentally and theoretically. Our results for the width of the resonance agree well with these earlier findings. © 1994 John Wiley & Sons, Inc.

DOI
10.1002/qua.560520813

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A coupled channel theory of resonances has been formulated within the propagator approach of many-body theory and applied to the 1s3s2 resonance of e-helium scattering. This system has previously been studied both experimentally and theoretically. Our results for the width of the resonance agree well with these earlier findings. © 1994 John Wiley & Sons, Inc.
We revisit the basic properties of Fano-Feshbach resonances in two-body systems with van der Waals tail interactions, such as ultracold neutral atoms. Using a two-channel model and two different methods, we investigate the relationship between the width and shift of the resonances and their dependence on the low-energy parameters of the system. Unlike what was previously believed [C. Chin et al., Rev. Mod. Phys. 82, 1225 (2010)] for magnetic resonances, we find that the ratio between the width and the shift of a resonance does not depend only on the background scattering length, but also on a closed-channel scattering length. We obtain different limits corresponding to different cases of optical and magnetic resonances. Although the generalization of the theory to the multichannel case remains to be done, we found that our two-channel predictions are verified for a specific resonance of lithium-6.
The coupled-channel model [Phys. Rev. A {\bf 59}, 363 (1999)] that yields converged low-energy phase shifts, and exact binding and resonance features in Ps-H [Phys. Rev. A {\bf 59}, 2058 (1999)] is applied to study Ps-He+^++ scattering. Similar to PsH, resonances appear in the S-, P-, D-, etc partial waves in the Ps-He+^++ system but in both the singlet and triplet scattering channels. The latter signifies possible Rydberg states of e+e^+e+ around singlet and triplet helium. The S-wave singlet resonance at 2.79 eV agrees to that predicted earlier in e+e^+e+-He entrance channel (energy difference 16.64 eV) at 19.27 eV [Chem. Phys. Lett. {\bf 262}, 460 (1996)].
The 2P^{2}P2P (2s2s2p2s2s2p2s2s2p) and 2D^{2}D2D (2s2p2p2s2p2p2s2p2p) resonance structure observed in the electron-helium scattering experiments has been investigated using a saddle-point technique. For 2P^{2}P2P we obtain for the energy --- 0.796 93 a.u. with an 82-term wave function. This agrees well with the experimental result. In the past, the 2D^{2}D2D structure was thought to be a Feshbach resonance. In this calculation, we show that the 2s2p2s2p2s2p 3P^{3}P3P target is repulsive to the third ppp electron in the sense that the variational energy of the ${\mathrm{He}}^{\ensuremath{-}}$ system is monotonically increased as the ppp electron approaches the target. Hence, the Feshbach resonance cannot be formed for this state. Some comments will be made concerning earlier theoretical calculations in the literature.
Using a two-channel model, we investigate theoretically the binding energy of confinement-induced Feshbach molecules in two- and one-dimensional ultracold atomic systems near a Feshbach resonance. We show that the two-channel prediction will evidently deviate from the simple single-channel theory as the width of Feshbach resonances decreases. For the one-dimensional system, we perform a full two-channel calculation, with the inclusion of bare interatomic interactions in the open channel. Away from the resonance, we find a sizable correction to the binding energy, if we neglect the bare interatomic interactions as in the previous work [D. B. M. Dickerscheid and H. T. C. Stoof, Phys. Rev. A 72, 053625 (2005)]. We compare our theoretical results with the existing experimental data and present predictions for narrow Feshbach resonances that could be tested in future experiments.