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arXiv:physics/0309105 · Physical Review A

Lowest open channels, bound states, and narrow resonances of dipositronium

Bao Cheng-guang, T. Y. Shi

Published Apr 29, 2003• 8 citations
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Abstract

The constraints imposed by symmetry on the open channels of dipositronium has been studied, and the symmetry-adapted lowest open channel of each quantum state has been identified. Based on this study, the existence of two more ${0}^{+}$ bound states has been theoretically confirmed, and a ${0}^{+}$ narrow resonance has been predicted. A variational calculation has been performed to evaluate the critical strength of the repulsive interaction. Two ${0}^{\ensuremath{-}}$ states are found to have their critical strengths very close to 1, they are considered as candidates of new narrow resonances or loosely bound states.

DOI
10.1103/physreva.67.042505

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The constraints imposed by symmetry on the open channels of dipositronium has been studied, and the symmetry-adapted lowest open channel of each quantum state has been identified. Based on this study, the existence of two more 0+{0}^{+}0+ bound states has been theoretically confirmed, and a 0+{0}^{+}0+ narrow resonance has been predicted. A variational calculation has been performed to evaluate the critical strength of the repulsive interaction. Two 0\ensuremath−{0}^{\ensuremath{-}}0\ensuremath− states are found to have their critical strengths very close to 1, they are considered as candidates of new narrow resonances or loosely bound states.
Symmetry has imposed very strong constraints on the internal structure of quantum mechanical system. In particular, whether a state can access a given outgoing channel is constrained by symmetry. For the dipositroniums, the most important channel is the Ps-Ps channel. However, based on symmetry consideration it was found that only a few excited states are allowed to access the Ps-Ps channel, thereby at least the existence of two higher L = 0 bound states (higher than the Ps-Ps threshold) has been affirmed.
1. Highlight “short-ranged,” “dilute,” and “low-energy” as three main features of interactions between ultracold atoms. 2. Introduce the important concept of the phase shift. 3. Introduce the sss-wave scattering length as a universal parameter describing the low-energy interaction between ultracold atoms. 4. Discuss the relation between divergent scattering length, low-energy bound state, and jump of phase shift. 5. Discuss the relation between the scattering length and the scattering amplitude. 6. Discuss under what condition a positive scattering length describes repulsive interaction. 7. Discuss the condition when an algebraically decayed potential can be treated as a finite range one. 8. Introduce two types of zero-range single-channel potentials to capture the universal low-energy sss-wave interaction between ultracold atoms. 9. Introduce the concept of renormalization condition and renormalizable theory. 10. Discuss how the spin rotational symmetry imposes constraints on interaction form for both alkali-metal and alkaline-earth-metal atoms. 11. Introduce Feshbach resonance as an important tool to tune scattering length. 12. Compare the two-channel Feshbach resonance with the single-channel shape resonance and compare the wide and the narrow resonances. 13. Introduce a zero-range two-channel model. 14. Introduce the confinement-induced resonance to tune interaction strength by an external potential. 15. Summarize three key conditions for a Feshbach resonance, and unify the optical Feshbach resonance, the orbital Feshbach resonance, and the confinement-induced resonance all in terms of these three conditions. 16. Introduce the Efimov effect as an important three-body effect at the vicinity of the two-body scattering resonance. 17. Highlight the symmetry aspect of the Efimov effect. 18. Discuss various connections between few-body and many-body physics. 19. Illustrate that few-body calculation can be used to determine properties of many-body systems by using high-temperature expansion as an example.
Detailed electron-correlation calculations which include the mixing of closed channel with open channels, suggest that ${\mathrm{He}}^{\ensuremath{-}}$ has only two bound states: The 1s2s2p4Po1s2s2p^{4}P^{o}1s2s2p4Po and the $2{p}^{3}^{4}S^{o}$. The $1s2{p}^{2}^{4}P$ and 2P^{2}P2P states are above the He 1s2p3Po1s2p^{3}P^{o}1s2p3Po threshold and therefore qualify only as core-excited shape resonances. This conclusion contradicts certain previous theoretical and experimental findings which implied the existence of bound ${\mathrm{He}}^{\ensuremath{-}}^{4}P$ and 2P^{2}P2P states. Both 4Po^{4}P^{o}4Po and 4So^{4}S^{o}4So autoionize to the adjacent continuum via spin-dependent forces---a well-known decay mechanism. However, there are two more decay mechanisms: nonrelativistic (for 4So^{4}S^{o}4So) and relativistic (for 4Po^{4}P^{o}4Po) radiative autoionization (RA). The probability for RA of the 4So^{4}S^{o}4So state in the Hartree-Fock approximation is computed to be 1.14\ifmmode\times\else\texttimes\fi{}1010{10}^{10}1010 ${\mathrm{sec}}^{\ensuremath{-}1}$
We reexamine the problem of calculating the positions and widths of the lowest-lying resonances in the Ps+H\mathrm{Ps}+\mathrm{H}Ps+H scattering system that consists of two electrons, one positron and one proton. The first of these resonances, for L=0,L=0,L=0, was found by the methods of complex rotation and stabilization, and later described as a Feshbach resonance lying close to a bound state in the closed-channel ${e}^{+}+{\mathrm{H}}^{\ensuremath{-}}$ system. Recently, results for the L=1L=1L=1 and 2 scattering states were published, and it was found, surprisingly, that there is a large shift in the positions of these resonances. In this paper we repeat the analysis for L=1L=1L=1 and find an unexpected explanation for the shift.
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.