Universality in Four-Body Scattering

The four-body system is studied in the limit of large two-body scattering length by solving momentum-space integral equations for the transition operators or, alternatively, configuration-space equations for wave function. A number of universal results for atom-trimer and dimer-dimer scattering observables are found. We furthermore address the question whether the universal four-body systems contain additional states besides the known two S-wave states. We have investigated two-cluster scattering in the universal four-body system. This complicated four-body problem can involve many channels with very different binding energies and momenta and poses thereby a serious technical challenge. In the case of multiple channels we have employed exact AGS equations for the transition operators and solved this problem successfully by using momentum-space techniques, while the application of the configuration-space Faddeev-Yakubovsky equations had technical limitation. Nevertheless, for reactions well below inelastic thresholds both methods are in perfect agreement. We have studied bosonic atom-trimer scattering in the unitary limit and obtained predictions for the atom trimer scattering length, the effective range, phase shifts, elastic and inelastic cross sections, and four-boson resonance parameters. We found that for reactions where the initial and final channel trimers are highly excited (at least 2nd excited state) these observables correlate with the corresponding trimer binding energies in a universal way. On the other hand, results for lower trimers or away from the unitary limit demonstrate that quantitative deviations from the universal results are possible; even more serious qualitative violation of the universal behavior may take place for the potentials with complicated structure. Our momentum-space technique was demonstrated to work also for dimer-dimer scattering, where a more detailed study will be performed in the near future. We have also analyzed some of the continuum properties of the four-nucleon system. This system is known to have a resonance in P-wave nucleon-triton scattering close to the threshold. The momentum scale in this problem is therefore similar to the binding momentum of the triton. Such a feature can be found in the pionless EFT if the triton is the ground state in the calculation. However, we find no resonance features when the triton is an excited state in the calculation (i.e. the cutoff is increased by roughly a factor of 22.7). Whether the pionless EFT at leading order can reproduce such features is important to answer since it has been proposed to use the pionless EFT for larger systems than 4He. This requires however, that the low-energy spectrum of the four-nucleon system is already reproduced qualitatively at leading order in the pionless EFT. The inclusion of a three-body force that will allow a continuous variation of the cutoff will be indispensable for a further analysis of this problem. (author)