Effective Field Theory Analysis of ThreeBoson Systems at NextToNextToLeading Order
Abstract
We use an effective field theory for shortrange forces (SREFT) to analyze systems of three identical bosons interacting via a twobody potential that generates a scattering length, a, which is large compared to the range of the interaction, ℓ. The amplitude for the scattering of one boson off a bound state of the other two is computed to nexttonexttoleading order (N^{2}LO) in the ℓ/ a expansion. At this order, two pieces of threebody data are required as input in order to renormalize the amplitude (for fixed a). We apply our results to a model system of three Helium4 atoms, which are assumed to interact via the TTY potential. We generate N^{2}LO predictions for atomdimer scattering below the dimer breakup threshold using the boundstate energy of the shallow Helium4 trimer and the atomdimer scattering length as our two pieces of threebody input. Based on the convergence pattern of the SREFT expansion, as well as differences in the predictions of two renormalization schemes, we conclude that our N^{2}LO phase shift predictions will receive higherorder corrections of < 0.2 %. In contrast, the prediction of SREFT for the binding energy of the "deep" trimer of Helium4 atoms displays poor convergence.
 Publication:

FewBody Systems
 Pub Date:
 December 2013
 DOI:
 10.1007/s0060101307105
 arXiv:
 arXiv:1212.1845
 Bibcode:
 2013FBS....54.2317J
 Keywords:

 Nuclear Theory;
 Physics  Atomic and Molecular Clusters
 EPrint:
 58 pages, 20 figures. Dedicated to Professor Henryk Witala at the occasion of his 60th birthday. Submitted in FewBody Systems