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arXiv:2308.09545

An alternative scheme for pionless EFT: neutron-deuteron scattering in the doublet S-wave

Ebert, M., H.‐W. Hammer, Akaki Rusetsky

Published Aug 18, 2023• 0 citations
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Abstract

Using the effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the breakdown of unitarity in the three-body amplitude. We discuss the extension of our alternative subtraction scheme for including effective range corrections in pionless effective field theory for spinless bosons to nucleons. In particular, we consider the neutron-deuteron system in the doublet S-wave channel explicitly.

DOI
10.48550/arxiv.2308.09545

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Using the effective-range expansion for the two-body amplitudes may generate spurious sub-threshold poles outside of the convergence range of the expansion. In the infinite volume, the emergence of such poles leads to the breakdown of unitarity in the three-body amplitude. We discuss the extension of our alternative subtraction scheme for including effective range corrections in pionless effective field theory for spinless bosons to nucleons. In particular, we consider the neutron-deuteron system in the doublet S-wave channel explicitly.
We investigate universal behavior in elastic atom-dimer scattering below the dimer breakup threshold calculating the atom-dimer effective-range function $ak\mathrm{cot}\ensuremath{\delta}$. Using the He-He system as a reference, we solve the Schr\"odinger equation for a family of potentials having different values of the two-body scattering length aaa and we compare our results to the universal zero-range form deduced by Efimov, $ak\mathrm{cot}\ensuremath{\delta}={c}_{1}(ka)+{c}_{2}(ka)\mathrm{cot}[{s}_{0}\mathrm{ln}({\ensuremath{\kappa}}_{*}a)+\ensuremath{\phi}(ka)]$, for selected values of the three-body parameter ${\ensuremath{\kappa}}_{*}$. Using the parametrization of the universal functions ${c}_{1},{c}_{2},\ensuremath{\phi}$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter ${\ensuremath{\kappa}}_{*}$.
We investigate the appearance of resonances in three-body systems using pionless effective field theory at leading order with two complementary methods. The Faddeev equation is analytically continued to the unphysical sheet adjacent to the positive real energy axis using a contour rotation. We consider both the three-boson system and the three-neutron system. For the former, we calculate the trajectory of Borromean three-body Efimov states turning into resonances as they cross the three-body threshold. For the latter, we find no sign of three-body resonances or virtual states at leading order. This result is validated by exploring the level structure of three-body states in a finite volume approach.
Systems, such as cold atoms and light halo nuclei, share universal features at low energies, for which details of inter-particle interactions are not essential.We study threebody physics in such systems in an effective-field-theory (EFT) framework.We will discuss universal behavior in three-body systems and higher-order effectiverange corrections beyond universality.We study effective-range effects perturbatively up to the next-to-next-to-leading order (N 2 LO) for the case of three identical bosons.We apply this analysis to recombination features in cold atomic gases and properties of Helium trimers.Effective range corrections also play an important role in the EFT study of fewnucleon systems and halo nuclei.The ground-state of Helium-6 can be treated as a two-neutron halo with an alpha core.This bound state is generated by the resonant neutron-neutron and neutron-alpha interactions.The latter is dominated by a shallow p-wave resonance.We present a calculation of Helium-6 in an EFT approach appropriate for halo systems.
We present the first five-body calculations of s-wave n-4He scattering within leading order and next-to-leading order (NLO) pionless effective field theory (π̸EFT). Using an harmonic oscillator trap technique and π̸EFT fitted to just six well-established experimental parameters, we predict the s-wave n-4He phase shifts, scattering length an4He1/2(NLO)=2.47(4num.)(17theor.)fm, and effective range rn4He1/2(NLO)=1.384(3num.)(211theor.)fm in agreement with experiment. The apparent cutoff independence of our results is used to estimate the theoretical errors coming as an integral part of our final results.
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