Four-boson system with short-range interactions

Abstract

We consider the nonrelativistic four-boson system with short-range forces and large scattering length in an effective quantum mechanics approach. We construct the effective interaction potential at leading order in the large scattering length and compute the four-body binding energies using the Yakubovsky equations. Cutoff independence of the four-body binding energies does not require the introduction of a four-body force. This suggests that two-and three-body interactions are sufficient to renormalize the four-body system. We apply the equations to 4 He atoms and calculate the binding energy of the 4 He tetramer. We observe a correlation between the trimer and tetramer binding energies similar to the Tjon line in nuclear physics. Over the range of binding energies relevant to 4 He atoms, the correlation is approximately linear.

Convergence properties of the effective theory for trapped bosons

“…The contact interactions lead to ultraviolet divergences which have to be renormalized by fixing one two-body energy (or, equivalently the scattering length a) and a three-body energy [3,27]. Since the trap only modifies the infrared properties of the system, the renormalization of the contact interactions is the same as in free space.…”

with effective field theory

“…For example nucleon-deuteron scattering in all channels expect the S 1/2 -wave can be calculated to high-orders using only two-nucleon input and the triton binding energy is found to be B 3 (EF T ) = 8.35MeV in next to leading order close to the experimental B 3 (exp) = 8.5MeV [11]. Pionless EFT has been recently applied to the four-body system with contact interactions and large scattering length at leading order by Platter [12]. The binding energies of the 4 He tetramer and the alpha-particle have been calculated and it is in a good agreement with experimental value.…”

The Three-Boson System at Next-to-Next-to-Leading Order

“…kR ≪ 1) behavior of any system with a particular value of that ratio can then be generated-either using an EFT or quantum-mechanical models. Since the EFT generates predictions for these systems which do not depend on the details of the short-distance physics it provides a powerful way of unifying apparently diverse physics problems: dimers, trimers and tetramers of Helium-4 atoms; deuterium, tritium, & Helium nuclei; and nuclei with neutron halos [4,5,6,7,8]. These systems differ in size and spin structure but share the same essential feature of a large two-body scattering length.…”