Binding energies and scattering observables in the 4He3 atomic system

Abstract

The 4 He3 bound states and the scattering of a 4 He atom off a 4 He dimer at ultra-low energies are investigated using a hard-core version of the Faddeev differential equations. Various realistic 4 He-4 He interactions were employed, amomg them the LM2M2 potential by Aziz and Slaman and the recent TTY potential by Tang, Toennies and Yiu. The ground state and the excited (Efimov) state obtained are compared with other results. The scattering lengths and the atom-diatom phase shifts were calculated for center of mass energies up to 2.45 mK. It was found that the LM2M2 and TTY potentials, although of quite different structure, give practically the same bound-state and scattering results.

Universality in the physics of cold atoms with large scattering length☆

“…Using the value of Λ * extracted from the excited state binding energy, a good agreement with a AD from the direct calculation of Ref. [ 4] is obtained [ 5]. Universality is also manifest in universal scaling functions.…”

“…The function ∆(ξ) was recently calculated in EFT [ 3]. Unfortunately, no 3-body observables have been measured for 4 He atoms up to now, so that Λ * can not be determined from experiment. However, extensive bound state calculations with modern potentials exist.…”

“…However, extensive bound state calculations with modern potentials exist. We have used recent calculations by Motovilov et al [ 4], to obtain the dimer binding energy and the 3-body parameter Λ * from the calculated binding energy of the trimer excited state B (1) 3 . We have then used this input to calculate the trimer ground state energy B (0) 3 for four different 4 He potentials [ 5].…”

“…2, we display the scaling function relating B (1) 3 /B 2 to B (0) 3 /B 2 [ 5]. The data points give various calculations using modern 4 He potentials while the solid line gives the universality prediction from EFT. Different points on this line correspond to different values of Λ * .…”

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

“…Since the atom-atom scattering length is a 2 = 104 +8 −18 Å while the typical van der Waal's forces between the Helium atoms have a range R ≈ 7Å, in this case the expansion parameter R/a 2 < ∼ 10%. The 4 He trimer, tetramer, and several larger 4 He clusters have been observed [15,16], but unfortunately there are no measurements of trimer binding energies, and so we use precise few-body calculations [17,18,19,20,21], based on quite complicated inter-atomic potentials [22,23], to provide the two input ratios for our EFT. We then compare the EFT's predictions with the corresponding results obtained in Refs.…”