Recently we have reported (Knoop et al. [arXiv:1404.4826]) on an experimental determination of metastable triplet $^4$He+$^{87}$Rb scattering length by performing thermalization measurements for an ultracold mixture in a quadrupole magnetic trap. Her
e we present our experimental apparatus and elaborate on these thermalization measurements. In particular we give a theoretical description of interspecies thermalization rate for a quadrupole magnetic trap, i. e. in the presence of Majorana heating, and a general procedure to extract the scattering length from the elastic cross section at finite temperature based on knowledge of the $C_6$ coefficient alone. In addition, from our thermalization data we obtain an upper limit of the total interspecies two-body loss rate coefficient of $1.5times 10^{-12}$ cm$^3$s$^{-1}$.
We have analyzed our recently-measured three-body loss rate coefficient for a Bose-Einstein condensate of spin-polarized metastable triplet 4He atoms in terms of Efimov physics. The large value of the scattering length for these atoms, which provides
access to the Efimov regime, arises from a nearby potential resonance. We find the loss coefficient to be consistent with the three-body parameter (3BP) found in alkali-metal experiments, where Feshbach resonances are used to tune the interaction. This provides new evidence for a universal 3BP, the first outside the group of alkali-metal elements. In addition, we give examples of other atomic systems without Feshbach resonances but with a large scattering length that would be interesting to analyze once precise measurements of three-body loss are available.
We discuss the stability of homonuclear and heteronuclear mixtures of 3He and 4He atoms in the metastable 2^3S_1 state (He*) and predict positions and widths of Feshbach resonances by using the Asymptotic Bound-state Model (ABM). All calculations are
performed without fit parameters, using emph{ab-initio} calculations of molecular potentials. One promising very broad Feshbach resonance (Delta B=72.9^{+18.3}_{-19.3} mT) is found that allows for tuning of the inter-isotope scattering length.
