Interactions between bosonic and fermionic metastable He atoms

Mixtures of spin-polarized metastable ${}^3\textrm{He}$ atoms and ${}^4\textrm{He}$ atoms are unique systems of current interest for studies of ultra-cold gases. The $s$-wave scattering length for collisions of ${}^4\textrm{He}$ atoms was measured to be ${}^{4-4}a=11.3$~nm ($+2.5,-1$~nm)~[1] and recent calculations find $8<{}^{4-4}a<12$~nm~[2]. The scattering length ${}^{3-4}a$ for fermion-boson collisions is presently indeterminate in sign and magnitude, but it has been predicted to fall in the ranges ${}^{3-4}a<-25$~nm or ${}^{3-4}a>46$~nm~[2,3]. In this talk, with regard to improving the theoretical value of ${}^{3-4}a$, the data characterizing ${}^3\textrm{He}(2\,{}^3S)$--${}^4\textrm{He}(2\,{}^3S)$ interactions primarily in the molecular ${}^5\Sigma_g^+$ state are reevaluated and additional calculations are presented. Supported in part by the NSF. [1]~S. Seidelin, \textit{et al.}, Phys. Rev. Lett. \textbf{93} (2004), 090409. [2]~A.~S. Dickinson, F.~X. Gad\'{e}a, and T. Leininger, J. Phys. B \textbf{37} (2004), 587. [3]~R.~J.~W. Stas, J.~M. McNamara, W. Hogervorst, and W. Vassen, Phys. Rev. Lett. \textbf{93} (2004), 053001.