Weakly bound small ⁴He clusters attracted considerable attention in recent years, in particular because of the booming interest in Bose-Einstein condensation of ultra-cold gases. Besides, the helium trimer is probably a first specific molecular system where a direct manifestation of the Efimov effect can be observed. Experimentally the ⁴He trimer was observed in [1]. Hyperspherical, variational and Faddeev-type techniques have successfully been employed to treat this system theoretically. In order to overcome technical complications due to the strong repulsive part in the atomic interaction, a hard-core version of the Faddeev differential equations has been developed and applied to helium trimer system [2]. This approach has been employed to the investigations of bound states, scattering length and phase shifts of the scattering of a ^3;4He atom off a ⁴He dimer. We present our recent results on the scattering length of the collision of a ⁴He atom with a ⁴He dimer. As compared to our previous calculations [2] of the same quantity, a much more refined grid is employed, as a step leading to an improvement of about 10%. Our results are compared with other ab initio, and with model calculations.

[1]    F. Luo, G. C. McBane, G. Kim, C. F. Giese, and W. R. Gentry, J. Chem. Phys. 98, 3564 (1993); W. Schöllkopf and J. P. Toennies, Science 266, 1345 (1994); F. Luo, C. F. Giese, and W. R. Gentry, J. Chem. Phys. 104, 1151 (1996).
[2]    E. A. Kolganova, A. K. Motovilov, and S. A. Sofianos, J. Phys. B. 31, 1279 (1998); A. K. Motovilov, W. Sandhas, S. A. Sofianos, and E. A. Kolganova, Eur. Phys. J. D 13, 33 (2001).