[en] Two adiabatic approaches: Born-Oppenheimer (BO) and hyperradial adiabatic (HA) are frequently used for (xμ)_n (n≥2) muonic atom scattering. In both cases the Coriolis coupling operator has the same form and is treated within the close-coupling scheme. Recently, we have developed a symmetry-adapted version of the HA approach (SAHA) in which Coriolis couplings are calculated as the 'fast' component of the dynamics. In SAHA the adiabatic problem should be solved for any pair of the total angular momentum J and total parity p repeatedly but the number of adiabatic states (and the number of channels in the close-coupling calculations) is reduced by J-factor.

[en] Following the analysis of [1,2], we define appropriate hyperradius-distorted free incoming and outgoing waves (HDFW ) that incorporate unphysical long-range effects of the hyperradial-adiabatic (HA ) treatment of the three-body scattering problem.

[en] For the ⁴He₃ trimer, calculations predict two bound states with total angular momentum J = 0. This result gave rise to speculations that also bound states with J ≠ 0 might exist. Using the symmetry-adapted version of the adiabatic hyperradial approach (SAHA) we search for such bound states. Our conclusion is that ⁴He₃ has no bound rotationally excited states.

[en] Recently, an involved approach has been used by Abramov (2008 J. Phys. B: At. Mol. Opt. Phys. 41 175201) to introduce a separable adiabatic basis into the hyperradial adiabatic (HA) approximation. The aim was to combine the separability of the Born-Oppenheimer (BO) adiabatic basis and the better asymptotic properties of the HA approach. Generalizing these results we present here three more different separable bases of the same type by making use of a previously introduced adiabatic Hamiltonian expressed in hyperspheroidal coordinates (Matveenko 1983 Phys. Lett. B 129 11). In addition, we propose a robust procedure which accounts in a stepwise procedure for the unphysical couplings that are inherently present in the hyperradial adiabatic multichannel scattering approach. The advantages of the new approach are demonstrated on the example of the basic reaction in muon-catalyzed fusion physics dμ + t → tμ + d.