Quadrupole response of a weakly bound bosonic trimer

Role of sharp avoided crossings in short hyper-radial range in recombination of the cold 4He3 system

The role of sharp avoided crossings (SACs) in a short hyper-radial range R≤ 50 a.u. in the calculation of recombination for a cold ⁴He₃ system is investigated in the adiabatic hyperspherical representation by "turning off and on" the relevant nonadiabatic couplings. The influence of SACs on the recombination is related with the channels of the system and with the scattering energy. For J^Π = 0⁺ symmetry, the two-body recombination channel has an attractive potential well, which makes radial wave functions of both two-body recombination channel and three-body continuum channels accessible in the short hyper-radial range where SACs are located. The SACs consequently play an important role in coupled-channel calculations and this is particularly the case for lower scattering energies. However, for excited nuclear orbital momenta, i.e., J^Π = 1^-, 2⁺,…, 7^- symmetries, the two-body recombination channel has a repulsive interaction and the radial wave functions are not accessible in the short hyper-radial range. Therefore, omission of SACs in the short range for these symmetries has no effect on the numerical results, which leads to great savings on hyper-radial grid points in the practical numerical calculations. Moreover, to make the nonadiabatic couplings among channels to be continuous in the hyper-radius, different methods associated with the application of consistent phase convention are discussed.