Energy-dependent phase-shift analysis ofH2+4He scattering in the energy range 0.87<Ed<5.24 MeV

An efficient method for construction of an analytic S matrix from experimental data based on the use of the statistical Padé approximation is proposed. The method is applied to the energy-dependent phase-shift analysis of the elastic scattering of deuterons by alpha particles in the energy range 0.87<${\mathit{E}}_{\mathit{d}}$<5.24 MeV, and partial-wave phase shifts for l=0,1,2 are obtained. In addition, the energies and widths of the three known ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ resonances are obtained, together with the energy of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ bound state and the vertex constant of the virtual decay ${}_{}{}^6{}_{}{}^{}\to _{}^2{}_{}{}^{}$H${+}^4$He.