Determination of theα6+dvertex constant (asymptotic coefficient) from theHe4+dphase-shift analysis

The ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$($1^{+}$0)${\to }^4$He+d virtual decay vertex constant ${\mathit{G}}_0$ and the respective asymptotic coefficient ${\mathit{C}}_0$ of the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ wave function in the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$+d channel are found using the analytic continuation of the solution of a novel energy-dependent phase-shift analysis of elastic d${\mathrm{-}}^4$He scattering to the pole corresponding to the ${}_{}{}^6{}_{}{}^{}\mathrm{Li}$ ground state. The reliability and accuracy of the method used have been corroborated independently by three other ways: by directly solving the inverse problem for d${\mathrm{-}}^4$He scattering and by two different methods for finding a solution for the three-body (α+n+p) problem. The values ${\mathit{G}}_0^2$=0.42±0.02 fm and ${\mathit{C}}_0$=2.93±0.15 have been found, which seem to be the most accurate and reliable among the values obtained so far.