  Experimental data on the n-alpha and dt collisions in the quantum state
J^pi=3/2+ near the dt-threshold are fitted using the semi-analytic
multi-channel Jost matrix with proper analytic structure and some adjustable
parameters. Then the spectral points are sought as zeros of the Jost matrix
determinant (which correspond to the S-matrix poles) at complex energies. The
correct analytic structure makes it possible to calculate the fitted Jost
matrix on any sheet of the Riemann surface whose topology involves not only the
square-root but also the logarithmic branching caused by the Coulomb
interaction. Within a distance of 100,keV above the dt-threshold, three 3/2+
resonances are found on the non-physical sheet of the Riemann surface. Several
S-matrix (shadow) poles on the other sheets of this surface are located as
well.
