Time-delay matrix analysis of several overlapping resonances: applications to the helium atom and the positronium negative ion

A useful method of analysing sets of several overlapping multichannel resonances, which are extremely difficult to analyse by other means, is presented. It exploits the Lorentzian profiles of eigenvalues{q(i)( E)} of the energy-dependent time-delay matrix, avoided at their crossings. The contribution to {qi( E)} from each S-matrix pole stands out clearly and uniquely from the contributions from the other poles. Thus the resonances that can be easily missed by the conventional technique of studying the eigenphase sum delta(E) or its derivative d delta/dE are singled out as diabatic resonances in a visually unambiguous way. The method is illustrated with the P-1(o) continuum states of the helium atom and the positronium negative ion Ps(-) below the threshold for He+(n = 5) or Ps(n = 5). Many new resonances are found for Ps(-).