Converging on Bound States in Coupled-Channel Calculations

We develop a robust algorithm for locating bound states in coupled-channel calculations. Bound states exist at energies where an individual eigenvalue of a log-derivative or ratio matching matrix passes through zero. We describe an algorithm to identify the required eigenvalue of the matching matrix over the full range of energy where it exists. This allows much simpler programming than previous methods. We also consider the choice of the matching distance Rmatch, where the matching matrix is defined; coupled-channel methods are most efficient if Rmatch is chosen to be in the classically allowed region for all channels that support bound states of interest, but not very close to a node in the wavefunction.