Isolated core excitation was used to produce low-energy continuum electrons in the l = 3 angular momentum state of barium. Data were taken over a region of energy that coincided with the energy of the 6p3/2nf doubly excited states. Analysis of the data using multichannel quantum defect theory allowed the measurement of the widths of the 6p3/2nf states and the energy-dependent phase of the continuum electronic wave functions due to interaction with the doubly excited states. The phase of the continuum electrons is shown to vary continuously with energy, due to the anomalously broad widths of the double excited states