The energies and widths of doubly excited states of the K- ion in the vicinity of the K(5 2D,7 2S,5 2F) thresholds have been measured in high resolution using a sensitive collinear laser-ion beam apparatus. These transient states appeared as resonances in the partial cross section for photodetachment via the K(5 2S)+e(-)(epsilon(p)) channel. Series of two states below the 5 2D threshold and four states below the 5 2F threshold have been found. The relative widths of members of the series below the 5 2F threshold exhibit anomalous behavior, as predicted by a semiclassical model.
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