Dicentric chromosomal aberrations produced by ionizing radiation probably result from pairwise interaction of DNA double strand breaks (dsbs). It has been suggested that high LET radiation may preferentially produce a subclass of 'severe' dsbs that are long-lived and/or exchange-prone, and that it is the production of these severe dsbs which account for the increased biological effectiveness of high-LET radiation. We present a quantitative formalism to describe the induction of these severe dsbs, and the subsequent production of exchange-type chromosomal aberrations. Using a Markov model and microdosimetric methods, we conclude that dicentric production by such severe dsbs has properties similar to those observed at high LET. Specifically, at high doses, the yield is nearly linear with dose even if dsbs from different tracks interact. The model is applied to published data on dicentric aberrations produced by irradiation of human lymphocytes in vitro. Corrections for the effects of interphase death are estimated. From comparisons with the experiments we conclude that interaction of severe dsbs could make a significant contribution to the observed dicentric production at high LET and also perhaps for low doses (though not high doses) at low LET. Proximity explanations of high-LET effects continue to offer the main prospect for obtaining a unified picture of chromosomal aberration formation by all ionizing radiation types, but a hybrid model in which severe dsbs contribute to the high-LET aberration yield cannot be ruled out. If all or part of high-LET radiation damage is qualitatively different from low-LET radiation damage, as this severe dsb model may suggest, there could be far-reaching implications for the field of radiation protection.