Optical absorption spectra are exactly calculated for direct interband transitions in a one-dimensional (1D) electron-hole system within the effective-mass approximation. We employ a modified Coulomb potential between an electron and a hole to avoid the well-known divergence problem in the 1D system. The Sommerfeld factor, which is the absorption intensity ratio of the unbound exciton to the free electron-hole pair above the band edge, is found for the first time to be less than unity for the direct allowed transition in striking contrast to the three- and two-dimensional cases. This feature can be understood in terms of anomalously strong concentration of oscillator strength on the lowest 1D exciton state.
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