We measure the photoluminescence spectra for an array of modulation doped, T-shaped quantum wires as a function of the 1d density n_e which is modulated with a surface gate. We present self-consistent electronic structure calculations for this device which show a bandgap renormalization which, when corrected for excitonic energy and its screening, are largely insensitive to n_e and which are in quantitatively excellent agreement with the data. The calculation (cf. cond-mat/9908349) shows the importance of including orthogonality between the screening electrons and the electron(s) bound to the hole. The calculations show that electron and hole remain bound up to 3 x 10^6 cm^-1 and that therefore the stability of the exciton far exceeds the conservative Mott criterion.
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