A time dependent theory for radiative recombination induced by strong pulses is presented. Analytic solutions in the adiabatic limit are derived and found to be in excellent agreement with exact numerical solutions. Both the pump-before-dump ''intuitive'' and dump-before-pump ''counter-intuitive'' schemes are considered. Resonantly enhanced two-photon recombination of ultracold atoms is shown to be an efficient mechanism for the production of ultracold molecules. We have performed detailed calculations on the radiative recombination of cold Na atoms by short laser pulses. Our calculations show that, per pulse, it is possible for up to 97% of all head-on Na-Na colliding pairs to end up as v=0, J=0 translationally cold Na-2 molecules. We show that these findings, translated to thermally cooled ensemble conditions, mean that the fraction of Na atoms at mu Kelvin which can be recombined by a pulse of 20 ns duration and 10(8) W/cm(2) peak intensity, to form J=0 molecules is 6x10(-6) per pulse. With the above parameters, a laser operating at 100 Hz can convert half of an ensemble of cold atoms to cold molecules in similar to 25 min. The efficiency of the process can be increased by going to longer pulses of lower intensity, by going to lower temperatures or by increasing the density of the ensemble. In particular, the ''counter-intuitive'' scheme which allows for use of longer pulses of lower intensities, with no spontaneous emission losses, considerably increases the yield. (C) 1997 American Institute of Physics.