The rate equations for the pumping of the Nd<sup>3+</sup> system are simplified to a single differential equation. This is solved for the population of the <sup>4</sup><i>F</i><sub>3/2</sub> level, <i>N</i>, under a pump waveform, <i>At</i><sup>2</sup>e<sup>-bt</sup>, assuming that the lifetime of the state is constant. The optimum <i>Q</i>-switch time (time at which N and the output energy of the laser pulse are maximum) is then calculated. The optimum <i>Q</i>-switch time is given as a function of pump input energy for a 5-wt% Nd<sub>2</sub>O<sub>3</sub> in barium crown glass, 80-mm-long clad laser rod, pumped with an FX38 flash tube driven by a simple LC circuit. From these results, the apparent lifetime of the <sup>4</sup><i>F</i><sub>3/2</sub>, level was shown to decrease from 157 µsec with 67.5-J input to 57 µsec with a 144-J input.
HARRY E. BATES, "Measurement of the Apparent Lifetime of the 4F3/2 State of Nd3+ in Glass under Superradiant Conditions," J. Opt. Soc. Am. 60, 902-904 (1970)