Abstract
The original Billiard Ball model1 was introduced to explain various echo phenomena in gases resulting from the application of short excitation pulses. The excitation pulses were required to be short to insure that their bandwidth uniformly covered the Doppler-broadened line of the transition being excited. In this treatment the atoms were localized by spherical wavepackets throughout. Recently, the Billiard Ball model has been expanded to include the effects of long excitation pulses that may not cover the entire Doppler-broadened line. Accommodating this introduces non-spherical wavepackets into the model. We call this extension the Elliptical Billiard Ball echo model.3
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