Radiative Decay of the2PState of Atomic Hydrogen: A Test of the Exponential Decay Law

In Jaynes's semiclassical radiation theory, the decay of an excited atomic state depends on its initial population. For the radiative decay of the $2P$ level in atomic hydrogen, produced by pulsed excitation from the $2S$ level, the theory predicts a decay rate $\Gamma =(1-f)\mathrm{}{\Gamma }_0+\beta P$, where $\beta =f{\Gamma }_0$. Here $f$ is the initial $2S$ population, ${\Gamma }_0$ is the natural $2P$ decay rate, and $P$ is the $2P$ population relative to $f$. For $f=0.086\mathrm{}\pm 0.016$, and $P$ values in the range 0.15 to 0.64, we have measured $\beta =-(2.8\mathrm{}\pm 2.8)\times {10}^6$ ${\sec }^{-1\mathrm{}}$. The corresponding value from the semiclassical theory is $\beta =+(53.8\mathrm{}\pm 10.0)\times {10}^6$ ${\sec }^{-1\mathrm{}}$.