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Physical Review Letters

Radiative Decay of the 2P State of Atomic Hydrogen: A Test of the Exponential Decay Law

John M. Wessner, David K. Anderson, R. T. Robiscoe

Published Oct 23, 1972• 30 citations
Publisher

Abstract

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 $\ensuremath{\Gamma}=(1\ensuremath{-}f){\ensuremath{\Gamma}}_{0}+\ensuremath{\beta}P$, where $\ensuremath{\beta}=f{\ensuremath{\Gamma}}_{0}$. Here $f$ is the initial $2S$ population, ${\ensuremath{\Gamma}}_{0}$ is the natural $2P$ decay rate, and $P$ is the $2P$ population relative to $f$. For $f=0.086\ifmmode\pm\else\textpm\fi{}0.016$, and $P$ values in the range 0.15 to 0.64, we have measured $\ensuremath{\beta}=\ensuremath{-}(2.8\ifmmode\pm\else\textpm\fi{}2.8)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. The corresponding value from the semiclassical theory is $\ensuremath{\beta}=+(53.8\ifmmode\pm\else\textpm\fi{}10.0)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$.

DOI
10.1103/physrevlett.29.1126

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An experiment is described which tests the semi-classical radiation theory proposed by E. T. Jaynes and his collaborators.Their work predicted that the n = 2 level of hydrogen will have a lifetime which varies linearly with the 2s state population for small excited state components.By applying a short electrical pulse to a 60 keV atomic hydrogen beam with a 2s population of approximately 9%, the variation of the lifetime could be measured as a function of the 2s occupation after the pulse.A total change of approximately + 4% is predicted while the observed change was -.2%.
Hydrogen atoms in supersonic expansions with velocities in the range from 700to800m∕s700\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}800\phantom{\rule{0.3em}{0ex}}\mathrm{m}∕\mathrm{s}700to800m∕s have been excited to Rydberg-Stark states with principal quantum number nnn between 20 and 40, decelerated to zero velocity in the lab frame using time-dependent inhomogeneous electric fields, and trapped in a two-dimensional electrostatic trap with an initial density of $\ensuremath{\approx}5\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$. The motion of the atomic cloud in the trap was observed by measuring the times of flight and images of the H+{\mathrm{H}}^{+}H+ ions produced by pulsed field ionization. The velocity distribution of the trapped atoms can be described by an effective temperature of 350mK350\phantom{\rule{0.3em}{0ex}}\mathrm{mK}350mK. The decay of the population of trapped atoms does not follow a single-exponential behavior and has contributions from radiative and collisional processes.
We have studied the radiative decay of atomic hydrogen in strong magnetic fields of up to 4T4\phantom{\rule{0.3em}{0ex}}\mathrm{T}4T. We have followed the radiative cascade from completely l,ml,ml,m mixed distributions of highly excited states as well as from distributions that involve highly excited states with $\ensuremath{\mid}m\ensuremath{\mid}\ensuremath{\sim}n$. We have found that the time it takes to populate the ground state is not affected by the magnetic field for the initial states with $n\ensuremath{\lesssim}20$. For higher nnn manifolds, the electrons in the most negative mmm states are substantially slowed down by the magnetic field resulting in a much longer lifetime. We show that less than 10% of the antihydrogen atoms with $n\ensuremath{\sim}35$ generated in antihydrogen experiments at 4K4\phantom{\rule{0.3em}{0ex}}\mathrm{K}4K will decay to their ground states before they hit the wall of the vacuum container unless they are trapped. We have also found that the decay time is mainly determined by the fraction of atoms that were initially in highest negative mmm states due to the fact that only $\ensuremath{\mid}\ensuremath{\Delta}m\ensuremath{\mid}+\ensuremath{\mid}\ensuremath{\Delta}\ensuremath{\pi}\ensuremath{\mid}=1$ transitions are allowed in the magnetic field. We give a semiclassical method for calculating the decay rates for circular states and show that when the initial states have high-$\ensuremath{\mid}m\ensuremath{\mid}$, semiclassical rates agree with the full quantum mechanical rates within a couple of percent for states with effective $n\ensuremath{\gtrsim}20$.
A sensitive test for any mixing of the 2S122{S}_{\frac{1}{2}}2S21​​ and 2P122{P}_{\frac{1}{2}}2P21​​ state of atomic hydrogen is the measurement of the rate for single-quantum decay of the 2S2S2S atom to the ground state. A new upper limit of this decay rate has been determined. A section along a beam of 2S2S2S atoms, produced by electron excitation of a ground-state atom beam, was viewed by an iodine-vapor-filled ultraviolet photon counter, which responds to the Lymanalpha radiation of the single-quantum decay process. From the counts observed when an electrostatic quenching field was superposed on the counter's field of view, the necessary experimental parameter (product of 2S2S2S atom current and counter efficiency) was determined. With the field removed, a portion of the remaining counts could be ascribed to quenching on collision of the 2S2S2S atoms with residual gases in the vacuum chamber, the quenching cross sections for which were measured. The decay rate not ascribable to known quenching effects was 420 ${\mathrm{sec}}^{\ensuremath{-}1}$. Since unknown quenching effects may have been operative, this figure must be considered only as an upper limit for the natural single-quantum decay rate.
A sensitive test for any mixing of the 2S122{S}_{\frac{1}{2}}2S21​​ and 2P122{P}_{\frac{1}{2}}2P21​​ state of atomic hydrogen is the measurement of the rate for single-quantum decay of the 2S2S2S atom to the ground state. A new upper limit of this decay rate has been determined. A section along a beam of 2S2S2S atoms, produced by electron excitation of a ground-state atom beam, was viewed by an iodine-vapor-filled ultraviolet photon counter, which responds to the Lymanalpha radiation of the single-quantum decay process. From the counts observed when an electrostatic quenching field was superposed on the counter's field of view, the necessary experimental parameter (product of 2S2S2S atom current and counter efficiency) was determined. With the field removed, a portion of the remaining counts could be ascribed to quenching on collision of the 2S2S2S atoms with residual gases in the vacuum chamber, the quenching cross sections for which were measured. The decay rate not ascribable to known quenching effects was 420 ${\mathrm{sec}}^{\ensuremath{-}1}$. Since unknown quenching effects may have been operative, this figure must be considered only as an upper limit for the natural single-quantum decay rate.