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Physical Review A

Comment on the decay curves of hydrogenlike atoms observed at long times following excitation

Richard M. Schectman

Published Oct 1, 1975• 24 citations
Publisher

Abstract

Explicit calculations demonstrate that cascade repopulation effects are a possible explanation of the ${t}^{\ensuremath{-}1.5}$ dependence in the decay of Ly-$\ensuremath{\alpha}$ radiation at long times after excitation observed recently by Braithwaite, Matthews, and Moore. Good agreement with all available experimental data is obtained with reasonable population models; excitation proportional to ${n}^{\ensuremath{-}m}$ with $m=2.2\ensuremath{-}4$ is indicated.

DOI
10.1103/physreva.12.1717

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Explicit calculations demonstrate that cascade repopulation effects are a possible explanation of the t\ensuremath−1.5{t}^{\ensuremath{-}1.5}t\ensuremath−1.5 dependence in the decay of Ly-\ensuremathα\ensuremath{\alpha}\ensuremathα radiation at long times after excitation observed recently by Braithwaite, Matthews, and Moore. Good agreement with all available experimental data is obtained with reasonable population models; excitation proportional to n\ensuremath−m{n}^{\ensuremath{-}m}n\ensuremath−m with m=2.2\ensuremath−4m=2.2\ensuremath{-}4m=2.2\ensuremath−4 is indicated.
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 $n\ensuremath{\gtrsim}20$.
We have studied the evolution of excited states in an atomic-hydrogen beam undergoing radiative cascade after formation by charge exchange in a gas cell. A simple one-parameter model of the charge-exchange excitation probability is used to estimate the initial population of long-lived Rydberg states. Special attention is paid to the n=2n=2n=2 state populations at long times (several microseconds). The persistent Lyman-$\ensuremath{\alpha}$ radiation from the 2P2P2P state can be a significant source of background for sensitive experiments using the metastable 2S2S2S state. Numerical and graphical results are presented.
We report on measurements of the time dependence of the populations of Rydberg states of Na with n=25--33 produced by stepwise excitation or deexcitation from the initially populated state 28s, stimulated by room-temperature blackbody radiation. We also present a theoretical modeling of the experiments, which mainly consists of solving the set of coupled rate equations for all the states involved. The results of the calculations show that for times of the order of the lifetime of 28s the populations of ns and nd states produced via two-step transitions can be up to 30% of the populations of np states. We also find that np states get repopulated via three-step transitions at the 2--12 % level. A comparison between the data and calculations shows good agreement.