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Canadian Journal of Research

DURATION OF META-STABLE STATES

John M. Anderson

Published Jan 1, 1930• 7 citations
Publisher

Abstract

The half-value time of absorption from meta-stable electronic atomic states is calculated on the hypothesis that the whole decay is due to collision phenomena. Definite assumptions, which include the atomic energy level scheme, are made as to the efficiency of collisions and the interaction of two meta-stable states in these processes. The assumption adopted as the only one producing an approximation to experimental facts shows that the probability of an exchange is dependent on the absolute value of the energy difference between the states concerned. The results calculated from the final formula, for helium, neon and argon at normal and very low temperatures depend on one arbitrary constant, which is the same for all states and gases considered, and show fair agreement with any experimental values so far published. An estimate is made of the energy tolerance of a quantum transition.

DOI
10.1139/cjr30-002

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The half-value time of absorption from meta-stable electronic atomic states is calculated on the hypothesis that the whole decay is due to collision phenomena. Definite assumptions, which include the atomic energy level scheme, are made as to the efficiency of collisions and the interaction of two meta-stable states in these processes. The assumption adopted as the only one producing an approximation to experimental facts shows that the probability of an exchange is dependent on the absolute value of the energy difference between the states concerned. The results calculated from the final formula, for helium, neon and argon at normal and very low temperatures depend on one arbitrary constant, which is the same for all states and gases considered, and show fair agreement with any experimental values so far published. An estimate is made of the energy tolerance of a quantum transition.
The rate of decay of absorption of six neon lines λ 6402, λ 6334, λ 6266, λ 6163, λ 6143 and λ 5945 has been measured for a series of pressures at room temperature and at the temperature of liquid air. Curves showing the variation of half-life with pressure have been plotted for each line at both temperatures. It is found that the function [Formula: see text] is exponential in the time, and that the rate of decay is markedly different at the same pressure and temperature for different lines ending in the same meta-stable state.
The temperature dependence of conversion of $\rm He(2\sp3S\sb1)$ metastable atoms to $\rm He\sb2(a\sp3\Sigma\sbsp{u}{+})$ metastable molecules in the three-body reaction $\rm He(2\sp3S\sb1)+ 2He(1\sp1S\sb0)\to He\sb2(a\sp3\Sigma\sbsp{u}{+}) + He(1\sp1S\sb0)$ has been investigated over the temperature range 65K-700K. This reaction is thermally activated as a consequence of a long range repulsive barrier in the $\rm He(2\sp3S\sb1)-He(1\sp1S\sb0)$ interaction potential. The data reveal that there are two reaction channels with distinctly different activation energies. The temperature dependence of the measured rate coefficient k$\sb{\rm s}($T) is accurately described by $\rm k\sb{s}(T) = \lbrack 87.4\ T\ exp({-750}/T) + 4.1 T\ exp({-200}/T)\rbrack \times 10\sp{-37}\ cm\sp{-6}sec\sp{-1}$. The first activation energy, 750 ±\pm± 70K (63 ±\pm± 6meV), is equal to the known $\rm He(2\sp3S\sb1)$-$\rm He(1\sp1S\sb0)$ repulsive barrier height. The second activation energy is 17 ±\pm± 2 meV. The temperature dependences of the rate constants for collision-induced mixing among $\rm He(2\sp3P\sb{J,m\sb{J}})$ levels, and for conversion of He(2$\sp3$P) atoms to $\rm He\sb2(b\sp3\Pi\sb{g})$ molecules in the three body reaction $\rm He(2\sp3P) + 2He(1\sp1S)\to He\sb2(b\sp3\Pi\sb{g}) + He(1\sp1S)$ have been investigated over the range 1.4$\sim$300K. The measured thermally-averaged cross section for $\rm He(2\sp3P\sb{J,m\sb{J}})$ mixing in collisions with ground state helium atoms are described by the function $\rm\sigma\sb{pm}(T) = (4.4 + 20.6/T\sp{1/3})\times 10\sp{-15}cm\sp2,$ and can be understood in terms of Langevin theory. The measured rate coefficients for the three body reaction exhibit a strong inverse temperature dependence, $\rm k\sb{p}(T) = (0.04 + 2.18/T)\times 10\sp{-30}\ cm\sp6{\cdot}s\sp{-1},$ which suggests that, unlike conversion of $\rm He(2\sp3S\sb1)$ to $\rm He\sb2(a\sp3\Sigma\sbsp{u}{+}),$ there is no activation energy required for this reaction. A magneto-optical trap for helium 2$\sp3$S metastable atoms has been designed and constructed, utilizing superconducting magnet gradient coils and a Ti:Sapphire ring laser for pumping the helium 2$\sp3$S-2$\sp3$P transition. He(2$\sp3$S) atoms are produced by a weak discharge in helium gas at temperature 1.3K. The discharge products flow through an orifice into the trap cell, where the He(2$\sp3$S) atoms are trapped and ground state helium atoms are rapidly cryopumped by zeolite pellets that cover most of the cell bottom. Preliminary experimental results suggest that $\sim101010\sp6$ atoms are trapped, with a trap lifetime of about 0.2 sec limited by He(2$\sp3$S) - He(2$\sp3$P) Penning reactions. Ultimately, it is estimated that a substantial number of atoms can be trapped and cooled for much longer times in a near-perfect vacuum. Measurements of decay times of the trapped atoms should yield rates for $\rm \sp{4,3}He(2\sp3S)$ - $\sp{4,3}$He(2$\sp3$S) and resonantly-enhanced He(2$\sp3$S) - He(2$\sp3$P) Penning reactions in the ultra-cold quantum regime, and perhaps the He(2$\sp3$S) natural lifetime.
Some phenomena cannot be solved using the exact solution of the Schrödinger equation. However, using approximated methods such as perturbation theory we are able to obtain remarkable results considering terms up to second order. The physical phenomena studied here are the absorption and stimulated emission by the classical feature. In addition, we are going to discuss the physical meaning of perturbation theory when we treat the behaviour how initial state ket evolves as time goes on. We will evaluate the transition of probability between states, the rate and the energy involved in the atomic transitions. It will be introduced fundamental concepts of quantum mechanics, such as interaction picture, and a general perturbation theory using constant and sinusoidal time-dependent perturbation term. Concerning to these phenomena, we considered the perturbed term of the Hamiltonian of the interaction between the vector potential and electron momentum.
A theoretical model for the collision of atoms in high Rydberg states (nl) with neutral atoms or molecules is proposed, based on the assumption that the electron-perturber interaction is of very short range compared with the mean radius of the Rydberg atom. A semiclassical method is used to derive a compact expression for the collision probability. The calculations need total cross sections for the scattering of a free and low-energy electron by the perturber. The model is applied to the calculation of a free and low-energy electron by the perturber. The model is applied to the calculation of cross sections for the quenching of n 2 D or n 2 F Rydberg states of Na and Rb by rare-gas atoms of N 2 . On the whole the calculated cross sections are in reasonable agreement with experimental data for n>10 approximately. The model and the results of the calculations are discussed and compared with other theoretical works.
Calculations of low-energy collisions of antiprotons p‾\overline{p}p​ with helium atoms in the ground (11S)(1\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})(11S) and metastable (23S(2\phantom{\rule{4pt}{0ex}}^{3}\mathit{S}(23S and 21S)2\phantom{\rule{4pt}{0ex}}^{1}\mathit{S})21S) states are carried out by using a semiclassical method and by further assuming that one of the two electrons is passive. Antiproton capture to form antiprotonic helium $(\ensuremath{\rightarrow}\overline{p}{\mathrm{He}}^{+}+e)$ and breakup ionization $(\ensuremath{\rightarrow}\overline{p}+{\mathrm{He}}^{+}+e)$ are investigated. The energy dependence of the capture and ionization cross sections and the distributions of the product states are presented and compared with previous theoretical calculations. For the metastable helium targets, most of the p‾He+\overline{p}{\mathrm{He}}^{+}p​He+ atoms produced in the capture have long lifetimes against subsequent Auger decays and can be observed experimentally. For the ground-state targets, however, the formation of such long-lived states is rather a rare event at low collision energies.