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 current and pressure dependence of the decay of the
3P0 metastable level of neon was measured by using a light absorption method. The decay was found to be nonexponential and current dependent at normal excitation currents. At extremely low excitation current, however, the
3P0 decay becomes exponential and current independent. The mean lives associated with such exponential decays were measured as a function of pressure. The results are in agreement with the usual theoretical relation based on metastable destruction by diffusion to the container walls at low pressure and two-body collisions at high pressures. The pressure dependence of the
3P2 level was also studied. It was found, as previously reported by Grant, that the experimental results for the pressure range from 2 to 20 mm of mercury, where diffusion loss is small, do not agree with the usual theoretical prediction.
In a positive column of a glow discharge, a linearly polarized laser pulse produces aligned neon atoms in the 2p 2 (Paschen notation) level, and the subsequent fluorescence is observed with its polarized components resolved. The relaxation rate of the alignment, or the disalignment rate, is thus determined. The populations of the 1s 2 – 1s 5 levels are found to be strongly dependent on the discharge current, and so are the degrees of radiation re-absorption of the transition lines from 2p 2 to these levels. A Monte Carlo simulation is performed by which the disalignment rate by radiation re-absorption for these transitions is determined, where the isotope splitting of the transition lines is taken into account. This rate is subtracted from the observed disalignment rate, resulting in the rate being independent of the degree of radiation re-absorption. Thus, disalignment due to atom collisions and that due to radiation re-absorption are separated. For the latter disalignment the disalignment rate deduced by the simulation, treating the four transitions simultaneously, is found to be virtually equal to the sum of the disalignment rates for each of the transitions. The approximate expression for the disalignment rate given by D’Yakonov and Perel’ (1965 Sov. Phys.–JETP 20 997) is quantified, so that it can be applied to estimating the disalignment rate of an upper level having several transition lines with finite optical thickness.
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 $\ensuremath{\beta}=+(53.8\ifmmode\pm\else\textpm\fi{}10.0)\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ${\mathrm{sec}}^{\ensuremath{-}1}$.
Values of rate of decay and mean life of atoms and molecules in upper quantum states calculated from data on the intensity of absorption lines.---By combining F\"uchtbauer's method of determining from the intensity of absorption lines the probability that a molecule will absorb a quantum of energy, with Einstein's views as to the mechanism of light absorption and emission, the following equation is derived for calculating the rate at which molecules jump from upper to lower quantum states: ${A}_{21}=\left(\frac{8\ensuremath{\pi}{\ensuremath{\nu}}^{2}}{{c}^{2}{N}_{1}}\right)\left(\frac{{p}_{1}}{{p}_{2}}\right)\ensuremath{\int}{0}^{\ensuremath{\infty}}\ensuremath{\alpha}d\ensuremath{\nu}$ where
A21 is the chance per unit time that a molecule will jump spontaneously from quantum state 2 to quantum state 1, $\ensuremath{\nu}$ is the frequency of the light emitted in such a jump,
p1 and
p2 are the a priori probabilities of quantum states 1 and 2, and $\ensuremath{\alpha}$ is the absorption coefficient of the substance measured under conditions such that
N1 is the number of molecules per unit volume in the lower quantum state 1. The integral $\ensuremath{\int}\ensuremath{\alpha}d\ensuremath{\nu}$ is to be taken over the total effective width of the absorption line corresponding to the passage of molecules from quantum state 1 to quantum state 2. The mean life $\ensuremath{\tau}$ of molecules which decay from state 2 to state 1 is the reciprocal of
A21. Values of
A21 and $\ensuremath{\tau}$ are calculated from existing data for the mercury line $\ensuremath{\lambda}2537$, for a number of lines belonging to the alkali doublets, for the iodine line $\ensuremath{\lambda}5461$, and for a very considerable number of lines belonging to the rotation-oscillation spectra of the hydrogen halides. The values obtained agree with the meager data made available by other experimental methods. From these results the following conclusions are drawn.The mean life of molecules and atoms in upper quantum states may vary for different states at least over the range 1 to ${10}^{\ensuremath{-}8}$ seconds. The rate of decay is not a simple function of the frequency of the emitted light. The rate corresponding to the emission of a line of high frequency may be greater or less than that for a line of lower frequency. The data now available for the alkali doublets $1s\ensuremath{-}m{p}_{1}$ and $1s\ensuremath{-}m{p}_{2}$ indicate a higher rate of decay the smaller the change in total quantum number for the line under consideration. The rate of decay from a given
mp1 state is
m times as great as from the corresponding
mp2 state (already stated in another form by F\"uchtbauer and Hofmann). In the case of the rotation-oscillation spectra of the hydrogen halides the rate of decay is greater for quantum states with one unit of oscillation and many of rotation, than for those with one unit of oscillation and only a few of rotation; and in the case of different molecules but the same quantum numbers the rate of decay is greater for the molecule with the greater frequency of oscillation.Finally the possibility and method of calculating absolute values of
A21 from the Bohr correspondence principle is indicated.
We have observed fluorescence and ionization signals resulting from two-photon resonant excitation of thallium in an atomic beam. The output of a pulsed dye laser is used to excite the resonance between the ground state (6('2)P(,1/2)) and an excited n('2)P state of thallium. Both two-photon absorption and three-photon absorption occur simultaneously; the latter results in photoionization of the atom. The excited states populated by two-photon absorption decay via cascade fluorescence back to the ground state; one or more of these spectral components constitute our fluorescence signal. The lifetimes of the excited n('2)P states of thallium have been measured directly by observing the exponential decay of this fluorescence. Calculations are included to ascertain the time required for the fluorescence signal to reach within 2% of a simple exponential decay. This decay is a measure of the lifetime of the initial state, under the condition that none of the fluorescence components arise from states which are populated by cascade through longer-lived states. The lifetimes of the n('2)P(,1/2) and n('2)P(,3/2) states of thallium for n = 7 to 11 are determined in this manner and compared with the values deduced from semi-empirical calculations of oscillator strengths by various authors. For calculations employing the effects of core polarizability in the electron wavefunctions and in the transition matrix elements, the agreement is very good--to within our experimental uncertainty, which is typically(, )<5%. Our measurements are also compared to the four other known experimental values for such excited states of thallium. Some of these previous experiments and calculations were carried out in conjunction with parity non-conservation experiments in thallium. Our measurements may provide useful checks on the accuracy of some of the calculations performed in the evaluation of such experiments. The ionization and fluorescence signals are also studied under conditions of strong saturation of the two-photon resonance with the 7('2)P states. The manifestation of saturation in the ionization signal is a broadening of the excitation spectrum, which is found to greatly exceed that of the fluorescence signal. Furthermore, the ratio of the ionization signal to the fluorescence signal at the peak of the resonance is found to vary linearly at intensities below about 10('9) W/cm('2); this too saturates at higher intensities. Various models are employed to simulate the observed behavior, encompassing both rate equations as well as density matrix formulations. The numerical solutions to these models are compared with the observed behavior; the agreement is found to depend strongly on the assumed experi- mental conditions to which the ensemble of atoms is subjected.