We have observed directly the time correlation between successively emitted photons in the $7^{3}S_{1}\ensuremath{-}6^{3}P_{1}\ensuremath{-}6^{1}S_{0}$ cascade of atomic mercury, and have deduced from it direct measurements of both the natural lifetime of the
63P1 state and the dependence of the mean correlation time (coherence time) on the density of the mercury vapor surrounding the primary radiation region. The density-dependent coherence time constitutes a direct observation of the imprisonment of resonance radiation and provides an experimental confirmation of the theory describing this phenomenon.
The predictions of the incoherent scattering theory of the transport of resonance radiation developed by Holstein and by Biberman are shown to agree with laboratory measurements of the decay constants for the intensity of the mercury 2537 A resonance radiation following a period of optical excitation. Also, the relative importance of the diffusion of resonance atoms and the escape of resonance radiation as mechanisms for the destruction of mercury atoms in the
3P1 or resonance state are determined from measurements of decay constants as a function of mercury density and cell radius. The experimental results show that diffusion of the resonance atoms is negligible and that the predictions of imprisonment theory are confirmed to within 15%. The experiment sets an upper limit to the diffusion coefficient at unit gas density for atoms in the
3P1 state of 5\ifmmode\times\else\texttimes\fi{}
1017 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ at 340\ifmmode^\circ\else\textdegree\fi{}K, which is consistent with a value of 4\ifmmode\times\else\texttimes\fi{}
1016 ${\mathrm{cm}}^{\ensuremath{-}1}$ ${\mathrm{sec}}^{\ensuremath{-}1}$ predicted using the frequency of excitation transfer collisions calculated by Holstein. The success of the theories based on completely incoherent scattering of resonance radiation points to the desirability of including this feature in the treatment of those astrophysical problems in which the spectral line shape is determined by Doppler broadening or by collision broadening.
On theoretical grounds it is expected that the decay time of imprisoned resonance radiation in the vapor of a single even isotope of mercury should be some six times larger than that observed with the natural samples of mixed isotopic constitution. To investigate this effect experimentally, decay measurements were carried out with samples of
Hg198 (3 percent
Hg199 and 0.1 percent
Hg200). For vapor densities $N\ensuremath{\lesssim}\frac{{10}^{14}}{\mathrm{cc}}$, the predicted effect was verified. For
N>cc1014, the observed decay time drops below that predicted theoretically for pure
Hg198. This secondary effect is here attributed to the transfer of excitation from
Hg198 to
Hg199 and
Hg200 by collisions of the second kind. Comparison of experimental data with an appropriately generalized theory permits estimation of the cross section for such collisions. The value so obtained is ${10}^{\ensuremath{-}13}$
cm2, some twenty times the gas-kinetic cross section, and in order-of-magnitude agreement with theoretical expectations.
Following (i) a sharp step or (ii) a pulse of applied magnetic field, the resonance fluorescence of an atomic vapour exposed to steady linearly polarized resonance radiation undergoes transient behaviour until a new steady state is reached; the form of the transient will be (i) modulation of the intensity with an exponential envelope, or (ii) simple exponential decay. From the modulation period the gJ value of the excited state is obtained. From the exponential decay the lifetime for the relaxation of atomic alignment is obtained directly. The technique, applied to the 63P1 state of mercury, gives 117.4+or-1.0 ns for the natural mean life.
Experimental investigations have been made of the transfer of mercury 2537-\AA{} radiation through a slab of natural mercury gas of various densities and dimensions, using a sinusoidally modulated ($\ensuremath{\omega}=2\ensuremath{\pi}f$,
f=5to50 kc/sec) radio-frequency-excited (50-Mc/sec) source of 2537-\AA{} radiation. Transmitted radiation has been found to gain in phase relative to the source wave, while that which is scattered at 90\ifmmode^\circ\else\textdegree\fi{} loses phase. From the radiation scattered at 90\ifmmode^\circ\else\textdegree\fi{}, decay time constants of the imprisoned photons have been calculated by using the relation between the time constant
T and the phase shift $\ensuremath{\varphi}$, $\ensuremath{\varphi}=invtan\ensuremath{\omega}T$. The relation $T\ensuremath{\propto}\frac{{C}^{2}}{{K}^{2}}+{C}^{2}$), where
K is a constant, has been found for the dependence on the breadth
C of the resonance tube as well as the well known dependence $\mathrm{ln}T\ensuremath{\propto}\mathrm{ln}n$ on the molecular density
n. On the other hand, the transmitted radiation obeys a relation ${T}_{c}\ensuremath{\propto}{(\mathrm{nA})}^{\frac{1}{2}}$ between the time constant
Tc corresponding to the advanced phase shift, the thickness
A of the resonance tube, and
n. The dependences on other factors have also been examined.
The effects of imprisonment of resonance radiation in potassium vapor and of collisions between excited potassium atoms and N2, H2, HD, and D2 molecules, on the measured lifetimes of the 42P states, have been investigated by the method of delayed coincidences. The potassium atoms were excited with short pulses of resonance radiation, and the delays between the exciting and fluorescent pulses were measured with a time-to-amplitude converter. At pure potassium densities below 1010 atoms/cm3, the measured lifetimes approach the constant values 27.8 ± 0.8 and 27.6 ± 0.8 ns, corresponding to the natural lifetimes of the 42P1/2 and 42P3/2 states, respectively. At higher densities the effective lifetimes are in satisfactory agreement with the predictions of Holstein's theory. The decrease in the measured decay rates observed upon addition of the diatomic gases yielded cross sections for quenching collisions with N2, H2, HD, and D2 which equal 34.0 ± 2.0 Å2, 9.4 ± 1.3 Å2, 11.9 ± 1.5 Å2, and 8.0 ± 2.0 Å2, respectively.