We have studied the dynamic properties of the
He(23S) and the ${\mathrm{He}}_{2}(a^{3}\ensuremath{\Sigma}_{u}^{+})$ atomic and molecular metastable states of helium that are produced in electron-bombarded superfluid helium. The steady-state concentration of ${\mathrm{He}}_{2}(a^{3}\ensuremath{\Sigma}_{u}^{+})$ molecules is shown to be limited by collisions between pairs of these molecules. Measurements of the rate coefficient for this bimolecular reaction as a function of temperature and pressure show that the reaction is diffusion limited and that the diffusion coefficient for the metastable molecules in the superfluid is determined by ${\mathrm{He}}_{2}(a^{3}\ensuremath{\Sigma}_{u}^{+})$-roton collisions. The bilinear destruction of metastable molecules has been monitored for times as long as 0.1 sec after the initial population of the state, and this establishes a lower bound of 0.1 sec on the radiative lifetime of the $(v=0) {\mathrm{He}}_{2}(a^{3}\ensuremath{\Sigma}_{u}^{+})$ state in superfluid helium. The lifetime and decay mode of the
He(23S) atoms are distinctly different from that of the corresponding ${\mathrm{He}}_{2}(a^{3}\ensuremath{\Sigma}_{u}^{+})$ molecule. In particular, the characteristic lifetime of the
He(23S) state in superfluid helium is essentially independent of the temperature between 2.08 and 1.4 \ifmmode^\circ\else\textdegree\fi{}K and is measured to be about 15 \ensuremath{\mu}sec. Our experimental observations indicate that the destruction of metastable atoms results in the population of high vibrational levels of the $a^{3}\ensuremath{\Sigma}_{u}^{+}$ molecular state. However, it is shown that the production of $(v=0) {\mathrm{He}}_{2}(a^{3}\ensuremath{\Sigma}_{u}^{+})$ molecules responds immediately to the electron beam (response time 3 \ensuremath{\mu}sec) and thus the formation of this state in the liquid does not depend upon the destruction of metastable atoms. Despite the fact that the lifetimes and decay modes of the metastable
He(23S) atoms and $(v=0) {\mathrm{He}}_{2}(a^{3}\ensuremath{\Sigma}_{u}^{+})$ molecules are not related, the production rates for these states are nearly equal and correspond to about 450 and 500 per incident 160-keV electron, respectively.
The possibility of lifetime measurement in a flowing medium with phase fluorometry is investigated theoretically. A 3-D time dependent partial differential equation of the number density of atoms (or molecules) in the upper level of the fluorescence transition is solved analytically, taking flow, diffusion, optical excitation, decay, Doppler shift, and thickness of the excitation light sheet into account. An analytical expression of the intensity of the fluorescence signal in the flowing medium is deduced. Conditions are given, in which the principle of lifetime measurement with phase fluorometry in the static sample cell can be used in a flowing medium.
We study the rotational predissociation of atom-molecule complexes with very small binding energy. Such complexes can be produced by Feshbach resonance association of ultracold molecules with ultracold atoms. Numerical calculations of the predissociation lifetimes based on the computation of the energy dependence of the scattering matrix elements become inaccurate when the binding energy is smaller than the energy width of the predissociating state. We derive expressions that represent accurately the predissociation lifetimes in terms of the real and imaginary parts of the scattering length and effective range for molecules in an excited rotational state. Our results show that the predissociation lifetimes are the longest when the binding energy is positive, i.e., when the predissociating state is just above the excited state threshold.