Very Low Temperature Environments

In systems where all of the degrees of freedom can be defined by a single temperature, rotational spectroscopic studies of linear and polyatomic molecules ordinarily have been done in the regime hν_r << kT, for thermally populated levels J_max ~10 - 100 and partition function Q_r ~ 10² - 10⁵. In this regime, there is in general spectral complexity, and for collisions a multitude of "open" channels, with "classical" collision properties which result from averaging over these many channels.

The temperature effect on collisions can be dramatic. At 1 K the orbital angular momentum of a He atom colliding with CO is L ~ 2 and the collisional channels associated with the J = 1 rotational state of CO are energetically marginally available. However, at 300 K, the orbital angular momentum associated with the collision is L ~ 30 and a multitude of collisional channels through J = 10 are open. The effect of the increase in open channels can be seen in Figure: CO Pressure Broadening , which shows the calculated pressure broadening cross section for the J = 1 - 0 transition of CO in He at 115 GHz as a function of collision energy. At low temperature (2 cm^-1 ~ 3 K) individual resonances, associated with the formation of quasi-bound states, are observable in the pressure broadening cross section (as well as in the state-to-state rates and the pressure shifts), while at higher temperature, the resonances slowly merge and disappear and the cross section over a very wide temperature range is reduced to essentially that of the classical "size" of the molecules. Because of our desire to explore these and related phenomena, we have sought to develop a general, expandable methodology to study the regime for which hν_r ≤ kT, J_max ~1 - 5, and Q_r ~ 1 - 10. In this regime, there is not only significant spectral simplification, but also a much closer and more interesting relation between experimental observables and fundamental molecular parameters. Additionally, in the millimeter and submillimeter (mm/submm) spectral region hν_r ~ hν ~ kT, and this spectral region is especially advantageous for many scientific studies. In the low temperature, non-equilibrium interstellar medium, rotationally inelastic collisions between assorted heavy molecules and the dominant gases, H₂ and He, are critical in determining the rotational state distributions of the molecules and the interpretation of the astronomical data themselves. These topics are considered in more detail in [1].

A second branch of laboratory astrophysics has involved studies of the collisional properties of astrophysically important species. In contrast to the spectroscopy just discussed (for which the line frequencies do not depend upon the laboratory environment), collision induced spectroscopic properties (e. g. linewidths and inelastic transition rates) are fundamentally dependent upon environment. Because interstellar temperatures are typically too low to allow adequate vapor pressure for experimental studies in the laboratory, much of the work has been theoretical work based on quantum chemical scattering calculations [2].

. This cell is initially filled with either He or H₂ and cryogenically cooled to low temperature. Small amounts of the spectroscopically active gas (e. g. CO) are then injected into the cell at a temperature for which the sample has adequate vapor pressure. Upon collision with the He or H₂ the spectroscopically active gas rapidly (~10 - 100 collisions) cools to the temperature of the buffer gas. However, at typical operating pressures (~10 mTorr) the spectroscopic gas takes ~10⁴ collisions to reach the cell wall and condense. It is interesting that much the same quasi-equilibrium exists in the interstellar medium, with the cold dust grains there playing the role of the walls for the condensation of the spectroscopic gas. However, the interstellar time scale is of the order 10⁵ - 10⁶ years rather than a few milliseconds. The latter time scale has certain advantages for the completion of PhD theses! Similar systems have been developed with liquid nitrogen as a coolant which are appropriate for the study of system under conditions similar to those in the atmospheres of the outer planets [6].

Figure: H₂S in Collision with He shows a comparison between pressure broadening and rotationally inelastic cross sections for the 1₁₀ - 1₀₁ transition of H₂S in collision with He. The scientifically interesting result shown here is the divergence between the cross sections at low temperature. This is a direct result of the transition between an essentially classical collision process at high temperature and a distinctly quantum mechanical one at low temperature. Perhaps the most dramatic result in this field has been produced by Willey and his coworkers [7].who have shown that an ammonia maser can be produced in such a cell as a result of differential rotational relaxation.

Figure: Inversion Transition of NH₃ shows a comparison of the emission at 10K with the absorption at 35K. This result is particularly interesting both in that ammonia is observed as a maser in the interstellar medium and that it represents an experimental realization of an early 'thermal' maser concept. Spectroscopy in the THz region can be a powerful probe of molecular systems.