Oka Ion Factory
October 7, 1996
Candidacy Committee: Berry, Light, Norris
Critical Review: Luo et al., JCP 104, 1151 (1996)
In this prospectus, I propose additional laboratory investigations of high energy overtone bands of , as well as new observations to detect in the interstellar medium.
In 1916, a paper appeared from A. J. Dempster in Chicago which demonstrated that the abundance of increased at higher pressures of , even surpassing that of and H+ under some conditions. Twenty years later, though, when deuterium was discovered, the interpretation of the line was questioned. In 1934, Thomson himself wrote ``the evidence seems to me to leave little doubt that the gas I called more than twenty years ago is the same as that which is now called heavy hydrogen.'' Thomson here refers to the alternate possibility of the line being due to HD+.
By the end of the 1930s, there was ample evidence to support the existence of , but little was known about this mysterious species. Henry Eyring was quoted as saying that the problem was ``the scandal of modern chemistry.'' By 1938, Hirschfelder had demonstrated that a triangular structure of was more stable than a linear one. Not until 1964, though, with the advent of modern computing, was it determined that an equilateral triangle was indeed the equilibrium structure.
By the early 1970s, the astrophysical significance of had been recognized. Its primary role in the chemistry of the interstellar medium, as discussed below in Section 6, was highlighted in several key papers. [6,7,8,9,10,11]
In 1978, experiments were carried out at Argonne, Lyon in France, and Rehovot in Israel to confirm the triangular geometry of .Accelerated (2 4 MeV) ions passed through carbon foils, thus losing their electrons. The three protons then repelled each other due to Coulomb interactions, and were detected on a photographic emulsion. This was perhaps the first experiment to yield information about itself (as opposed to its reactions), beyond the simple fact that it exists.
Since possesses three indistinguishable nuclei (fermions), and since the Pauli principle demands that the total wavefunction of the molecule be antisymmetric with respect to permutations (12), etc. of the nuclei, the permutation operations are rigorous symmetry operations for .Consequently, the symmetry labels of the rovibrational wavefunctions are rigorous quantum numbers. The wavefunctions may be labelled with the symmetries = A1, A2, or E, according to their character in the permutation-inversion group S3* (which is isomorphic to D3h).
The quantum numbers discussed above are completely rigorous, in that they depend only on the properties of space and on the Pauli principle. If the very small nuclear spin-rotation interaction is neglected, the total nuclear spin I and the rotational angular momentum J can also be considered good quantum numbers.
A normal mode analysis of the equilibrium geometry of yields (see Figure 1) a symmetric stretch (Q1, frequency , A1' symmetry), which is formally IR inactive, and a degenerate bending mode (Q2x and Q2y, frequency , E' symmetry), which is IR active. Hence, we obtain two approximate quantum numbers, v1 and v2, corresponding to the number of quanta in each vibrational mode. [The limitations of the traditional formalism are belied by the fact that the band has been observed with infrared spectroscopy. ]
Because the mode is degenerate, any linear combination of its two components may be considered. It is convenient to form linear combinations with two components 90 out of phase. As can be seen in Figure 1, this leads to a vibrational angular momentum, and therefore a new approximate quantum number, l2, where .
At least at low values of v2 and J, then, we can label the rovibrational states as . However, for states with and , states with different k and l2 but the same G = will mix, and as a result at higher levels only G will be a good approximate quantum number. When mixing is not too severe, a label = |l2| is often used as well.
Of course, it should be kept in mind that at high enough levels, all of these approximate quantum numbers, including G, will cease to be good quantum numbers. In the final analysis (and when considering high overtone bands), the only good quantum numbers are F, , , I, and J.
The traditional perturbation approach to the calculation of energy levels of a symmetric top such as is to use polynomials of vibrational and rotational quantum numbers with coefficients of various molecular constants. The usual approach to predicting spectra is to fit experimentally observed transitions by varying the set of molecular constants and then using these determined constants to predict higher transitions. However, since is so anharmonic, this process requires nearly as many parameters as there are experimentally observed transitions (since so many higher order terms must be included) -- this fact implies that the fit Hamiltonian will have very little predictive power for higher transitions.
Because of this, Bawendi et al. commented that ``probably the best strategy for this molecule is to provide the ab initio theorists with our experimentally determined energy levels so that they can further adjust with their potentials and accurately predict new rovibrational transitions.'' Thus, theorists use electronic structure calculations to develop a potential energy surface and solve for the eigenvalues of the motion of the three protons by using supercomputers. Then they adjust the parameters of the potential surface to try to better fit the experimental data.
In the most recent fit, for example, Dinelli et al.  fit nearly 1600 data points for and its isotopomers by adjusting 36 constants and holding 51 at the values obtained by ab initio methods. Their standard deviation for vibration-rotation energy levels was 0.015 cm-1! This constitutes more than an order of magnitude improvement over pure ab initio potentials.
As can be seen, is a wonderful playground where spectroscopists and theorists meet -- in 1994 and 1995, at least eleven theoretical papers reported calculations on this system.[15,16,17,18,19,20,21,22,23,24,25] The spectroscopists provide data for the theorists to fit to their potentials (as well as to test new ab initio potentials). The theorists in turn predict higher energy transitions, which guide the work of the spectroscopists in assigning new spectra. The spectroscopists feed the new transition energies back to the theorists, and the cycle begins anew.
The first observation of 's fundamental transition did not occur until 1980, after a four year search by Oka. Figure 2 shows the observed spectra of the fundamental band with water cooling (top) and liquid nitrogen cooling (bottom).
One thing that is easily noted is the complicated nature of this spectrum. We do not observe symmetrical and regular peaks in P, Q, and R bands as we see in ordinary molecules -- indeed, as J becomes larger, the picture gets increasingly complicated.
Another thing to note from Figure 2 is the lack of an R(0) band. This suggests that the J=k=0 state of the vibrational ground state is unoccupied! This is a consequence the Pauli principle, which demands that the total wavefunction be antisymmetric with respect to permutation.
|Year of Discovery||Investigator||Laboratory||Band||Lines Observed to Date|
|1980||Oka||Herzberg Institute||> 190|
|1989||Drossart et al.||Jupiter||> 54|
|1991||Lee et al.||Oka Ion Factory||15|
|1992||Xu et al.||Oka Ion Factory||9|
With these motivations in mind, I am proposing laboratory observations of four vibrational overtones of . Table 2 lists the transitions to be examined, along with the predicted frequencies of their band origins, and their relative intensities with respect to the fundamental.
The plasma in the discharge cell is a highly non-equilibrium system quite different from the gas phase. Hence it is often referred to as the ``fourth state of matter.'' The electrons may have temperatures on the order of 104 K, while the ions have rotational and translational temperatures on the order of room temperature. Due to inefficient energy transfer between vibrational energy and rotational and translational energy, the characteristic temperature of vibration may be on the order of 103 K. In our laboratory plasmas, the number density of is measured to be about 3 x 1010 cm-3.
There are three key reactions involved in the chemistry of in this type of discharge: the production of ions, the production of itself, and the destruction of . The first reaction
proceeds with a rate constant of 2.5 x 10-11 cm3/s in our discharge. The ion, however, is incredibly reactive, and reacts easily with hydrogen:
where is a Langevin rate constant of about 2.0 x 10-9 cm3/s. In the plasma discharge cell, is primarily destroyed by wall collisions, which are limited by the ambipolar diffusion rate of 3 x 105 s-1.
The New Focus diode lasers utilize an external cavity design, shown in Figure 4. A high-reflection coating on one end of the diode forms one end of the cavity, while a high-reflecting tuning mirror forms the other. From the diode, the beam passes through a collimating lens and strikes a diffraction grating at near grazing incidence. The beam is diffracted toward the tuning mirror, which reflects the light back on itself for the reverse path. Part of the light from the diode is reflected, not diffracted, by the grating -- this forms the output beam. The grating serves as a narrow spectral filter which forces the laser to operate in a single longitudinal mode. This is because only one of the many wavelengths of light diffracting off the grating will be exactly perpendicular to the tuning mirror, and only this wavelength will survive many round trips. The angle of the tuning mirror can therefore be adjusted to change the lasing wavelength.
For the investigation of the band at 9108 cm-1 and the extremely weak band at 10883 cm-1 [which is particularly exciting, as it lies above the barrier to linearity], we will use our group's Coherent Ti:sapphire laser, which offers an increased power of 1-2 W with a 500 kHz linewidth.
As illustrated in Table 2, the overtones targeted in this investigation have much lower intensities than the fundamental band. It is worth noting, however, that in the investigation of overtones we have been blessed by the anharmonicity of , which causes these intensities to be orders of magnitude larger than those of more ordinary harmonic molecules! While the higher output power of the lasers used will help offset the weakness of these transitions, we still must employ other techniques to increase the signal-to-noise ratio.
One such technique is velocity modulation. As alluded to in Section 5.1, this involves operating the discharge with an alternating current. In an AC discharge, molecular ions are alternately accelerated towards one end of the tube, then towards the other, at a frequency of about 8 kHz. Under these conditions, an incident radiation beam of a fixed frequency in the laboratory frame of reference appears frequency modulated to the molecular ions. As the frequency of the radiation in the molecule's frame moves back and forth across the molecule's transition, the amount of radiation absorbed rises and falls. However, neutral species are not moved by the AC potential, and have a constant absorption. By using a lock-in amplifier, then, we can easily subtract out noise due to neutral species.
Another, conceptually simpler, technique is that of multipassing. The incident laser beam is passed through the discharge cell multiple times (usually around 4) so as to increase the effective path length for absorption. Of course, when used in conjunction with velocity modulation it is important that the beam be passed through the cell in the same direction, or the modulation will be lost.
In these experiments, I will also utilize an advanced form of noise subtraction. A beam splitter will divide the laser beam into two beams of approximately equal intensity I1 and I2. One beam will be multipassed through the cell in one direction, while the other will be multipassed in the opposite direction. These two beams will then be sent to a new two-input autobalancing photoreceiver being developed by New Focus. This receiver outputs a signal proportional to (I1 - g I2), where g is a constant adjusted electronically by a low frequency feedback loop so as to cancel out laser intensity noise.
One final method which will be used to increase the signal-to-noise ratio is the introduction of computer control and data collection. For the first time in the Oka Ion Factory, scans will be controlled completely by computer and all data will be collected by computer. This will allow many (N) scans to be performed over a given wavelength range, and further reduce noise by a factor of .
Since the fundamental band was observed with a signal-to-noise ratio of > 3000, we feel confident that we can detect the , , and overtones. The overtone will provide us with a significant challenge, and we will have to do everything possible to optimize signal-to-noise.
To appreciate the importance of in the universe, several things should be borne in mind. First of all, protons are far more abundant than any other nucleons -- approximately 92.1% of nucleons are protons, while another 7.8% are helium nuclei. Since helium is chemically inert (the only astrophysically important compound it forms is HeH+), the chemistry of hydrogen is dominant in the universe.
Second, a great deal of the universe's protons form molecular hydrogen. For example, the galaxy-merger system NGC 6240 (see Figure 5) emits the luminosity of 108 Suns in the S(1) line alone! Molecular hydrogen has also been observed in the absorption of the light from a distant quasar by an interfering galaxy. Based on the redshift of the absorption lines, this hydrogen is about 13 billion years old!
Once we have molecular hydrogen, all that is needed to form is a source of ionization to start Reaction 1 above. In space, there are numerous ionization sources. In planetary systems, stellar winds will produce gigantic planetary magnetospheres in which charged particles are accelerated by the planet's rotating magnetic field and ionize to . In interstellar space, the omnipresent cosmic rays provide a source of ionization.
While the first (unsuccessful) searches for in nature were in the interstellar medium, the first successful discovery of was an accidental one!
In late 1987, Trafton et al.  observed Jupiter's S(1) quadrupole transition using a grating spectrometer at the McDonald Observatory. Along with the expected emission at 2.121 m, they also observed a strong unidentified emission feature at 2.093 m. In late 1988, Drossart and others  studied this feature at higher resolution using the Fourier transform infrared spectrometer at the Canada-France-Hawaii Telescope. This emission was only observed in the auroral regions near the poles.
After a month's work, and with the help of the hot band data from the Oka Ion Factory and ab initio calculations for this band, J. K. G. Watson identified the Jovian spectrum as due to the overtone band of .In this case, as in many others, had spawned a close collaboration between not only theorists and spectroscopists, but astronomers as well.
In 1989, Oka and Geballe observed the more intense fundamental band of in the Jovian ionosphere. From the relative intensities of the two bands, a temperature of about 1100 K has been derived. However, during the C fragment impact of the recent Shoemaker-Levy 9 comet-Jupiter collision, the intensities of observed hot bands suggested a temperature of 5000 K! Clearly, the laboratory spectra of that have been obtained thus far are insufficient to explain such hot phenomena.
It is also interesting to note that the fundamental band has also been observed on Uranus and on Saturn. In the case of Jupiter, the observation of the spatial variations of using narrow-band imaging has already provided a wealth of information on the morphology and temporal variations of plasma activity in the Jovian ionosphere. It is hoped that similar observations in the future will help elucidate the nature of the Saturnian and Uranian ionospheres.
In 1987, the light from an exploding star in the Large Magellenic Cloud reached Earth. Astronomers quickly began observing the supernova with various techniques, including infrared spectroscopy. By the 110th day after the first light reached Earth, strong features appeared at 3.41 and 3.53 m, and they reached their maximum signal-to-noise ratio by day 192. In a recent paper, Miller et al.  fit these lines to a computed spectrum of in this wavelength region. Although the detection is nowhere near as convincing as that in planetary ionospheres because of the lack of rotational structure, their fit is reasonable. While their observation cannot be confirmed (until another equally bright supernova's light arrives), there is not yet another plausible explanation for these lines. Their fit of the spectrum assumes a temperature of 2050 K, yet again demonstrating the need for laboratory data on higher energy transitions.
About thirty years ago, Townes et al.  discovered the microwave emission spectrum of ammonia in Sagittarius B2. Since then, a host of familiar and unfamiliar [such as HC9N] molecules have been observed in the interstellar medium. These discoveries have brought the previously nonexistent field of interstellar chemistry into the limelight.
These molecules are found in so called ``dense'' clouds in the interstellar medium, with densities of  = cm-3. These molecular clouds are now established as fertile breeding grounds for molecules, as well as the birthplace of stars.
At these low densities, two-body processes completely dominate the chemistry. Since the clouds' temperatures are very low (10-100 K), only reactions which are exothermic and have little or no activation energy can proceed at reasonable rates. Under these conditions, and with the lifetimes of the clouds estimated to be in the range of only 105 to 107 years, reactions between neutral species are unable to explain the observed abundance of molecules in dense clouds.
In the 1970s, a theory of ion-neutral reactions was advanced [6,7,8,9,11,10] to explain the extraordinarily high abundance of molecules in dense clouds, and is now generally accepted. Ion-neutral reactions proceed with Langevin rates on the order of 10-9 cm3 s-1, several orders of magnitude faster than neutral-neutral reactions.
This ion-neutral reaction scheme begins with the two key reactions discussed in Section 5.1 -- ionization of , followed by reaction of with to form . In the interstellar space, ionization is caused not by electron impact or the influence of stellar winds, but by cosmic rays, at a rate estimated to be s-1.
, with its low proton affinity of 4.4 eV, initiates the chains of chemical reactions which produce the wide variety of species in the dense clouds, through the proton hop reaction ,where X can be just about any atom or molecule present (with the notable exception of He). The most abundant reactive species X is CO, with [CO]/ .
The protonated ions thus produced begin a network of ion-neutral reactions which produce the wide variety of molecules observed by radioastronomers. Thus plays a very crucial role in interstellar chemistry and hence in the chemical evolution of dense clouds, an important step in star formation.
Because of its symmetry, however, has no pure rotational spectrum and is therefore inaccessible to radioastronomy. We are therefore consigned to search for using infrared spectroscopy, which has much lower sensitivity than radio/submillimeter techniques. Since the detection of its infrared spectrum in the laboratory,  has been sought unsuccessfully in molecular clouds. [42,43,44]
The observation of the infrared spectrum of in molecular clouds would indeed be a significant breakthrough in interstellar chemistry. It would provide the most direct evidence for the the ion-neutral reaction scheme, and also would allow us to estimate absolute number densities of the most important molecular species , CO, and . Additionally, it would provide estimates of effective column lengths, and thereby measure the size of the molecular clouds. The discovery of in interstellar space has often been referred to as the Holy Grail of observational molecular astrophysics.
In the laboratory, we produce in a cell, pass monochromatic radiation through it from behind, and detect it using a broad bandpass detector. In interstellar space, though, we are clearly unable to put a laser behind the molecular clouds. However, we can select molecular clouds which have young stars embedded within them -- while the visible light from the young stars does not make it out of the cloud, most of the infrared does. By selecting this type of target, we have effectively placed a continuum source behind the cloud. We then use an infrared spectrometer to look for the absorption lines that are expected to be strongest.
An additional trick we can use is to concentrate our telescope time on systems that are known to be depleted in molecules that destroy (especially CO) -- these systems will have a higher steady-state abundance of .
While it might sound unrealistic to expect success in the search for the Holy Grail, there are reasons to believe that observational detection of is on the horizon.
First, the technology of infrared spectrometers has been steadily improving since the first searches for began in 1981. While early spectrometers had to scan over wavelength and were thus more at the mercy of atmospheric fluctuations, today's spectrometers use CCD-like arrays which enable the observation of a range of wavelengths simultaneously. Additionally, the inherent sensitivity of the detectors has improved considerably, and the resolution has increased to (or 0.136 cm-1 at the wavenumber of our interest) at the United Kingdom InfraRed Telescope (UKIRT). The column densities of that are currently predicted by models are just at the threshold of sensitivity of state-of-the-art infrared spectrometers.
Second, Oka and Geballe recently reported a tentative detection of at 3.7 m towards the deeply embedded young stellar objects AFGL 2136 and W33A, using the CGS4 spectrometer of UKIRT. While the signal-to-noise ratio was low ( 2 or 3), this is nevertheless an encouraging sign that the Grail is within sight.
Third, a brand new spectrometer (named Phoenix) is just coming on line at the Kitt Peak National Observatory in Arizona. This spectrometer has five times better resolution than UKIRT, or about 0.027 cm-1. This is an important development, because observed millimeter wave lines of CO indicate that the intrinsic linewidths of molecules in these sources should be 0.07 cm-1. With Phoenix, we should be able to fully resolve lines, whereas UKIRT could not.
The high resolution of Phoenix will therefore allow us not only to unequivocally confirm (or refute) the detection at UKIRT, but also to detect and measure the abundance of in many other molecular clouds.
In pursuit of this objective, I recently participated in a ten night test and engineering run of Phoenix at Kitt Peak in late August. While we were plagued with the expected engineering and software problems, and the weather of August in Arizona was far from favorable, we were able to set up the special filter needed for detection and perform several short test integrations on various sources. While these observations did not detect , an important collaboration was established with the PI of the Phoenix instrument, and we have fully characterized the instrument in this wavelength region.
We have applied for two three-night Phoenix runs in the first half of 1997 to search for . The first run, in January, will allow us to search clouds with particularly bright infrared sources behind them. The second run, in June, will allow us to confirm or deny the tentative detections at UKIRT. Additionally, the Phoenix PI has just performed additional observations during his most recent test and engineering run. At the time of this writing, I am in the process of reducing the data.
In our search for we use the following three transitions in the fundamental band which start from the lowest two rotational levels -- the only levels that are appreciably populated at the low temperatures of dense clouds.
Perhaps most significantly, has led to perhaps unprecedented collaborations between laboratory spectroscopists, theoretical chemists, and observational astronomers. Herein lies the ultimate beauty of this simple molecule.
Shortly after his discovery of its infrared spectrum, Oka wrote that ``is a beautiful jewel of nature left for the laser spectroscopist.'' Not to mention the theorist -- and the astronomer.