Jim Watson And The Theory Of Vibration-rotation Interaction

Based on the the Coriolis interaction conceived by Teller and Tisza (1932), the fundamental Wilson-Howard Hamiltonian (WHH), formulated in 1936\footnote{Wilson, Jr., E. B. \& Howard, J. B. 1936 J. Chem. Phys. 4, 260}, includes everything about the vibration-rotation interaction. Enormous technical advances followed both in vibrational and rotational spectroscopy and have produced extremely rich data. Then God sent us the genius Jim Watson to deeply study the WHH and harvest all its fruits in the most sublime and direct manner. \vspace{0.05in} Out of the many jewels Watson left us I single out three works. (1) The theory of the centrifugal distortion of asymmetric-top molecules (1966)\footnote{Watson, J. K. G. 1966 J. Chem. Phys. 45, 1360; 46, 1935; 1968 J. Chem. Phys. 48, 4517}: To solve the indeterminacy of centrifugal distortion constants of non-planar asymmetric tops, Watson discovered an angular momentum operator P$_x$P$_y$P$_z$ + P$_z$P$_y$P$_x$ which commutes with the rotational Hamiltonian and produces an additional relation between centrifugal constants making the solutions possible. This is the most frequently quoted paper in the field of molecular spectroscopy. (2) Simplification of the WHH (1968)\footnote{Watson, J. K. G. 1968 Mol. Phys. 15, 479}: For the first term of rearranged WHH H = 1/2$\Sigma$($\Pi$$_\alpha$-$\pi$$_\alpha$)$\mu$$_{\alpha\beta}$($\Pi$$_\beta$-$\pi$$_\beta$) Watson discovered commutation relation [$\pi$$_\alpha$, $\mu$$_{\alpha\beta}$]=0. using absolutely beautiful tensor algebra, thus simplifying the Hamiltonian. This is the most fundamental work in the field of molecular spectroscopy and represents the triumph of tensor algebra. (3) Forbidden rotational transitions (1971)\footnote{Watson, J. K. G. 1971 J. Mol. Speectrosc. 40, 536}: The $\Delta$K=0 selection rule of a symmetric top molecule corresponds to cylindrical symmetry. Since the actual symmetry is C$_3$ rather than cylindrical for say NH$_3$, $\Delta$K=3 forbidden transitions are weakly allowed. Watson's theory showed that non-polar molecules such as CH$_4$ and H$_3^+$ are polar in some rotational levels and undergo forbidden rotational transitions. This theory has greatly influenced molecular astrophysics. \footnote{e.g. Oka, T., Geballe, T. R., Goto, M., Usuda, T., McCall, B. J., \& Indriolo, N. 2019 ApJ, 883, 54

Infrared, Submillimeter, and RadioAstronomy Program Astophysics Division

The object of my research for the NASA grant NAGW-4769 was to observe infrared spectra of molecular ions with special astrophysical interest in plasmas both in the laboratory and in space. Progress made during the period from September 1995 to September 1996 is summarized in the following: 1. Detection of Interstellar H3(+) The discovery of interstellar H3(+) through its mid-infrared absorption spectrum was by far the most inspiring development during this fiscal year. H3(+), the simplest stable polyatomic system, has been postulated to play the central role in the ion-neutral reaction scheme of interstellar chemistry, but its presence had not been directly observed in spite of intensive searches by several groups. 2. Observation of High Revibrational States of H3(+). The initial discovery of H3(+) in the Jovian aurora region was made through the identification of the 2(nu)(sub 2)(sup 2) approaches O overtone band indicating the population of H3(+) in high revibration state. 3. Observation of Ortho-Para H3(+) selection rules in plasma chemistry. Celection rules that relate quantum states before and ufter various processes are fascinating subject based on the symmetry argument. 4. Spectroscopy of other ions. Spectroscopy of carbocations ch3(+), CH2(+), C2H3(+) and C2H2(+) has been continued

Laser spectroscopic studies of the pure rotational U_0(0) and W_0(0) transitions of solid parahydrogen

High resolution spectrum of multipole-induced transitions of solid parahydrogen was recorded using diode and difference frequency laser spectroscopy. The J=4<--0 pure rotational U_0(0) transition observed in the diode spectrum agrees well in frequency with the value reported by Balasubramanian et al. [Phys. Rev. Lett. 47, 1277 (1981)] but we observed a spectral width smaller by about a factor of 4. The J=6<--0 W_0(0) transition was observed to be exceedingly sharp, with a width of ~70 MHz, using a difference frequency spectrometer with tone-burst modulation. This transition is composed of three components with varying relative intensity depending upon the direction of polarization of laser radiation. These components were interpreted as the splitting of the M levels in the J=6 state due to crystal field interactions. In addition, a new broad feature was found at 2452.4 cm^(−1) in the low resolution Fourier-transform infrared (FTIR) spectrum of solid hydrogen and was assigned to be the phonon branch W_R(0) transition of the W_0(0) line. The selection rules, crystal field splitting of J=4 and J=6 rotons, and the measured linewidth based on these observations are discussed

Top down chemistry versus bottom up chemistry

The idea of interstellar top down chemistry (TDC), in which molecules are produced from decomposition of larger molecules and dust in contrast to ordinary bottom up chemistry (BUC) in which molecules are produced synthetically from smaller molecules and atoms in the ISM, has been proposed in the chemistry of PAH \footnote{Duley, W. W. 2006, Faraday Discuss. 133, 415}$^,$\footnote{Zhen,J., Castellanos, P., Paardekooper, D. M., Linnartz, H., Tielens, A. G. G. M. 2014, ApJL, 797, L30} and carbon chain molecules\footnote{Huang, J., Oka, T. 2015, Mol. Phys. 113, 2159}$^,$\footnote{Guzmán, V. V., Pety, J., Goicoechea, J. R., Gerin, M., Roueff, E., Gratier, P., Öberg, K. I. 2015, ApJL, 800, L33} both for diffuse$^{a,c}$ and dense clouds$^{b,d}$. A simple and natural idea, it must have occurred to many people and has been in the air for sometime\footnote{L. Ziurys has sent us many papers beginning Ziurys, L. M. 2006, PNAS 103, 12274 indicating she had long been a proponent of the idea.} The validity of this hypothesis is apparent for diffuse clouds in view of the observed low abundance of small molecules and its rapid decrease with molecular size on the one hand and the high column densities of large carbon molecules demonstrated by the many intense diffuse interstellar bands (DIBs) on the other. Recent identification of C$_{60}^+$ as the carrier of 5 near infrared DIBs with a high column density of 2$\times$10$^{13}$ cm$^{-2}$ by Maier and others\footnote{Campbell, E. K., Holz, M., Maier, J. P., Gerlich, D., Walker, G. A. H., Bohlender, D, 2016, ApJ, in press} confirms the TDC. This means that the large molecules and dust produced in the high density high temperature environment of circumstellar envelopes are sufficiently stable to survive decompositions due to stellar UV radiaiton, cosmic rays, C-shocks etc. for a long time ($\geq$ 10$^7$ year) of their migration to diffuse clouds and seems to disagree with the consensus in the field of interstellar grains\footnote{Draine, B. T. 2003, ARA\&A, 41, 241}. The stability of molecules and aggregates in the diffuse interstellar medium will be discussed

Central 300 PC of the galaxy probed by the infrared spectra of H3+ and CO: I. Predominance of warm and diffuse gas and high H2 ionization rate

A low-resolution 2.0-2.5 $\mu$m survey of $\sim$500 very red point-like objects in the Central Molecular Zone (CMZ) of our Galaxy, initiated in 2008, has revealed many new bright objects with featureless spectra that are suitable for high resolution absorption spectroscopy of H$_3^+$ and CO.\footnote{Geballe, T. R., Oka, T., Lambridges, E., Yeh, S. C. C., Schlegelmilch, B., Goto, M., Westrick, C. W., WI07 at the 70th ISMS, Urbana, IL, USA,2015} We now have altogether 48 objects mostly close to the Galactic plane located from 142 pc to the west of Sgr A to 120 pc east allowing us to probe dense and diffuse gas by H$_3^+$ and dense gas by CO. Our observations demonstrate that the warm ($\sim$250 K) and diffuse ($\leq$100 cm$^{-3}$) gas with a large column length ($\geq$30 pc) initially observed toward the brightest star in the CMZ, GCS3-2 of the Quintuplet Cluster,\footnote{Oka, T., Geballe, T. R., Goto, M., Usuda, T., McCall, B. J. 2005, ApJ, 632, 882} exists throughout the CMZ with the surface filling factor of $\sim$ 100\% dominating the region. The column densities of CO in the CMZ are found to be much less than those in the three foreground spiral arms except in the directions of Sgr B and Sgr E complexes and indicate that the volume filling factor of dense clouds of 10\% previously estimated is a gross overestimate for the front half of the CMZ. Nevertheless the predominance of the newly found diffuse molecular gas makes the term "Central Molecular Zone" even more appropriate. The ultra-hot X-rays emitting plasma which some thought to dominate the region must be non existent except near the stars and SNRs. Recently the H$_2$ fraction $\mathit{f}$(H$_2$) in diffuse gas of the CMZ has been reported to be $\sim$0.6\footnote{Le Petit, F., Ruaud, M., Bron, E., Godard, B., Roueff, E., Languignon, D., Le Bourlot, J. 2016, A\&A, 585, A105}. If we use this value, the cosmic ray H$_2$ ionization rate $\mathit{\zeta}$ of a few times 10$^{-15}$ s$^{-1}$ reported earlier$^b$ on the assumption of $\mathit{f}$(H$_2$)=1 needs to be increased by a factor of $\sim$3 since the value is approximately inversely proportional to $\mathit{f}$(H$_2$)$^2$

H3+, THE IDEAL PROBE FOR IN SITU MEASUREMENT OF GALACTIC COSMIC RAYS

Cosmic rays are mysterious particles mostly atomic nuclei with extremely high energy from 10$^{6}$ eV to 10$^{21}$ eV. Their energy spectra for many nuclei are known in detail from the measurements on the earth. To measure cosmic rays in the Galaxy, however, we need a chemical method using spectroscopy. H$_{3}^{+}$ provides the ideal probe for this purpose because of (1) its ubiquity, (2) simple chemistry, and (3) concise spectrum. For about 30 years from the classic paper by Spitzer and Tomasko\footnote{Spitzer, Jr, L. and Tomasko, H. G. 1968, ApJ, 152, 972(1968)}, when H$^{+}$ was used as the probe, the cosmic ray ionization rate of H$_{2}$ was thought to be on the order of $\zeta$ $\sim$ 10$^{-17}$ s$^{-1}$ and uniform throughout the Galaxy. The 1997 discovery of H$_{3}^{+}$ in diffuse clouds and in the Galactic center (GC), however, changed this picture drastically. It is now established that $\zeta$ in diffuse clouds is 10 times higher than in dense clouds\footnote{Indriolo, N. and McCall, B. J. 2012, ApJ, 745, 91} and $\zeta$ in the Central Molecular Zone of the GC is 1000 times higher\footnote{Oka, T., Geballe, T. R., Goto, M., Usuda, T., McCall, B. J., and Indriolo, N. 2019, ApJ, submitted}. The uniformity of cosmic ray energy density throughout the Galaxy which was once thought to be reasonable because of its high penetrability has been negated. I will analyze these results using the Bethe formula for the cross section of ionization and discuss their implication in astrophysics and astrochemistry