Assignment Of Quantum Numbers Research Articles

Laboratory Spectroscopy of Hot Water near 2 Microns and Sunspot Spectroscopy in the H‐Band Region

The infrared spectrum of sunspots is analyzed in the H-band region (5540-6997 cm-1) with the aid of a new, hot (T = 1800 K) laboratory emission spectrum of water covering 4878-7552 cm-1. There are 682 lines in the sunspot spectrum and 5589 lines in the laboratory spectrum assigned quantum numbers corresponding to transitions due to H216O using a combination of previously known experimental energy levels for water and variational line lists. A further 201 unassigned lines common to both spectra can also be associated with water.

Quantum Monodromy in the Spectrum of Schrödinger Equation with a Decatic Potential

In this study the spectral problem of the two-dimensional Schrodinger equation with the cylindrically symmetrical decatic potential is carried out. The concept of quantum monodromy is introduced to give insight into the energy levels of system with this potential. It is shown that quantum monodromy occurs at ρ = 0 in the distribution of eigenstates around a critical point on the spectrum at E = 0 with zero angular momentum, such that there can be no smoothly valid assignment of quantum number. Cases with the three-well and four-well potentials are presented to give rise to the double degeneracies with respect to energy except for the angular momentum m = 0.

Disentangling the mystery of green bands of yttrium monohydride with the help of Stark spectroscopy

YH molecules were produced by laser vaporizing yttrium in the presence of He doped with H 2 or NH 3. Stark spectra were recorded for four bands in the 19 300–19 800 cm −1 region at electrostatic fields up to 16 kV/cm. Stark measurements proved useful in establishing rotational and Ω quantum number assignments. The permanent electric dipole moments (in Debye) were measured to be: 1.569(64), 2.325(8), 3.316(11), 2.273(6), and 1.537(8) for the X 1Σ + ground state and the 19 385, 19 746, 19 572, and 19 575 cm −1 excited states, respectively. Strong variation of the effective Ω quantum number with J was detected for the 19 572 cm −1 state.

Discrete variable approaches to tetratomic molecules: Part II: application to H 2O 2 and H 2CO

We have carried out large-scale calculations for accurate vibrational energy levels of formaldehyde and hydrogen peroxide. The discrete variable representations of the radial and angular coordinates are employed together with the contraction scheme resulting from several diagonalization/truncation steps. The global potential energy surface due to Carter et al. [J. Mol. Spectrosc. 90 (1997) 729] is used for H 2CO and due to Koput et al. [J. Phys. Chem. A 102 (1998) 6325] for H 2O 2. For both molecules, the calculated vibrational energy levels are characterized by combining vibrationally averaged geometries and expectation values of rotational constants with several adiabatic projection schemes for automatic quantum number assignments. The energy levels of H 2CO involving the excited ν 2 and ν 3 vibrations appear as resonances beyond the zero-order picture consisting of uncoupled 3D stretching and 2D bending modes. The torsional energy levels of H 2O 2 are studied in great detail and different energy patterns occurring below and above the cis barrier are discussed. Our full dimensional calculations for H 2O 2 have shown that the OH triad levels, 2 ν OH, are symmetry adapted local mode states.

Magnetospectroscopy of acceptors in “blue” diamonds

Naturally occurring, nitrogen-free, p-type diamond—now known to be boron-doped—as well as man-made diamonds deliberately doped with boron display an electronic Raman transition, Δ′, originating in the 1 s( p 3/2) : Γ 8 ground state of the acceptor and terminating in its 1 s( p 1/2) : Γ 7 spin–orbit partner. With magnetic field B along [0 0 1] , [1 1 1] , or [1 1 0] , the electronic Raman spectrum displays eight Zeeman transitions and four Raman lines ascribed to transitions between the Zeeman sublevels of Γ 8 (Raman-electron-paramagnetic-resonance: Raman-EPR). They exhibit polarizations expected from the polarizability tensors formulated in terms of the Luttinger parameters γ 1, γ 2 , and γ 3 characterizing the top of the valence band. The selection rules and the relative intensities of the Zeeman components as well as of the Raman-EPR lines, observed in diverse polarization configurations and scattering geometries, have led to: assignments of magnetic quantum numbers; the level ordering of the Zeeman sublevels, or equivalently, the magnitudes and signs of g 1 and g 2, the orbital and spin g-factors of the acceptor-bound hole; the extreme mass anisotropy as reflected in the ratio ( γ 2/ γ 3)=0.08±0.01. Magnetic-field-induced mixing of zero field states, time reversal symmetry, and the diamagnetic contributions which characterize the different sublevels are fully taken into account in the interpretation of the experimental results. These include the striking mutual exclusion of the Stokes spectrum from its anti-Stokes counterpart in specific polarization configurations.

Signatures of quantum integrability and nonintegrability in the spectral properties of finite hamiltonian matrices

For a two-spin model which is (classically) integrable on a five-dimensional hypersurface in six-dimensional parameter space and for which level degeneracies occur exclusively (with one known exception) on four-dimensional manifolds embedded in the integrability hypersurface, we investigate the relations between symmetry, integrability, and the assignment of quantum numbers to eigenstates. We calculate quantum invariants in the form of expectation values for selected operators and monitor their dependence on the Hamiltonian parameters along loops within, without, and across the integrability hypersurface in parameter space. We find clear-cut signatures of integrability and nonintegrability in the observed traces of quantum invariants evaluated in finite-dimensional invariant Hilbert subspaces. The results support the notion that quantum integrability depends on the existence of action operators as constituent elements of the Hamiltonian.

Using Laboratory Spectroscopy to Identify Lines in theK‐ andL‐Band Spectrum of Water in a Sunspot

The infrared spectrum of a sunspot is analyzed in the L-band region 3.1-4.0 μm (2497-3195 cm-1) and 2.02-2.35 μm (4251-4962 cm-1) in the K band. A new laboratory emission spectrum covering 2500- 6000 cm-1 is analyzed to help make the assignments. Quantum number assignments are made using linelists computed using variational calculations, assisted by tabulations of experimental energy levels. There are 1207 new H216O lines assigned in the L band and 508 new lines in the K band. Vibrational band origins of 11242.8 ± 0.1 cm-1 and 12586 ± 1 cm-1 are obtained for the (051) and (061) states.

Lasing properties of disk microcavity based on a circular Bragg reflector

The lasing properties of quantum well structures, where the cavity is defined in the plane of the wells by circular Bragg reflectors are investigated. Diffraction of the in-plane lasing modes into the vertical direction by the circular distributed Bragg reflector (DBR) allows the simultaneous measurement of near-field emission patterns and emission spectra, allowing unambiguous assignment of azimuthal quantum numbers to the lasing modes. The radial quantum number is determined by fitting the lasing spectrum to theory. Lasing is shown to occur in modes whose wave vector is mainly radial, confined by the circular DBR structure, rather than in whispering gallery type modes which are mainly azimuthal.

Electronic Spectroscopy of the Al−CH4/CD4Complex

The weakly bound Al−CH4 complex, and the fully deuterated version, Al−CD4, were prepared in a pulsed supersonic beam and probed with laser fluorescence excitation spectroscopy. Transitions to bound vibrational levels in electronic states correlating with the Al(5s,4d) + CH4/CD4 dissociation asymptotes have been observed. Resonance fluorescence from the excited levels could not be detected. Rather, these excited levels decay nonradiatively, and the excitation spectrum was obtained by monitoring emission from the lower Al atomic levels and AlH A → X chemiluminescence from formation of AlH(A1Π) within the excited complex. The band systems were dominated by progressions in the excited-state Al−CH4/CD4 van der Waals stretch vibrational mode. It was not possible to make unambiguous upper-state vibrational quantum number assignments, and lower bounds to excited-state binding energies were obtained. Band contour analysis of the AlH chemiluminescence spectra indicates that the excited AlH(A1Π) product is formed wi...

High resolution electronic spectroscopy of 4-fluoroaniline in a molecular beam: new experimental results and their interpretation in terms of molecular geometry

We measured two vibronic bands in the S 1 ← S 0 electronic transition of 4-fluoroaniline with high resolution technique and obtained accurate rotational constants by a direct assignment of the rotational quantum numbers to the levels involved in the transitions. An attempt was made to evaluate the change of the molecular geometry in the different vibrational levels of the S 1 state, with particular emphasis on the problem of the planarity of the molecular skeleton in both the ground and the first singlet excited state. Evidence is given for non-planar equilibrium geometry of both the molecules in the S 1 electronically excited state.

Spectroscopy from first principles: a breakthrough in water line assignments

Variational calculations of the spectrum of both hot and room temperature water vapor have led to a major increase in the number and scope of observed vibration–rotation transitions that have full quantum number assignments. The calculations are performed using high accuracy ab initio potential energy surfaces. As demonstrated, it is also necessary to consider corrections due to adiabatic effects, non-adiabatic effects and the relativistic motions of the electrons. The result of this work has been to double the number and energy range of the measured energy levels for water. New energy levels for the (010), (100), (020), (001), (110), (030), (011), (040), (050) and (060) states are presented here. Analysis of these levels and the associated transitions shows unanticipated features, including rotational difference bands, and an absence of clustering. The prospects of observing quantum monodromy in the spectrum of water are discussed.

High resolution electronic spectroscopy of Kr⋅OH/D and an empirical potential energy surface

The high resolution laser-induced fluorescence spectra of the Kr⋅OH van der Waals complex and its deuterated analog are reported. The rotational analysis provides information about the observed fine, hyperfine, spin-rotation, and parity interactions in these two complexes. The molecular parameters allow a direct comparison with previously reported results on the analogous Kr⋅SH/D complexes. Additionally, lower resolution scans have revealed vibronic bands that have not been reported in the previous work of Fei, Zheng, and Heaven [J. Chem. Phys. 97, 1655 (1992)], while high resolution results of the Kr·OH/D86,Kr·OH/D84, and Kr·OH/D82 isomers confirmed the previous vibrational quantum number assignment. The results of the high resolution analysis are used in conjunction with measured vibrational intervals to develop an empirical potential energy surface for Kr⋅OH/D. This is compared to the recently reported potentials by Korambath et al. [J. Chem. Phys. 107, 3460 (1997)] for the other R⋅SH/D (R=Ar, Kr) complexes.

Investigation of vibrational states of the ArHCl+ cation in the electronic ground state

Abstract The potential energy surface (PES) of the electronic ground state of the ArHCl + molecular ion is calculated by the multireference single- and double-excitation configuration interaction (MRD-CI) technique. An analytical representation of the potential energy data is obtained in the form of a power series. The vibrational eigenvalue problem is treated with high accuracy on the basis of the variational method using a direct product basis contracted in two steps (truncation/recoupling method). Unexpectedly for such a weakly bound system the spectrum turns out to be of a rather regular nature up to the first dissociation energy, allowing for an assignment of quantum numbers to a major part of the vibrational states. Furthermore, the wave functions are analysed together with several geometrical and energetic characteristics of the various vibrational states.

SUBMILLIMETER, MILLIMETER, AND MICROWAVE SPECTRAL LINE CATALOG

This paper describes a computer-accessible catalog of submillimeter, millimeter, and microwave spectral lines in the frequency range between 0 and 10 000 GHz (i.e. wavelengths longer than 30 μm). The catalog can be used as a planning guide or as an aid in the identification and analysis of observed spectral lines in the interstellar medium, the Earth’s atmosphere, and the atmospheres of other planets. The information listed for each spectral line includes the frequency and its estimated error, the intensity, the lower state energy, and the quantum number assignment. The catalog is continuously updated and at present has information on 331 atomic and molecular species and includes a total of 1 845 866 lines. The catalog has been constructed by using theoretical least-squares fits of published spectral lines to accepted molecular models. The associated predictions and their estimated errors are based upon the resultant fitted parameters and their covariance. Future versions of this catalog will add more atoms and molecules and update the present listings as new data appear. The catalog is available on-line via anonymous FTP at spec.jpl.nasa.gov and on the world wide web at http: //spec.jpl.nasa.gov.

Pure bending dynamics in the acetylene X̃ 1Σg+ state up to 15 000 cm−1 of internal energy

We investigate the large-amplitude bending dynamics of acetylene, in its ground electronic state, using an effective Hamiltonian model that reproduces all relevant experimental data, up to 15 000 cm−1 in internal energy, with 1.4 cm−1 accuracy (1σ). The experimental data which make this analysis possible are derived from the dispersed fluorescence (DF) data set that we recently reported [J. P. O’Brien et al., J. Chem. Phys. 108, 7100 (1998)] for the acetylene à 1Au→X̃ 1Σg+ system, which includes DF spectra recorded from five different vibrational levels of the à 1Au state. A numerical pattern recognition technique has permitted the assignment of polyad quantum numbers to observed transitions in these spectra, with up to 15 000 cm−1 in internal energy. Here we analyze a special subset of the identified polyads, those which involve excitation exclusively in the trans and cis bending modes: the pure bending polyads. The bending dynamics that is encoded in these polyads is analyzed using both frequency and time-domain formalisms. Among the conclusions of this analysis is that, in many ways, the observed bending dynamics is somewhat simpler at 15 000 than it is at 10 000 cm−1; this rather surprising result is explained in terms of qualitative changes in the structures of the pure bending polyads as a function of increasing internal energy.

Initial state resolved electronic spectroscopy of HNCO: Stimulated Raman preparation of initial states and laser induced fluorescence detection of photofragments

Stimulated Raman excitation (SRE) efficiently prepares excited vibrational levels in the ground electronic state of isocyanic acid, HNCO. Photofragment yield spectroscopy measures the electronic absorption spectrum out of initially selected states by monitoring laser induced fluorescence (LIF) of either NCO (X 2Π) or NH (a 1Δ) photofragments. Near threshold, the N–H bond fission is predissociative, and there is well-resolved rotational and vibrational structure in the NCO yield spectra that allows assignment of Ka rotational quantum numbers to previously unidentified vibrational and rotational levels in the ν1 N–H stretch and ν3 N–C–O symmetric stretch fundamentals in the ground electronic state of HNCO. The widths of NCO yield resonances depend on the initial vibrational state, illustrating one way in which initial vibrational state selection influences dissociation dynamics. Initial excitation of unperturbed ν1 (N–H stretch) states leads to diffuse NCO yield spectra compared to excitation of mixed vibrational levels. The higher energy dissociation channel that produces NH (a 1Δ) has coarser structure near its threshold, consistent with a more rapid dissociation, but the resonance widths still depend on the initially selected vibrational state.

High resolution electronic spectroscopy of the R⋅SH complexes (R= Ne, Ar, Kr)

The high resolution laser induced fluorescence spectra of the à 2Π3/2 electronic transition of the R⋅SH/D (R= Kr, Ar, Ne) van der Waals (vdW) complexes are reported. Analysis of these bands requires the inclusion of rotation, fine and hyperfine structure, spin-rotation interactions, and parity splittings. A number of molecular parameters are determined, along with internuclear bond distances between the R and the SH moiety. Comparison of the present results for R⋅SH/D is made with the analogous R⋅OH/D species where applicable. In addition, the detailed “rotational” structure and the highly precise determinations of the band origins of the different heavy atom isotopomers are critical for absolute vibrational quantum number assignment in the à state.

Exact six-dimensional quantum calculations of the rovibrational levels of (HCl)2

Results of comprehensive full-dimensional (6D) quantum calculations of the rovibrational levels of (HCl)2, for total angular momentum J=0,1 are presented. The calculations employed two 6D potential energy surfaces (PES)—the ab initio PES of Bunker and co-workers, and the semiempirical PES of Elrod and Saykally. This 6D study provides the first rigorous, approximation-free description of the bound state properties of (HCl)2, including the dissociation energy, tunneling splittings and their J, K dependence, frequencies of intermolecular vibrations and associated J=0→1 spacings, and quantum number assignments of the 6D eigenstates. Detailed comparison with 4D bound state calculations (for fixed HCl bond length) was made in order to assess the importance of including the intramolecular vibrations of the two HCl subunits for accurate calculation of various spectroscopic properties of (HCl)2. Comparison of the 6D results with experimental data, while confirming that the ES1 PES is substantially more accurate than the ab initio PES, shows that there is room for further refinements, preferably using 6D bound state calculations.

Radiative decays and transition form factors of strange mesons in the relativistic constituent quark model

Motivated by the recent lattice QCD results indicating that the topological charge contribution to the flavor singlet axial vector current can be traded off by the constituent quark masses, we investigate the radiative decays of pseudoscalar (π,K, η, η′), vector (ρ,K*, ω, ϕ) and axial vector (A 1) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock-state expansion of meson wavefunctions are not contaminated by the vacuum fluctuation, (2) the assignment of meson quantum numbers are given by the Melosh transformation. Except the well-known constituent quark masses of (u,d,s) quarks and the spin-averaged meson masses, the only parameter in the model is the gaussian parameter β which determines the broadness (or sharpness) of radial wavefunction. The computed decay widths and the transition form factors of ρ, ω → π(η)γ*,K* →Kγ* andA 1 → πγ* at 0≤Q 2≤5 GeV2 and π0(η) → γ*γ at 0≤Q 2≤3 GeV2 are in a remarkably good agreement with the experimental data and the result forA 1 + → π+ γ* transition is quite consistent with the experiments of pion scattering on a nucleus using Primakoff effect. This model is potentially useful in the cocktail analyses of the dilepton productions in proton-proton, proton-nucleus and nucleus-nucleus collisions at SPS energies and a little above.

New Interpretation of the Observed Heavy Baryons

I suggest that the conventional assignment of quantum numbers to the observed charm and bottom baryons is not correct, as these assignments imply large violation of the heavy spin-flavor and light SU(3) symmetries. I propose an alternative interpretation of the observed states, in which the symmetries are preserved. If these novel assignments are right, there is a new state with mass approximately 2380 MeV which decays to ${\ensuremath{\Lambda}}_{c}+\ensuremath{\gamma}$, and another with mass approximately 5760 MeV which decays to ${\ensuremath{\Lambda}}_{b}+\ensuremath{\gamma}$. Although such states have not been seen, neither are they excluded by current analyses.