Changes In Rotational Quantum Number Research Articles

Near-threshold β-parameter measurements of state-selected rotational transitions to the v+ = 0 level of normal and ortho-D2

Photoelectron angular distributions in D2 have been measured for the first time with rotational selectivity. The study focuses on the R(2) 5pπ and R(0) 5pπ Rydberg states, converging on the v+ = 4 vibrational level of the D2+ ion. These Rydberg states autoionize to populate the X2Σg+ (v+ = 0) state of the ion. The angular asymmetry parameter (β) has been determined, across the photon energy region 15.671–15.684 eV, for transitions involving changes in rotational quantum number, between the initial neutral and final ion state, ΔN, of +2 and +4. The β-parameter values obtained for the ΔN = +2 transition indicate that the channel is populated via both p- and f-wave photoemission. The β-parameter value for the R(2) n = 5pπ Rydberg state was found to be closer to zero, particularly for the ΔN = +4 transition. It is suggested that this near-isotropic emission is associated with the photo-excited D2 molecule rotating before the autoionizing decay has had a chance to occur. Measurements have been made in both normal and ortho-D2, confirming the results and verifying that the resonant features originate in even rotational levels of the D2 molecule.

Dissection of Rovibronic Structure by Polarization-Resolved Two-Color Resonant Four-Wave Mixing Spectroscopy

A synergistic theoretical and experimental investigation of stimulated emission pumping (SEP) as implemented in the coherent framework of two-color resonant four-wave mixing (TC-RFWM) spectroscopy is presented, with special emphasis directed toward the identification of polarization geometries that can distinguish spectral features according to their attendant changes in rotational quantum numbers. A vector-recoupling formalism built upon a perturbative treatment of matter-field interactions and a state-multipole expansion of the density operator allowed the weak-field signal intensity to be cast in terms of a TC-RFWM response tensor, RQ(K)(epsilon4*epsilon3epsilon2*epsilon1;Jg,Je,Jh,Jf), which separates the transverse characteristics of the incident and generated electromagnetic waves (epsilon4*epsilon3epsilon2*epsilon1) from the angular momentum properties of the PUMP and DUMP resonances (Jg,Je,Jh,Jf). For an isolated SEP process induced in an isotropic medium, the criteria needed to discriminate against subsets of rovibronic structure were encoded in the roots of a single tensor element, R0(0)(epsilon4*epsilon3epsilon2*epsilon1;Jg,Je,Jh,Je). By assuming all optical fields to be polarized linearly and invoking the limit of high quantum numbers, specific angles of polarization for the detected signal field were found to suppress DUMP resonances selectively according to the nature of their rotational branch and the rotational branch of the meshing PUMP line. These predictions were corroborated by performing SEP measurements on the ground electronic potential energy surface of tropolone in two distinct regimes of vibrational excitation, with the near-ultraviolet 1B2-1A1 (pi*<--pi) absorption system affording the requisite PUMP and DUMP transitions.

Quantum Interference as the Source of Steric Asymmetry and Parity Propensity Rules in NO−Rare Gas Inelastic Scattering

Rotationally inelastic scattering of rare gas atoms and oriented NO molecules exhibits a remarkable alternation in the sign of steric asymmetry between even and odd changes in rotational quantum number. This effect has also been found in full quantum-mechanical scattering calculations. However, until now no physical picture has been given for the alternation. In this work, a newly developed quasi-quantum treatment (QQT) provides the first demonstration that quantum interferences between different orientations of the repulsive potential (that are present in the oriented wave function) are the source of this alternation. Further, from application of the treatment to collisions of nonoriented molecules, a previously unrecognized propensity rule is derived. The angular dependence of the cross sections for excitation to neighboring rotational states with the same parity is shown to be similar, except for a prefactor. Experimental results are presented to support this rule. Unlike conventional quantum-mechanical (or semiclassical) treatments, QQT requires no summation over the orbital angular momentum quantum number l or integration over the impact parameter b. This eliminates the need to solve large sets of coupled differential equations that couple l and rotational state channels among which interference can occur. The QQT provides a physical interpretation of the scattering amplitude that can be represented by a Legendre moment. Application of the QQT on a simple hard-shell potential leads to near-quantitative agreement with experimental observations.

Symmetry-breaking collisional energy transfer in the 4 νCH rovibrational manifold of acetylene: spectroscopic evidence of a quasi-continuum of background states

Collision-induced molecular energy transfer in the 12 700 cm −1 '4 ν CH' rovibrational manifold of acetylene is studied by infrared–ultraviolet double-resonance spectroscopy. As in previous work, there is evidence of (formally forbidden) odd-numbered changes in rotational quantum number J. Such 'symmetry-breaking' processes are invariant to choice of fluorescence-monitored vibronic band. The prominent (1 0 3 0 0) 0 J=12 rovibrational state appears to be a likely gateway and is rationalised in terms of a combination of quasi-resonant Coriolis and Stark mixing. An unusual collision-induced quasi-continuous background, underlying the discrete rovibrational states of the 4 ν CH manifold, offers a mechanistic key to the apparent symmetry breaking.

Photoelectron spectra ofN2+:Rotational line profiles studied with He I–excited angle-resolved spectroscopy and with synchrotron radiation

We have recorded angle-resolved He I photoelectron spectra of the three outermost valence states in ${\mathrm{N}}_{2}^{+},$ with high enough resolution to observe rotational line profiles. For the two $\ensuremath{\Sigma}$ states, the $X{}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ and the $B{}^{2}{\ensuremath{\Sigma}}_{u}^{+},$ we found that the rotational branches corresponding to different changes in rotational quantum number can differ dramatically in $\ensuremath{\beta}$ value. The well-known difference in $\ensuremath{\beta}$ value for the $\ensuremath{\nu}=0$ and \ensuremath{\nu}=1 vibrations of the $X{}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ state was found to be due to different rotational branching ratios and also different $\ensuremath{\beta}$ values of the rotational branches. For the $\ensuremath{\nu}=0--2$ vibrations of the $A{}^{2}{\ensuremath{\Pi}}_{u}$ state, the $\ensuremath{\beta}$ value difference between rotational branches is much less pronounced than in the X and B states. We have also recorded synchrotron-radiation-excited photoelectron spectra of the $\ensuremath{\nu}=0$ vibrational peaks of the $X{}^{2}{\ensuremath{\Sigma}}_{g}^{+}$ and $B{}^{2}{\ensuremath{\Sigma}}_{u}^{+}$ states where rotational line profiles are resolved. The intensities of the rotational branches were studied as function of photon energy, the X state between 23 and 65 eV, and the B state between 23 and 45 eV. The results for the X state have recently been presented in a Letter [G. \"Ohrwall, P. Baltzer, and J. Bozek, Phys. Rev. Lett. 81, 546, 1998]. The rotational branching ratios of the two states have very different behaviors as functions of photon energy. The relative intensities of the rotational branches in the X state change significantly over the studied energy range. The $3{\ensuremath{\sigma}}_{g}\ensuremath{\rightarrow}k{\ensuremath{\sigma}}_{u}$ shape resonance apparently gives rise to a non-Franck-Condon-like behavior for the rotational branching ratio of the X state. In the B state, the rotational branching ratios remain essentially constant over the studied energy range.

State-to-state photoionization of VO: Propensity for large, positive changes in rotational quantum number

State-to-state threshold photoionization cross sections from specific spin–rotation levels N′=7, J′=8.5, v′=3 of C 4∑− VO to specific levels N+J+ of X 3∑− VO+ show a remarkable propensity for large, positive ΔN. Observed transitions span the ranges ΔN=−5 to +7 and ΔJ=−5.5 to +4.5. The adiabatic ionization potential of VO is 7.2386±0.0004 eV. The mean bond length of v+=0, X 3∑− VO+ is 1.561±0.003 Å.

Optical–optical double resonance studies of rotational autoionization of NO

Optical–optical double resonance spectroscopy is used to probe Rydberg series converging to the first ten rotational levels of NO+ X 1Σ+, v+=0. Above the lowest ionization threshold, rotational autoionization of Rydberg series converging to higher thresholds is observed. Predissociation of these Rydberg states is found to compete with rotational autoionization in much the same manner as predissociation competes with vibrational autoionization in the region of the first few vibrational limits of NO+. The presence of this competing decay process, which has a decay rate similar to that of rotational autoionization, permits the comparison of rotational autoionization rates for different changes in rotational quantum number (ΔN+). Rotational autoionization by ΔN+=2 is found to be faster than by ΔN+=1 or 3. This results from the requirement that ΔN+=even processes require interactions between levels that both have even or both have odd values of orbital angular momentum l, while ΔN+=odd processes require interactions between levels of which one has even l and the other has odd l. In NO, the latter interactions are known to be quite weak. The electric field dependence and pressure dependence of the ionization threshold are also discussed.

Vibrational deactivation of diatomic molecules by collisions with solid surfaces

A model is proposed for vibrational deexcitation of diatomic molecules by collisions with a solid surface. The expressions obtained are analyzed to yield insight into the collision dynamics and used to predict the rotational and translational energy distributions, and other properties of interest. The method is developed in the approximation of a stationary surface, and is closely related to a recent model for vibrational relaxation in atom–molecule collisions. From considerations based on the scales of the relevant energy spacings and coupling strengths applied to the vibrational, rotational, and diffraction states involved, the scattering equations are greatly simplified by several approximations. For a simple but realistic class of potentials, analytical expressions are obtained for the deactivation probabilities pertaining to all final translational–rotational channels. Using the expressions of the model, a detailed study is made of: (i) The rotational–translational energy distribution produced by the vibrational energy release, and its dependence on system parameters; (ii) isotope and collision-energy dependence of the deactivation probabilities; (iii) scaling properties of the transition probabilities with regard to ΔJ = J′−J, the change in rotational quantum number. The model is applied numerically to collisions of vibrationally excited H2, D2, T2, HD with a noncorrugated surface over a wide range of energies. The most striking feature of the model results is that a highly dominant fraction of the vibrational energy goes into molecular rotation, the main channel being an almost resonant V–R process in all cases.

Quantum mechanical study of elastic scattering and rotational excitation of CO by electrons

We report close coupling calculations of differential, integral, and momentum transfer cross sections for pure elastic scattering and rotational excitation of CO by electron impact. The calculations are based on a static charge distribution that has correct dipole and quadrupole moments, has cusps at the nuclei, and is augmented by an SCF treatment of charge polarization and a local approximation for exchange. The rotationally summed cross sections, with no adjustable parameters in the scattering calculation, are in reasonably good agreement with the experimental cross sections but are somewhat larger at small scattering angles. The state-to-state differential cross sections show several interesting features, including very large contributions to small-angle scattering from large angular momenta and a ’’propensity rule’’ favoring even Δj over odd Δj at almost all scattering angles for Δj≲4 where Δj is the change in rotational quantum number.

Continuum resonance Raman scattering of light by diatomic molecules. II. Theoretical study of the Q branches of Δn=1 profiles of molecular bromine

The methods developed in Part I for the calculation of continuum resonance Raman scattering amplitudes are applied to the calculation of the Q branches of the Δn=1 profiles of Br2 which have been measured by Baierl and Kiefer [J. Raman Spectrosc. 3, 353 (1975)]. The experimental conditions being such as to imply many initial and final rovibrational states, we first of all study the effect of rotation on the scattering amplitudes. It is observed that while the amplitudes may vary substantially with the rotational number of the initial state, almost no effect is introduced by taking into account the changes in rotational quantum numbers which accompany transitions between different electronic states. This is useful to derive an efficient formula for the scattering cross section. The profiles are then calculated with the potentials available for the 1Π1u and B (3Π+0u) excited states which, as shown by previous workers, interfere strongly in producing the spectra. These calculations make it possible to examine the effect of (1) using semiclassical scattering amplitudes rather than the more accurate coupled channel results, (2) using R-dependent electronic transition moments instead of constant ones, (3) introducing the effect of the angular momentum quantum number J instead of using the amplitudes calculated for J=0, (4) choosing the potentials among those derived from absorption data. The conclusions which emerge from these calculations are that: (a) The semiclassical procedure is fairly accurate. This success indicates that a Raman profile for a giving exciting wavelength represents in fact a very local test (over a range of ∼0.03 Å) of the excited states potentials. Changing the wavelength from 5017 to 4579 Å (two of the lines available from an argon ion laser) amounts to scanning each of the potentials over a region of no more than 0.1 Å; (b) The changes in the scattering amplitudes brought about by the introduction of varying electronic transition moments can be correlated with the values taken by the moments at the radiative crossing points. This is supported both by a detailed analysis of the coupled channel amplitudes and by the form taken by the semiclassical amplitudes; (c) The effect of J on the amplitudes is masked in the profiles as a result of superposition effects; (d) None of the published potentials was able to fit all five profiles. A local downward displacement of the potentials for the 1Π1u and B (3Π+0u) states removes the main unsatisfactory features of the spectra.

Quantum number and energy scaling of rotationally inelastic scattering cross sections

A general formula for rotationally inelastic cross sections in atom-diatomic collisions is derived. This result is achieved by assuming the transition probability is a function of rotational quantum number differences, the kinetic energy in the upper states, and is inversely proportional to the number of accessible states within an effective hamiltonian formalism. The scaling law is able to predict all rows, or columns, of the inelastic cross section matrix, σ jj, given any one row, or column, as a function of energy. Finally, we applied this scaling theory to a variety of collision systems; in general, good agreememt between predicted and exact results is exhibited. We have developed and tested a scaling law for rotationally inelastic transitions which predicts all rows or columns of the inelastic cross section matrix, σ jj, given any one row or column. The agreement between exact and predicted cross sections was good for the HeHF [20], HeHCl [21], H 2CS [17], HeCO [16] and Li +H 2 [18] systems which vary in reduced mass from approximately 2–4 an and rotor constant from 0.82–60.0 cm −1. However, for ArN 2 [13,14, 19,24] collisions (μ = 16.5 au, B e = 2.01 cm −1) the error increased with increasing j and/or Δ. In every case the disagreement was in the opposite direction from the prediction of eqs. (15a)–(15c) which are based upon fully degenerate statistics instead of the effective hamiltonian non-degenerate statistics of eqs. (2a) and (2b). Finally, we state two general conclusions: 1. (1) Whenever the initizil kinetic energy ( E—ϵ j) is greater than approximately five times the energy gap (ϵ j+Δ—ϵ j), the scaling theoretic cross sections are accurate within 20%; and 2. (2) at total energies much larger than that of the internal states of interest, all cross sections with the same change in rotational quantum number become approxinutely equal.

Theory of Microwave Transitions in the Vibronic Ground State of Tetrahedral Molecules

Vibration-rotation interactions in the motion of tetrahedral molecules, which are conventionally nonpolar in their ground vibrational and electronic states, permit pure rotational transitions. These transitions, which are electric dipole in nature, occur at microwave frequencies for the following changes in rotational quantum numbers: $\ensuremath{\Delta}J=0$ and $\ensuremath{\Delta}K=\ifmmode\pm\else\textpm\fi{}2$. General expressions for spectral line positions and absolute intensities are calculated for $J=0\ensuremath{-}20$. The effects of tetrahedral fine-structure splittings and nuclear-spin statistical weights have been included. Detailed results are established for methane, the prototype of molecules with tetrahedral symmetry. Possible competing transitions are discussed.

Pure rotational excitation in CO +-Ar interactions by ion beam collision spectroscopy

The energy loss spectra observed in collisions of a CO + ion beam with a neutral Ar beam reveal inelastic processes occurring with an energy loss below that required for the ν = 0 → 1 vibrational transition. These inelastic events correspond to pure rotational excitation of the incident ion beam with a large change in rotational quantum number.

Nuclear Spin Relaxation in 1,1-Difluoroethylene in Solution

An experimental method for the determination of the relative values of τ1 and τ2 by the nuclear Overhauser effect proposed by Kuhlmann and Baldeschwieler is applied to 1,1-difluoroethylene, where τ1 and τ2 are the correlation times for the change in rotational quantum number and for molecular reorientation, respectively. The proton transition probability WH, the fluorine transition probability between the levels belonging to the same symmetry representation WF(A), and the fluorine transition probability between states of different symmetry WF(B) are obtained by NMR and NMDR experiments in solutions of CF2CH2 in various solvents. The temperature dependence of these transition probabilities measured between −40° and 33°C shows that τ1≪τ2. The ratio of diagonal and off-diagonal components of the spin—rotation interaction tensor is (Cxx2+Cyy2+Czz2)/(Cyz2+Czy2)≃40.The change in anisotropic intermolecular interactions obtained by a change of solvent affects τ1 more than τ2.

Measurements of Collisional Energy Transfer between Rotational Energy Levels in CN

A microwave-optical technique which selectively populates a single rotational level of CN and permits the observation of the redistribution of this population was utilized to measure the rates of collisional energy transfer between rotational energy levels of the B2Σ state of CN. CN was formed in the A 2Π state by the addition of CH2Cl2 to the afterglow of a nitrogen discharge. The near coincidence of the K=4, v=10 level of the A 2Π state with the K=4, v=0 level of the B 2Σ state permits microwave transitions near 10 GHz from the more populated Π level to the Σ level. The increased population in the rotational levels neighboring the K=4 level of the B 2Σ state was detected by measuring the increased optical emission due to the B 2Σ—A 2Σ transition near 3875 Å. Collisional energy transfer was measured over a pressure range from 0.1 to 5 Torr for changes in rotational quantum number ranging from one to ten. It is shown that rotational transitions having changes in rotational quantum number greater than unity take place with high probability, contrary to the optical selection rule ΔK=±1, and that approximately every gas kinetic collision produces a rotational transition. The relaxation time for the fourth rotational level was found to be 1.2×10−7 (±30%) sec at a pressure of 1 Torr.

Inelastic Scattering from a Diatomic Molecule: Rotational Excitation upon Collision between He andH2andH2andH2

The formalism developed by Arthurs and Dalgarno has been used in the distorted wave approximation to calculate the inelastic scattering cross section for rotational excitation from the $j=0$ to the $j=2$ rotational state in collisions between a helium atom and a hydrogen molecule or two hydrogen molecules. All necessary computations were done with a digital computer, thus, allowing the Arthurs-Dalgarno formalism to be applied with no added approximations. The interaction energy between He and ${\mathrm{H}}_{2}$ obtained in the preceding paper was used for the He-${\mathrm{H}}_{2}$ calculation while the interaction energy given by Takayanagi was used for the ${\mathrm{H}}_{2}$-${\mathrm{H}}_{2}$ problem. Values for the total inelastic cross sections are given as well as graphs for the He-${\mathrm{H}}_{2}$ differential scattering cross section. Incident kinetic energies up to only 0.25 eV in the center-of-mass system were considered; for these low energies, vibrational or electronic excitation is impossible so that change in rotational quantum number is the only inelastic process possible. The results obtained for the ${\mathrm{H}}_{2}$-${\mathrm{H}}_{2}$ cross section do not agree with the rate of de-excitation from the $j=2$ rotational level in ${\mathrm{H}}_{2}$ gas as measured by dispersion experiments with ultrasonic waves. The disagreement may be due to an incorrect ${\mathrm{H}}_{2}$-${\mathrm{H}}_{2}$ interaction potential or failure to consider all important de-excitation mechanisms.

The Molecular Scattering of Light from Ammonia Solutions. The Fine Structure of a Vibrational Raman Band

The Raman band of the ammonia molecule corresponding to the infrared absorption at 3 \ensuremath{\mu} has been partially resolved into its fine structure. The experiments have been made not with gaseous or liquid ammonia but with aqueous solutions of relatively high concentration. The lines have been assigned to $Q$, $P$, $R$, $\mathrm{PP}$, and $\mathrm{RR}$ branches, corresponding to changes in rotational quantum number $\ensuremath{\Delta}k=0, \ifmmode\pm\else\textpm\fi{}1, \mathrm{and} \ifmmode\pm\else\textpm\fi{}2$. The moment of inertia about a line normal to the axis of symmetry calculated from the spacing of the lines is I = 2.82\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}40}$ g ${\mathrm{cm}}^{2}$. As far as the present, somewhat incomplete results may be taken to indicate the structure of the N${\mathrm{H}}_{3}$ molecule is largely uninfluenced by the force fields of the solvent molecules.