Pure Rotational Energy Research Articles

Pairing effects on pure rotational energy of nuclei

By applying the angular-momentum projection to the self-consistent axial mean-field solutions with the semi-realistic effective Hamiltonian M3Y-P6, the pairing effects on the pure rotational energy of nuclei, i.e. the rotational energy at a fixed intrinsic state, have been investigated. While it was shown at the Hartree–Fock (HF) level that the individual terms of the Hamiltonian contribute to the rotational energy with ratios insensitive to nuclides except for light or weakly-deformed nuclei, the pair correlations significantly change the contributions, even for the well-deformed heavy nuclei. The contribution of the interaction to the rotational energy is found to correlate well with the degree of proximity between nucleons, which is measured via the expectation value that two nucleons exist at the same position. While the nucleons slightly spread as the angular momentum increases at the HF level, accounting for the positive (negative) contribution of the attractive (repulsive) components of the interaction, the pair correlations reduce or invert the effect.

Rotational excitation of highly excited H2O by H2

ABSTRACT Water is a key molecule for interstellar chemistry. Observations with Herschel telescope show significant population of very high rotational transitions (j ≳ 8) in young stellar objects, indicating significant amounts of water in hot (T ≳ 1500 K) and dense (n ≳ 106 cm−3) gas. Non-local thermodynamic equilibrium (LTE) modelling of these observations requires the knowledge of the collisional and radiative properties of highly excited water at high temperature. The aim of this work is to calculate a new set of excitation rate coefficients for both para- and ortho-H2O induced by collisions with H2 for energy levels up to j = 17. Quantum scattering calculations were performed using a reduced dimensional approach and the coupled states approximation. Rate coefficients were obtained for 97 pure rotational energy levels of both para- and ortho-H2O and for temperatures up to 2000 K. With the forthcoming launch of the James Webb Space Telescope, these new collisional data will allow us to gain more insight into the physical conditions in star- and planet-forming regions.

Molecular Parameters of Tert-Butyl Chloride and Its Isotopologues Determined from High-Resolution Rotational Spectroscopy

A broadband chirped-pulse Fourier transform microwave spectrometer was used to detect the rotational spectra of the products of a chemical reaction in the gas phase from 1-18 GHz under the supersonic expansion condition. In natural abundance, pure rotational energy level transitions of tert-butyl chloride and its isotopologues (13C, 37Cl) were observed and assigned. The rotational spectral parameters (rotational constant, quadrupole coupling constant and centrifugal distortion constant) of these isotopologues were determined. The experimental results are in great agreement with the calculated values of quantum chemistry and the spectral parameters in the literature. The accuracy and the capability for chemical detection of our homemade rotational spectrometer were verified by this experiment.

A comparative study of quaternionic rotational Dirac equation and its interpretation

In this study, we develop the generalized Dirac-like four-momentum equation for rotating spin-1/2 particles in four-dimensional quaternionic algebra. The generalized quaternionic Dirac equation consists of the rotational energy and angular momentum of particle and antiparticle. Accordingly, we also discuss the four-vector form of quaternionic relativistic mass, moment of inertia and rotational energy-momentum in Euclidean space-time. The quaternionic four-angular momentum, (i.e. the rotational analogy of four-linear momentum) predicts the dual energy (rest mass energy and pure rotational energy) and dual momentum (linear-like momentum and pure rotational momentum). Further, the solutions of quaternionic rotational Dirac energy-momentum are obtained by using one-, two- and four-component of quaternionic spinor. We also demonstrate the solutions of quaternionic plane wave equation which gives the rotational frequency and wave propagation vector of Dirac particles and antiparticles in terms of quaternionic form.

A full-dimensional potential energy surface and quantum dynamics of inelastic collision process for H2-HF.

A full-dimensional ab initio potential energy surface for the H2-HF van der Waals complex was constructed by employing the coupled-cluster singles and doubles with noniterative inclusion of connected triples with augmented correlation-consistent polarised valence quadruple-zeta basis set plus bond functions. Using the improved coupled-states approximation including the nearest neighbor Coriolis couplings, we calculated the state-to-state scattering dynamics for pure rotational and ro-vibrational energy transfer processes. For pure rotational energy transfer, our results showed a different dynamical behavior for para-H2 and ortho-H2 in collision with hydrogen fluoride (HF), which is consistent with the previous study. Interestingly, some strong resonant peaks were presented in the cross sections for ro-vibrational energy transfer. In addition, the calculated vibrational-resolved rate constant is in agreement with the experimental results reported by Bott et al. These dynamics data can be further applied to the numerical simulation of HF chemical lasers.

Energy transfer dynamics for H+HF(<italic>v, j</italic>)→H+HF(<italic>v</italic><italic><x content-type="symbol">¢</x></italic><italic>, j</italic><italic><x content-type="symbol">¢</x></italic>)

A series of vibrational relaxation rate constants for H+HF( v =1, j )→H+HF( v ′ =0, j ′ ) were calculated by time-independent close coupling approach, based on the CSZ potential energy surface. Within the temperature range from 295 to 500 K, all the rotational-resolved rate constants increase monotonically with temperature, and the rotational quantum number of the dominating final state is larger than the initial rotational quantum number. At room temperature, the vibrational-resolved rate constant is in reasonably agreement with some experimental data. The rate constants for the pure rotational energy transfer process H+HF( v =1, j )→H+HF( v ′ =1, j ′ ) at 500 K were also calculated. They are several magnitudes larger than the ro-vibational relaxation rates. It was found that the rate constants of Δ j = − 1 are approximately twice as large as those of Δ j = 1 , except for the (1,1) initial state.

Rotational-state resolved coupling of CH A 2Δ and B 2Σ- in collisions with CO2

Inelastic collisions of selected rovibronic levels of the CH A2Δ and B2Σ− states with CO2 have been investigated experimentally. Initial levels in A2Δ, = 1 and B2Σ−, = 0 were prepared by selective laser excitation. Time-gated emission from the initial and product levels was dispersed at rotational resolution for the first time. Conditions were established where 60–80% of the population remained in the initially populated rovibronic level. The rotational state propensities were established for electronically inelastic collisional transfer from A2Δ, = 1 to B2Σ−, = 0. The reverse transfer is complicated by the spectral overlap of the A–X(1,1) and (0,0) bands. A high N′ component can unambiguously be assigned to A2Δ, = 0. The distributions of ΔN for inter-electronic state transfer are generally broader than for pure rotational energy transfer within either state, particularly at higher N where the results are more clear-cut. For these levels the redistribution of rotational population during electronic transfer is, however, less complete than implied by a statistical prior distribution. This suggests that the electronic state-changing collisions sample more strongly interacting regions of the CH···CO2 excited state potentials than are required to cause pure rotational relaxation. These interactions are not sufficiently strong, however, to promote complete rotational (or vibrational) energy redistribution during the collision.

State-resolved collisional energy transfer in highly excited NO2. II. Vibrational energy transfer in the presence of strong chemical interaction

The state-resolved collisional self-relaxation of highly (optically) excited NO2 (Eint≈18 000 cm−1) in a thermal cell has been probed directly using time-resolved optical double resonance spectroscopy. The thermally averaged state-to-state cross sections have been derived from a master equation analysis of the kinetic traces. Rovibrational energy transfer (intramolecular V–V,V–T,R) was found to be more than an order of magnitude less efficient than pure rotational energy transfer (R–T,R–RT) within a vibrational state. The obtained cross sections for vibrational energy transfer are discussed with respect to the different relaxation mechanisms of the molecule, i.e., direct “fast” relaxation NO2(νi)+NO2→NO2(νf)+NO2 and complex forming collisions NO2(νi)+NO2→N2O4→NO2(νf)+NO2, and compared with high pressure recombination rates k∞. The experiments show that the observed collisions are closer to the impulsive than to the complex forming limit. In addition, we have discussed the magnitude of the experimental relaxation rates in terms of excited state couplings and the influence of vibronic chaos on the relaxation of highly excited NO2.

Mode-specific energy analysis for rotating-vibrating triatomic molecules in classical trajectory simulation

A method for the mode-specific energy analysis in a classical trajectory calculation is developed. The pure rotational energy is evaluated by invoking the Eckart condition. To evaluate the vibrational energy in each normal mode, the vibrational velocity is divided into two parts, the angular motion part and the angular motion free part, and the latter is analyzed with the Cartesian and internal coordinate systems. The potential energy of each normal mode is also evaluated in the two coordinate systems. A simple algorithm to include some anharmonicity correction is presented. Sample calculations with nonreacting triatomic molecules, H2O and HCN, show that the internal coordinate system is more adequate than the Cartesian, especially for the linear molecule HCN. An excellent result is obtained for the product (CHO+) of a reaction, suggesting that the present method is adequate for the mode-specific energy analysis of classical trajectory results.

Rotational energy transfer in highly vibrationally excited HCN

The state-resolved collisional self-relaxation of HCN at a vibrational energy content of 10 000 cm−1 is probed directly by combining direct overtone vibration excitation, to prepare energized molecules in the (0,00,3) level, with a laser induced fluorescence monitor of the population evolution from different rotational states. Pure rotational energy transfer dominates the collision dynamics while vibrational relaxation results from only a small fraction of the inelastic events. The depopulation of single j levels proceeds with high efficiency. It is characterized by rates up to 14 times faster than the Lennard-Jones gas kinetic rate conforming to a j dependent distribution which peaks near the Boltzman population maximum and decreases to higher and lower angular momentum values. Approximately 70% of the collisional population removal from the j=4 level proceeds via the ΔJ=±1 channel and 28% proceeds via the ΔJ=±2 direct population transfer step. The results support a long range dipole–dipole mechanism for the energy transfer. This work also investigated various empirical scaling relations and determined that a two parameter fitting law based on the momentum gap or a three parameter modified scaling expression based on the energy gap successfully models the rotational relaxation.

Comparison of near and far infrared spectral data for the water molecule

Differences of the pure rotational energy levels of the water molecule obtained from high-resolution near infrared data (i.e., the combination relations) are compared with appropriate sums or differences of pure rotational transitions obtained from high-resolution far infrared data. The comparison indicates no inconsistency between the near and far infrared data. A sample calculation by least squares method demonstrates that significant improvements in the determination of the pure rotational energy levels of the water molecule are possible.

Energy-Transfer Processes in Monochromatically Excited Iodine Molecules. I. Experimental Results

The fluorescence excited in iodine by the green emission line of mercury, in the presence of foreign gases, has been examined by high-resolution photoelectric photometry. Cross sections for quenching, vibrational, and rotational energy transfer for the v′ = 25, J′ = 34 level of the B 3Π0u+ state of iodine have been obtained, for collisions with 3He, 4He, Ne, Ar, Kr, Xe, H2, O2, CO2, SO2, CH3Cl, and NH3. Emission bands have been rotationally analyzed to yield partial total cross sections for the inelastic processes. These have been corrected for multiple scattering by a computer simulation procedure. The correlation of quenching efficiency with the mass and polarizability of the collision partner, found by Brown for the quenching of the v′ = 15 level of iodine, holds for the v′ = 25 level as well. There is no contribution to quenching efficiency from a permanent electric dipole moment. The data suggest that a complex set of interactions, including electrostatic polarization, spin—orbit forces, and specific chemical effects, are responsible for quenching, indicating a multiplicity of repulsive states contributing to the induced predissociation process. The vibrational energy-transfer efficiency is maximum when the mean collision time equals the period of oscillation of the molecule, which corresponds to a collision reduced mass ≃40 for T = 370°K, v′ = 25 of I2; vibrational transfer is largely independent of the internal structure of the collision partner. The efficiency of pure rotational energy transfer (Δv′ = 0) shows a similar smooth dependence on reduced mass of the collision system, with the exception of the molecules SO2, CO2, and CH3Cl, which are more efficient. Quantitative measurements have been made on partial components of total inelastic cross sections for ΔJ′ up to ±20 angular momentum units, with evidence for a total spread of ΔJ′ up to 30 or 40. The width of the distribution of partial cross section components decreases in the order Δv′=+2>−2≳+1>−1≫0; also, the ΔJ′ distribution is broader for collisions with heavier particles.

Additional Rotational Energy Levels ofH2O andD2O Molecules

An extension of the pure rotational energy levels for ${\mathrm{H}}_{2}$O and ${\mathrm{D}}_{2}$O is made in order to obtain new possible microwave transitions. For ${\mathrm{H}}_{2}$O the levels are given through $J=14$ and for ${\mathrm{D}}_{2}$O through $J=15$. Additional assignments are made in the previously observed absorption spectra. The Wang secular determinant for the asymmetric rotator is expanded, and equations for the energy levels of $J=12$, 13, 14, and 15 are given in terms of the asymmetry parameter.