Cross Sections For Transitions Research Articles

Optical properties and spectroscopic study of different modifier based Pr3 +:LiFB glasses as optical amplifiers

In this paper, we report the preparation and optical characterization of Pr3+ doped lithium fluoro borate (LiFB) glasses for six different chemical compositions of Li2B4O7-BaF2-NaF-MO (where M=Mg, Ca, Cd and Pb), Li2B4O7-BaF2-NaF-MgO-CaO and Li2B4O7-BaF2-NaF-CdO-PbO. The structural and optical properties of these glasses were characterized by X-ray powder diffraction (XRD), scanning electron microscope (SEM), Fourier transform infrared spectroscopy (FTIR), optical absorption and photoluminescence techniques. The optical absorption spectra of Pr3+ ions in LiFB glasses have been recorded in the UV–VIS-NIR region. The optical absorption data are used to calculate various spectroscopic parameters such as Racah (E1, E2, E3) and spin-orbit interaction (ξ4f) parameters. Judd-Ofelt (J-O) (Ωλ where λ=2, 4 and 6) intensity parameters were determined by applying J-O theory, which in turn used to calculate the radiative properties such as radiative transition probabilities (A), radiative lifetimes (τR), integrated absorption cross-sections (Σ) and branching ratios (βr) for all emission levels of Pr3+ ion in different LiFB glass matrices. By using the J-O theory and luminescence parameters, stimulated emission cross sections (σp) of prominent transitions, 3P0→3H4 and 1D2→3H4 of Pr3+ ion in all LiFB glasses were calculated. 3P0→3H4 possesses higher branching ratios and stimulated emission cross-sections for the Pr3+:LiFB(Mg-Ca) glass, which can be used as a best laser excitation. The optical gain parameter (σpxτR) was noticed higher in Pr3+:LiFB(Mg-Ca) and Pr3+:LiFB(Cd-Pb) glasses for the transition 3P0→3H4 transition, and these glasses have potential for optical amplification at 488 nm wavelength.

High-multipole excitations of hydrogen-like atoms by twisted photons near a phase singularity

We calculate transition amplitudes and cross sections for excitation of hydrogen-like atoms by the twisted photon states, or photon states with angular momentum projection on the direction of propagation exceeding ℏ. If the target atom is located at distances of the order of atomic size near the phase singularity in the vortex center, the transition rates into the states with orbital angular momentum become comparable with the rates for electric dipole transitions. It is shown that when the transition rates are normalized to the local photon flux, the resulting cross sections for are singular near the optical vortex center. The relation to the ‘quantum core’ concept introduced by Berry and Dennis is discussed.

First direct measurement of theC11(α,p)N14stellar reaction by an extended thick-target method

The $^{11}$C($\alpha$, p) reaction is an important $\alpha$-induced reaction competing with $\beta$-limited hydrogen-burning processes in high-temperature explosive stars. We directly measured its reaction cross sections both for the ground-state transition ($\alpha$, $p_{0}$) and the excited-state transitions ($\alpha$, $p_{1}$) and ($\alpha$, $p_{2}$) at relevant stellar energies 1.3 - 4.5 MeV by an extended thick-target method featuring time of flight for the first time. We revised the reaction rate by numerical integration including the ($\alpha$, $p_{1}$) and ($\alpha$, $p_{2}$) contributions and also low-lying resonances of ($\alpha$, $p_{0}$) using both the present and the previous experimental data which were totally neglected in the previous compilation works. The present total reaction rate lies between the previous ($\alpha$, $p_{0}$) rate and the total rate of the Hauser-Feshbach statistical model calculation, which is consistent with the relevant explosive hydrogen-burning scenarios such as the $\nu p$-process.

Inelastic Scattering of Identical Molecules within Framework of the Mixed Quantum/Classical Theory: Application to Rotational Excitations in H2 + H2.

Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes.

Rotational excitation of AlCl induced by its collision with helium: cross sections and collisional rate coefficients

In this work, inelastic rotational collision of AlCl with helium was studied. The CCSD(T) method was used for the computation of an accurate two dimensional potential energy surface (PES). In the calculation of the PES, Al-Cl bond was frozen at the experimental value $4.02678~\mbox{a}_{0}$ . The aug-cc-pVQZ basis sets of Dunning was used throughout the computational process. This basis was completed with a set of 3s3p2d2f1g bond functions placed at mid-distance between the center of mass of AlCl and He atom for a better description of the van der Waals interaction energy. The PES of AlCl-He was found to have a global minimum at ( $R=8.65~\mbox{a}_{0}$ , $\theta=0$ degree), a local minimum at ( $R=7.45~\mbox{a}_{0}$ , $\theta=82$ degree) and a saddle point at ( $R=7.9~\mbox{a}_{0}$ , $\theta=56~\mbox{degree}$ ). The depths of the minima were $20.2~\mbox{cm}^{-1}$ and $19.8~\mbox{cm}^{-1}$ respectively for $\theta=0$ and 84 degrees. The height of the saddle point with respect to the global minimum was $1.3~\mbox{cm}^{-1}$ . The PES, the result of an analytical fit, was expanded in terms of Legendre polynomials, then used for the evaluation of state-to-state rotational integral cross sections for the collision of AlCl with He in the close coupling approach. The collisional cross sections for the transitions occurring among the 17 first rotational levels of AlCl were calculated for kinetic energies up to $4000~\mbox{cm}^{-1}$ . Collisional rate coefficients between these rotational levels were computed for low and moderate kinetic temperatures ranging from 30 to 500 K. A propensity rule that favors odd $\Delta j$ transitions was found.

Inverse Laplace transformation for evaluation of state-specific cross sections for dissociation reaction and vibrational energy transitions

Inverse Laplace transformation for evaluation of state-specific cross sections for dissociation reaction and vibrational energy transitions

Resolution of the vibrational energy distribution function using a direct simulation Monte Carlo-master equation approach

The direct simulation Monte Carlo (DSMC) method is the primary numerical technique for analysis of rarefied gas flows. While recent progress in computational chemistry is beginning to provide vibrationally resolved transition and reaction cross sections that can be employed in DSMC calculations, the particle nature of the standard DSMC method makes it difficult to use this information in a statistically significant way. The current study introduces a new technique that makes it possible to resolve all of the vibrational energy levels by using a master equation approach along with temperature-dependent transition rates. The new method is compared to the standard DSMC technique for several heat bath and shock wave conditions and demonstrates the ability to resolve the full vibrational manifold at the expected overall rates of relaxation. The ability of the new master equation approach to the DSMC method for resolving, in particular, the high-energy states addresses a well-known, longstanding deficiency of the standard DSMC method.

Rotational character of the12Cspectrum investigated through inelastic cross sections via photon emission

In this work the bremsstrahlung and photon dissociation cross sections for transitions between 0+ , 2+ , and 4+ states in 12 C are computed. The nucleus is described within the three-alpha model, and the wave functions are computed by means of the hyperspherical adiabatic expansion method. The continuum states are discretized by imposing a box boundary condition. The transition strengths are obtained from the cross sections, and compared to schematic rotational model predictions. The computed results strongly suggest that the two lowest bands are made, respectively, by the states with angular momentum and parity {01 + , 21 + , 42 + } and {02 + , 22 + , 41 + }. The transitions between the states in the first band are consistent with the rotational pattern corresponding to three alphas in an equilateral triangular structure. For the second band, the transitions are also consistent with a rotational pattern, but with the three alphas in an aligned distribution.

Some Observations about the MOLSCAT

For calculation of cross sections for collisional transitions between rotational levels in a molecule, a computer code, MOLSCAT is available. For the transitions between rotational levels in H2CS due to collisions with He atom, we have calculated cross sections under the CS approximation, for example, for total energy 11 cm−1. The calculations have been done for the single energy 11 cm−1 and for ten combinations. We have found that the cross sections for the single energy 11 cm−1, differ from those in the first seven combinations, but are in agreement with those in the last three combinations. The reason for the difference in the results appears that the MOLSCAT uses the intermediate data of calculations for one energy, in the calculations for other energies. The agreement with the last three combinations may be understood that when the energy of combination is in the decreasing trend, the cross sections for the first (common) energy are equal. It may be suggested to run the MOLSCAT for a single energy at a time.

The realization of the dipole (γ, γ) method and its application to determine the absolute optical oscillator strengths of helium.

The dipole (γ, γ) method, which is the inelastic x-ray scattering operated at a negligibly small momentum transfer, is proposed and realized to determine the absolute optical oscillator strengths of the vanlence-shell excitations of atoms and molecules. Compared with the conventionally used photoabsorption method, this new method is free from the line saturation effect, which can seriously limit the accuracies of the measured photoabsorption cross sections for discrete transitions with narrow natural linewidths. Furthermore, the Bethe-Born conversion factor of the dipole (γ, γ) method varies much more slowly with the excitation energy than does that of the dipole (e, e) method. Absolute optical oscillator strengths for the excitations of 1s2 → 1 snp(n = 3 − 7) of atomic helium have been determined using the high-resolution dipole (γ, γ) method, and the excellent agreement of the present measurements with both those measured by the dipole (e, e) method and the previous theoretical calculations indicates that the dipole (γ, γ) method is a powerful tool to measure the absolute optical oscillator strengths of the valence-shell excitations of atoms and molecules.

A study of internal energy relaxation in shocks using molecular dynamics based models

Recent potential energy surfaces (PESs) for the N2 + N and N2 + N2 systems are used in molecular dynamics (MD) to simulate rates of vibrational and rotational relaxations for conditions that occur in hypersonic flows. For both chemical systems, it is found that the rotational relaxation number increases with the translational temperature and decreases as the rotational temperature approaches the translational temperature. The vibrational relaxation number is observed to decrease with translational temperature and approaches the rotational relaxation number in the high temperature region. The rotational and vibrational relaxation numbers are generally larger in the N2 + N2 system. MD-quasi-classical trajectory (QCT) with the PESs is also used to calculate the V-T transition cross sections, the collision cross section, and the dissociation cross section for each collision pair. Direct simulation Monte Carlo (DSMC) results for hypersonic flow over a blunt body with the total collision cross section from MD/QCT simulations, Larsen-Borgnakke with new relaxation numbers, and the N2 dissociation rate from MD/QCT show a profile with a decreased translational temperature and a rotational temperature close to vibrational temperature. The results demonstrate that many of the physical models employed in DSMC should be revised as fundamental potential energy surfaces suitable for high temperature conditions become available.

Rovibrational Energy Transitions and Coupled Chemical Reaction Modeling of H+H2and He+H2in DSMC

A method of describing the rovibrational energy transitions and coupled chemical reactions in the direct simulation Monte Carlo (DSMC) calculations is constructed for H( 2 S)+H₂(X 1 Σg) and He( 1 S)+H₂(X 1 Σg). First, the state-specific total cross sections for each rovibrational states are proposed to describe the state-resolved elastic collisions. The state-resolved method is constructed to describe the rotational-vibrational-translational (RVT) energy transitions and coupled chemical reactions by these state-specific total cross sections and the rovibrational state-to-state transition cross sections of bound-bound and bound-free transitions. The RVT energy transitions and coupled chemical reactions are calculated by the state-resolved method in various heat bath conditions without relying on a macroscopic properties and phenomenological models of the DSMC. In nonequilibrium heat bath calculations, the state-resolved method are validated with those of the master equation calculations and the existing shock-tube experimental data. In bound-free transitions, the parameters of the existing chemical reaction models of the DSMC are proposed through the calibrations in the thermochemical nonequilibrium conditions. When the bound-free transition component of the state-resolved method is replaced by the existing chemical reaction models, the same agreement can be obtained except total collision energy model.

Exchange and Inelastic OH(+) + H Collisions on the Doublet and Quartet Electronic States.

The exchange and inelastic state-to-state cross sections for the OH(+) + H collisions are computed from wave packet calculations using the doublet and quartet ground electronic potential energy surface (PES) correlating to the open shell reactants, for collision energies in the range of 1 meV to 0.7 eV. The doublet PES presents a deep insertion well, of ≈6 eV, but the exchange reaction has a rather low probability, showing that the mechanism is not statistical. This well is also responsible of a rather high rotational energy transfer, which makes the rigid-rotor approach overestimate the cross section for low Δj transitions and for high collisonal energies. The quartet PES, with a much shallower well, also presents a low exchange reaction cross section, but the inelastic state-to-state cross sections are very well reproduced by rigid-rotor calculations. When the electronic partition is used to obtain the total state-to-state cross section, the contribution of the doublet state becomes small, and the resulting total cross sections become close to those obtained for the quartet state. Thus, the total (quartet and doublet) cross sections for this open shell system can be reproduced rather satisfactorily by those obtained with the rigid-rotor approximation on the quartet state. Finally, we compare the new OH(+)-H cross sections with OH(+)-He ones recently computed. We found significant differences, especially for transitions with large Δj showing that specific OH(+)-H calculations had to be performed to accurately analyze the OH(+) emission from interstellar molecular clouds.

Direct molecular simulation of nitrogen dissociation based on an ab initio potential energy surface

The direct molecular simulation (DMS) approach is used to predict the internal energy relaxation and dissociation dynamics of high-temperature nitrogen. An ab initio potential energy surface (PES) is used to calculate the dynamics of two interacting nitrogen molecules by providing forces between the four atoms. In the near-equilibrium limit, it is shown that DMS reproduces the results obtained from well-established quasiclassical trajectory (QCT) analysis, verifying the validity of the approach. DMS is used to predict the vibrational relaxation time constant for N2–N2 collisions and its temperature dependence, which are in close agreement with existing experiments and theory. Using both QCT and DMS with the same PES, we find that dissociation significantly depletes the upper vibrational energy levels. As a result, across a wide temperature range, the dissociation rate is found to be approximately 4–5 times lower compared to the rates computed using QCT with Boltzmann energy distributions. DMS calculations predict a quasi-steady-state distribution of rotational and vibrational energies in which the rate of depletion of high-energy states due to dissociation is balanced by their rate of repopulation due to collisional processes. The DMS approach simulates the evolution of internal energy distributions and their coupling to dissociation without the need to precompute rates or cross sections for all possible energy transitions. These benchmark results could be used to develop new computational fluid dynamics models for high-enthalpy flow applications.

Free-free Transitions of the Hydrogenic Systems Inside A Dense Plasma Irradiated by A Laser Field

In previous papers [Sinha and Bhatia, Phys. Rev. A 83, 063417 (2011), and Bhatia and Sinha, Phys. Rev. A 86, 053421 (2012)] cross sections for the freefree transitions are calculated for a low energy (external) electron hydrogen scattering in the presence of an external homogeneous, monochromatic, and linearly polarized laser field, without and with the presence of plasma screening, respectively. The present calculation is extended to hydrogenic systems with nuclear charge greater than one. The Debye-Hückel approximation is used to investigate the effect of plasma screening. Calculations are carried out in the soft photon limit. The incident electron is considered to be dressed by the laser field non-perturbatively by choosing the Volkov solutions in both the initial and final states. The scattering wave function for the electron is obtained in the exchange approximation. The laserassisted differential and total cross sections are calculated for single photon emission or absorption and no photon-exchange in the soft-photon limit, the laser intensity being much less than the atomic field intensity. The calculations have been carried out for various values of Debye parameter $\mu$, ranging from 0.08 to 0.30. A strong suppression is noted for the laser-assisted singlet and triplet cross sections compared to the field-free situation. The suppression depends on $\mu$, state of the system as well as on the incident electron momentum. This is unlike in the case of the hydrogen atom in the laser field where the suppression was much more for the triplet cross sections compared to the field-free situation.

Electron impact excitation of helium atom**Project supported by the National Basic Research Program of China (Grant Nos. 2011CB921501 and 2013CB922200), the National Natural Science Foundation of China (Grant Nos. 11274035, 11275029, 11328401, 11371218, 11474031, 11474032, and 11474034), and the Foundation of Development of Science and Technology of Chinese Academy of Engineering Physics (Grant Nos. 2013A0102005 and 2014A0102005).

A method to deal with the electron impact excitation cross sections of an atom from low to high incident energies are presented. This method combines the partial wave method and the first Born approximation (FBA), i.e., replacing the several lowest partial wave cross sections of the total cross sections within FBA by the corresponding exact partial wave cross sections. A new set of codes are developed to calculate the FBA partial wave cross sections. Using this method, the convergent e–He collision cross sections of optical-forbidden and optical-allowed transitions at low to high incident energies are obtained. The calculation results demonstrate the validity and efficiency of the method.

Theoretical calculations of rotationally inelastic collisions of He with NaK(A (1)Σ(+)): Transfer of population, orientation, and alignment.

We have performed extensive calculations to investigate thermal energy, rotationally inelastic collisions of NaK (A(1)Σ(+)) with He. We determined a potential energy surface using a multi-reference configuration interaction wave function as implemented by the GAMESS electronic structure code, and we have performed coupled channel scattering calculations using the Arthurs and Dalgarno formalism. We also calculate the Grawert coefficients B(λ)(j, j') for each j → j' transition. These coefficients are used to determine the probability that orientation and alignment are preserved in collisions taking place in a cell environment. The calculations include all rotational levels with j or j' between 0 and 50, and total (translational and rotational) energies in the range 0.0002-0.0025 a.u. (∼44-550 cm(-1)). The calculated cross sections for transitions with even values of Δj tend to be larger than those for transitions with odd Δj, in agreement with the recent experiments of Wolfe et al. (J. Chem. Phys. 134, 174301 (2011)). The calculations of the energy dependence of the cross sections and the calculations of the fraction of orientation and alignment preserved in collisions also exhibit distinctly different behaviors for odd and even values of Δj. The calculations also indicate that the average fraction of orientation or alignment preserved in a transition becomes larger as j increases. We interpret this behavior using the semiclassical model of Derouard, which also leads to a simple way of visualizing the distribution of the angles between the initial and final angular momentum vectors j and j'. Finally, we compare the exact quantum results for j → j' transitions with results based on the simpler, energy sudden approximation. That approximation is shown to be quite accurate.

Quantum scattering calculations for ro-vibrational de-excitation of CO by hydrogen atoms.

We present quantum-mechanical scattering calculations for ro-vibrational relaxation of carbon monoxide (CO) in collision with hydrogen atoms. Collisional cross sections of CO ro-vibrational transitions from v = 1, j = 0 - 30 to v' = 0, j' are calculated using the close coupling method for collision energies between 0.1 and 15,000 cm(-1) based on the three-dimensional potential energy surface of Song et al. [J. Phys. Chem. A 117, 7571 (2013)]. Cross sections of transitions from v = 1, j ≥ 3 to v' = 0, j' are reported for the first time at this level of theory. Also calculations by the more approximate coupled states and infinite order sudden (IOS) methods are performed in order to test the applicability of these methods to H-CO ro-vibrational inelastic scattering. Vibrational de-excitation rate coefficients of CO (v = 1) are presented for the temperature range from 100 K to 3000 K and are compared with the available experimental and theoretical data. All of these results and additional rate coefficients reported in a forthcoming paper are important for including the effects of H-CO collisions in astrophysical models.

Open-Ended Recursive Approach for the Calculation of Multiphoton Absorption Matrix Elements.

We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange–correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange–correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties.

Absorption and luminescence characteristics of transitions of the holmium ion in -doped aluminosilicate preforms and fibres

We have obtained the spectral dependences of the absorption cross sections for the and transitions in -doped aluminosilicate fibres and the spectral dependence of the stimulated emission cross section for the laser transition in -doped aluminosilicate fibre preforms. The lifetime of the upper laser level in the preforms has been determined.