Coupled-state Calculations Research Articles

A failing of coupled-states calculations for inelastic and pressure-broadening cross sections: Calculations on CO2–Ar

Fully quantal benchmark calculations of pressure-broadening cross sections for infrared and Raman lines of CO2 perturbed by Ar are carried out using both close-coupling (CC) and coupled-states (CS) calculations. CS calculations are found to underestimate the cross sections by up to 15%. The effect occurs even for isotropic Raman cross sections, which are not affected by reorientation contributions. The discrepancy arises mostly for collisions with large orbital angular momenta l, occurring on the long-range part of the potential. It may be attributed to collisions that are adiabatic rather than sudden in nature. A hybrid computational method, employing CS calculations for low l and decoupled l-dominant (DLD) calculations for high l, offers a promising solution.

Quantum mechanical study of the vibrational relaxation of O2+ colliding with Kr

Coupled states calculations on the vibrational relaxation of O2+(v=1) colliding with Kr are reported. In the first stage, calculations have been done on single potential energy surfaces and different surfaces have been used. Then treating O2+ as a molecule in a Π ground electronic state, we have performed quantum scattering calculations on the vibrational relaxation on two 1 2A″ and 1 2A′ surfaces. A significant effect due to the inclusion of the second potential surface is reported. A comparison of the calculated rate constants with available experimental data is made.

Rotationally resolved differential scattering cross sections for the reaction F+para-H2 (v=0, j=0)→HF(v′=2, 3, j′)+H

Time-of-flight spectra of HF products in the v′=2 vibrational state from reactive scattering of F atoms from para-H2 exhibit at least four smaller peaks which are assigned to the rotational states j′=7, 8, 9, and 10. The center-of-mass rotational distributions are in good agreement with accurate quantum mechanical and approximate coupled states calculations.

Algebraic coupled-state calculations of positron-hydrogen scattering near the positronium-formation threshold

The algebraic coupled-state method is used to investigate the various anomalies of the cross sections near the positronium-formation threshold in positron-hydrogen scattering. In particular, our calculations confirm the existence of the S-wave Wigner's cusp of the elastic ${e}^{+}\ensuremath{-}\mathrm{H}$ cross sections that was published in the recent literature. We show that these so-called anomalous behaviors can actually be understood well within the framework of the theory of scattering near thresholds and that they should exist independently of whether the cross sections are calculated accurately or not. The complete results of a fairly comprehensive calculation in the vicinity of the positronium-formation threshold using several different coupling schemes (large and small) are presented to demonstrate our finding.

Microwave electronic spectrum of the Ne···Ne+ long-range complex

We have used an ion beam method to observe 276 transitions in the microwave electronic spectrum of the long-range Ne···Ne+ ionic complex, involving levels which lie within 10.2 cm-1 of the lowest dissociation limit. An electric field dissociation technique has been used to access directly levels with binding energies of up to 6.8 cm-1 and we have been able to construct an experimental energy level pattern for at least 17 vibration–rotation progressions in this region of the potential. Microwave–microwave double resonance and Zeeman effect measurements have been crucial in establishing this energy level pattern. The levels are populated by the vertical electron impact ionisation of the neutral neon dimer, produced by means of a nozzle beam, with some population of higher rotational levels of the dimer ion probably resulting from larger cluster fragmentation. A case (c) effective Hamiltonian analysis has been successful in describing the levels in six of the progressions but a full theoretical analysis requires a coupled-states calculation. Analysis of Zeeman splittings for the microwave lines identifies the J values of the levels involved. The observed g-factors provide information about the transition from case (c) to case (e) coupling as both the rotational quantum number increases and the energy levels become more weakly bound.

Energy corrected sudden calculations of linewidths and line shapes based on coupled states cross sections: The test case of CO2–argon

The accuracy of the energy-corrected sudden (ECS) formalism for line shape calculations is investigated, using coupled states calculation for CO2–Ar collisions on the recently developed “single repulsion” potential of Hutson et al. [J. Chem. Phys. 107, 1824 (1997); 105, 9130 (1996)]. Inelastic cross sections σ0(L→0,E)≡QL′(E) are calculated using the MOLSCAT program, and then averaged over Maxwell–Boltzmann kinetic energy distributions to give the thermally averaged “basic rates” QL′(T) needed in the ECS formalism. The ECS linewidths for low initial J, Ji⩽16, are sensitive only to the low-L basic rates, for which the CS calculations are converged; comparing them with directly calculated CS linewidths thus gives a stringent test of the ECS model, and it works well (within 10%). However, for higher Ji lines and for band shape calculations, basic rates for higher L are needed for convergence. These are obtained by an extrapolation procedure based on experimental data, using an exponential power law and the adiabaticity factor recently suggested by Bonamy et al. [J. Chem. Phys. 95, 3361 (1991)] ECS calculations using the resulting basic rates are designated “extrapolated CS-ECS calculations,” and are found to give accurate results for high-J linewidths, for near-wing absorption and for band profiles over a very wide range of perturber pressures (up to 1000 atm).

A combined experimental and theoretical study of rotational energy transfer in collisions between NO(X 2Π1/2, v=3,J) and He, Ar and N2 at temperatures down to 7 K

Infrared-ultraviolet double resonance (IRUVDR) experiments have been implemented in the ultra-cold environment provided by a CRESU (Cinétique de Réaction en Ecoulement Supersonique Uniforme) apparatus. With this technique rate coefficients of two kinds have been measured for rotational energy transfer in collisions between NO and He, Ar and N2: (a) rate coefficients for total removal from specific states of NO(X 2Π1/2; v=3; J=0.5, 3.5 or 6.5) and (b) state-to-state rate coefficients for rotational energy transfer from these levels to specific final states. Using different Laval nozzles, results have been obtained at several different temperatures: for He as collision partner, 295, 149, 63, 27, 15 and 7 K; for Ar, 139, 53, 44 and 27 K; and for N2, 86 and 47 K. The thermally averaged cross-sections for total removal show remarkably little variation, either with temperature or with initial rotational state. The variation of state-to-state rate coefficients with ΔJ shows three general features: (i) a decrease with increasing ΔJ; (ii) a propensity to favor even ΔJ transitions over odd ΔJ changes; and (iii) at lower temperatures, decreases in J are increasingly favored over increases in J and the distribution of rate coefficients against ΔJ becomes narrower. The experimental rate coefficients for collisions with He and Ar are compared with those from both close coupled and coupled states calculations based on potential energy surfaces determined within the coupled electron pair approximation (CEPA) with a large atomic orbital basis set. The agreement between theory and experiment of both the total and the state-to-state rate coefficients is excellent over the complete range of temperatures covered in the experiments.

Positron scattering by atoms

We describe the present status of coupled-state calculations for positron scattering by ‘one-electron’ atoms. We show how pseudostates are used to represent the continuum channels. Illustrative results from positron scattering by atomic hydrogen and the alkali metals are presented.

Differential cross sections and polarization of in collisions

The presence of an axially symmetric angular distribution of energetic protons in astrophysical plasmas can be detected by measuring the linear polarization of the lines emitted from collisionally excited levels of atoms. Another signature of proton beams can be found in the study of line profiles. For a quantitative interpretation of the observations of the line one needs to know all the relevant integrated and differential cross sections and the polarization fraction. Coupled-state calculations based on a two-centre expansion in atomic orbitals and pseudostates were carried out for protons colliding with H(1s) in the impact energy range 1-100 keV. Differential cross sections for excitation and capture from the level n = 1 to the level n = 3 as well as the total and differential polarization fraction of the line are presented. It is shown that the differential cross sections reach a maximum for an angle varying from 1 to degree when the collision energy varies from 1 to 40 keV. For 1 keV collisions, this leads to large recoil velocities and, as a consequence, to a large Doppler broadening. At the same energy, the resulting polarization fraction is found to have only small variations with the deflection angle.

Simulation of Coherent Nonadiabatic Dynamics Using Classical Trajectories

In this paper, we describe a trajectory-based implementation of the semiclassical-limit Liouville equation approach to molecular dynamics on multiple electronic surfaces. The formalism is briefly reviewed, and a realization of the general theory in the context of a classical trajectory-based molecular dynamics algorithm is described. The method is applied to a model problem consisting of one-dimensional motion on two coupled electronic surfaces, and the results are compared with coupled-state wave packet calculations. Excellent agreement is obtained, even for the detailed phase space structure of the nonclassical electronic coherences, demonstrating that electronic coherent effects can be included naturally in generalized classical molecular dynamics simulations.

Coupled-state calculations of positron-hydrogen scattering

An algebraic coupled-state calculation of positron-hydrogen scattering carried out with an enlarged eight-state (E8S) coupling scheme, that is composed of a sufficiently high number of short-ranged correlation terms and eight hydrogen and positronium states $[(1s,2s,2p,3\overline{p})\mathrm{H}\ensuremath{-}(1s,2s,2p,3\overline{p})\mathrm{Ps}],$ provides results of the phase shift and cross section, agreeing excellently with our accurate enlarged six pseudostate (E6PS) values in both ${e}^{+}\ensuremath{-}\mathrm{H}$ and $\mathrm{Ps}(1s)\ensuremath{-}p$ entrance channels. Our results serve to assert that very accurate values of the phase shift and cross section in both entrance channels have been attained with our E6PS, E8PS, and E8S Harris-Nesbet calculations. The present E8S calculation supersedes our deficient modified enlarged six-state one done previously.

Positron-hydrogen collisions at low energies

The Harris-Nesbet algebraic method was used to carry out a large coupled-state calculation of ${\mathrm{e}}^{+}$ -H scattering at energies below the first excitation threshold of hydrogen. The six-state (1s,2s,2p H--1s,2s,2p Ps) coupling scheme was extended to include an adequate number of short-ranged functions of both hydrogenic and positroniumic types and the H 3p-bar pseudostate. Phase shifts and cross sections of partial waves from L=0 to 6 were obtained for ${\mathrm{e}}^{+}$ -H (1s) scattering as well as for Ps(1s)-p scattering. Our results are to be compared with those obtained by other research groups with some large-scale calculations employing, however, different numerical methods of approach. Our results agree excellently with the values calculated with a variational method by Bhatia et al. and by Humberston and co-workers and with the 21-state close-coupling approximation by Mitroy and co-workers.

Excitation and ionization of atomic hydrogen by antiprotons

Single-centred coupled states calculations of cross sections for excitation and ionization of atomic hydrogen by antiprotons are compared to previous calculations and to experiment for projectile energies in the range 1 - 300 keV. A noticeable disagreement between experiment and theory is found for the antiproton ionization results in the range 30 - 80 keV.

Double ionization of helium by slow antiprotons

Coupled-states calculations with large target-centred basis sets have been used to compute ionization probabilities and cross sections for at collision energies down to 10 keV. The results are in good agreement with recent theoretical calculations based on numerical solution of the time-dependent Schrödinger equation but there are no experimental data. Both an independent particle model and an independent event model were used to carry out calculations for . These results are in good agreement with experiment at 40 keV and above but differ at lower energies. The impact-parameter-dependent probabilities for these collisions were used in the independent event model to calculate helium double-ionization cross sections and excellent agreement was found with experimental measurements between 13 and 200 keV, but this simple way of treating correlation fails at higher collision energies.

Investigation of the vacancy sharing process in L-shell ionization of gold and bismuth by boron ions

Coupled-states calculations have been made to interpret the L-subshell ionization cross section data measured by Padhi et al for collisions of B ions with Au and Bi in the energy range 0.48 - 0.88 MeV . The calculated cross sections are in a reasonable agreement with the measured values. It has been shown that simple static Stark mixing of the target 2s and 2p atomic wavefunctions is inadequate for the description of the ionization process, and the dynamical treatment of the subshell couplings based on the solution of the coupled equations of the problem is necessary for the satisfactory description of the process.

Sequences of threshold resonances in - H scattering

Sequences of S, P and D resonances in positron - hydrogen scattering were shown to still exist below the n = 2 H excitation threshold in a coupled-state calculation employing a large coupling scheme. The positions of the resonances were found to shift slightly away from the threshold and their widths to broaden slightly, compared with those previously determined with smaller schemes. The energy ratios and width ratios of the successive resonances of a sequence still reasonably satisfy the predicted `scaling law'.

Positron scattering by potassium

Coupled-state calculations in a K(4s,4p,5s,5p,3d) + Ps(1s,2s,2p,3s,3p,3d) approximation are reported for positron scattering by ground-state potassium in the energy range 0.5 - 60.0 eV. Comparison is made with the earlier work of Hewitt and co-workers in a K(4s,4p,5s,5p) + Ps(1s,2s,2p) approximation. For the first time cross sections for positronium formation in n = 3 states are obtained. We support the conclusion of Hewitt et al that above about 4 eV positronium formation is mainly into excited states, although we disagree significantly on the distribution of the excited state population. Fairly good agreement is obtained with the measurements of Zhou and co-workers for total positronium formation when scaling is used to estimate the amount of positronium in states with . Our cross sections for elastic scattering, 4s - 4p, 4s - 5s and 4s - 5p excitation of potassium are in relatively good agreement with those of Hewitt and co-workers but our calculations also emphasize the importance of the 4s - 3d excitation which is omitted in their approximation. Atom excitation to the n = 5 level is found to be a relatively minor process. Good agreement is obtained with the total cross section measurements of Kwan and co-workers and Parikh and co-workers when these are normalized upwards by 10% and corrections made for near forward elastic scattering. This upward normalization lies within the quoted overall 21% error on the measurements. Below 4 eV the calculated total cross section is dominated by elastic scattering while at high energies 4s - 4p excitation is the main contributor. In the vicinity of 6 eV, and consistent with the measurements of Parikh and co-workers, the total cross section displays a pronounced peak which derives largely, although not totally, from positronium formation. Positronium formation is not important above about 30 eV.

Cross-channel coupling in positron-atom scattering

Coupled-state calculations including positronium channels are reported for positron scattering by atomic hydrogen, lithium and sodium. Integrated cross sections and total cross sections are presented for all three atoms. For lithium differential cross sections are also given. Throughout, comparison is made between results calculated with and without inclusion of the positronium channels. S-wave cross sections for positron scattering by atomic hydrogen in the Ps(1s, 2s, 2p)+H(1s, 2s, 2p) approximation show the high energy resonance first observed by Higgins and Burke in the coupled-static approximation. This resonance has now moved up to 51.05 eV and narrowed in width to 2.92 eV. Other pronounced structure is seen in the S-wave cross sections between 10 and 20 eV; it is tentatively suggested that this structure may be due to the formation of a temporary pseudo-molecular collision complex. Results calculated in the Ps(1s, 2s, $$\overline {3s} ,\overline {4s} $$ , 2p, $$\overline {3p} ,\overline {4p} ,\overline {3d} ,\overline {4d} $$ ,+H(1s, 2s, $$\overline {3s} ,\overline {4s} $$ , 2p, $$\overline {3p} ,\overline {4p} ,\overline {3d} ,\overline {4d} $$ approximation show convergence towards accurate values in the energy region below and in the Ore gap. Contrary to previous work on lithium using only an atomic basis, it is found that coupling to the 3d state of lithium is not so important when positronium channels are included; this is because a mixed basis of atom and positronium states gives a more rapidly convergent approximation than an expansion based on atom states alone. The threshold behaviour of the elastic cross section and the Ps(1s) formation cross section for lithium is investigated. Results in the Ps(1s, 2s, 2p)+Na(3s, 3p) approximation for sodium show good agreement with the total cross section measurements of Kwan et al.

L-shell X-ray production cross sections in 26Fe, 28Ni, 29Cu, 30Zn, 31Ga and 32Ge by 0.5 to 8.0 MeV He ions

L-shell X-ray production cross sections by 0.5 to 5.0 MeV He+ and 5.5 to 8.0 MeV He2+ ions are reported for elements with X-rays between 0.70 keV and 1.19 keV. Thin targets of 26Fe, 28Ni, 29Cu, 30Zn, 31Ga and 32Ge were manufactured using a cleaning process that reduced the level of light element impurities. The X-rays were measured with a windowless Si(Li) detector, whose efficiency was determined by the atomic-field bremsstrahlung method. The data are compared to the predictions of the first-order Born and the ECPSSR theories using the single- and multiple-hole fluorescence yields. The ECPSSR theory is clearly superior to the first-order Born approximation, although the data fall-when single-hole fluorescence yields are used-on the average about 5% below the ECPSSR. At the lowest velocity, however, on the average this theory underestimates our measurements by 15% when single-hole fluorescence yields are employed. When multiple-hole fluorescence yields are used, the theory is within 3% of the averaged data at the lowest ion velocity. Coupled-state calculations that account for intrashell transitions and recently proposed modifications to the ECPSSR treatment of the binding effect give larger cross sections than the ECPSSR and hence-when multiple-hole fluorescence yields are used-they are in larger disagreement with our measurements.

On the generation of preferential Λ-doublet populations in the collisional relaxation of highly rotationally excited CH(X 2Π)

By means of full quantum close-coupling and coupled states calculations based on an ab initio potential energy surface for the Ar–CH system, we confirm a propensity seen experimentally by Hancock, Stuhl, and their co-workers. During the rotational relaxation of high rotational levels of the CH(X 2Π) radical, produced by photolysis of a suitable precursor, there appears a clear population imbalance in favor of the Λ-doublet levels of Π(A″) symmetry. A full kinetic simulation, based on the calculated cross sections, reproduces nearly quantitatively the experimental observations of both the temporal evolution and the pressure dependence of this Λ-doublet asymmetry. This asymmetry is a consequence of both an enhanced depletion of high N Π(A′) levels and the enhanced formation of Π(A″) levels in the next lower (N−1) manifolds. The physical origin of this propensity involves a crossing between two adiabatic bender potentials which follow, respectively, the A′ and A″ potential energy surface (PES). This crossing occurs only for the ‘‘helicopter-like’’ approach of the CH molecule, in which its rotational angular momentum is aligned along the initial relative velocity vector. Thus, a strong v, N correlation in the reactant channel results in a strong Λ, N correlation in the product channel.