R matrix calculations

Comparisons between experimental spectra and R matrix calculations 

In this chapter we have shown that complicated spectra can be understood using QDT. We have considered examples of fitting spectra to QDT. Now we would like to compare the results of R matrix calculations of spectra to the experimental spectra in cases in which fitting would have been hopeless or nearly so. 

The first spectra which were synthesized using the R matrix approach were, not surprisingly, vuv spectra, and synthetic spectra of Mg, Ca, Sr, and Ba have all been calculated.22-25 In Fig. 19.2 we show the Ba vuv spectrum. While the region above the Ba+ 6p1/2 limit is understandable, the region below the limit exhibits 

Neukammer, H. Rinneberg, G. Jonsson, W.E. Cooke, H. Hieronymus, A. Konig, K. Vietzke, and H. Springer-Bolk, Phys. Rev. Lett. 55,1979 (1985). 

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Stewart WE, Prober R. Matrix calculation of multicomponent mass transfer in isothermal systems. Ind Eng Chem Fundam 1964 3 224-235. 

Nesbet, R.K., Noble, C.J., Morgan, L.A. and Weatherford, C.A. (1984). Variational R-matrix calculations of c + H2 scattering using numerical asymptotic basis functions, J. Phys. B 17, L891-L895. 

Nestmann, B.M., Nesbet, R.K. and Peyerimhoff, S.D. (1991). A concept for improving the efficiency of R-matrix calculations for electron-molecule scattering,... 

Initially the molybdenum fluxes in [55] measured via atomic Mo-lines (379.8 nm, 386.4 nm and 390.3 nm) led to unreasonably high flux values. This was the case because for the calculation of the respective excitation rates the formula of van Regemorter was used [56], as these lines are optically coupled to the ground state (resonance lines). Therefore, experiments were performed to measure the excitation and ionization rates directly both in a linear plasma machine [57] and in a crossed beam experiment with a thermal molybdenum emitter [58], The results can be seen in Fig. 6.17 and show that the experimental values for excitation are about a factor of 5 larger than those from the van Regemorter formula, which leads to a reduction of the flux by the same order according to the smaller S/XB. More refined R-Matrix calculations have later confirmed the same factor and are included in Fig. 6.3. 

These are R-matrix calculations, which are part of the international Opacity Project (OP) [15], theoretical results from the MCHF database collection by Tachiev and Froese Fischer [16], and calculations by Blackford and Hibbert with the CIV 3 code [17]. In Fig. 17.9 the ratios of the OP and CIV oscillator strengths to the MCHF results are plotted on a logarithmic scale versus the MCHF oscillator strength (/-value) data. 

For heavier atoms the pure fine-structure effect is expected to break down due to relativistic effects. In the very heavy open-shell target atom thallium (Z=81) the ground-state atoms populate only one of the fine-structure levels, and the effect may be important at low energies. In an R-matrix calculation using magnetic potentials derived from the Dirac equation, Goerss, Nordbeck and Bartschat (1991) showed that... 

In fig. 9.8 the experimental results for the Stokes parameters Pi, P3, P5, Pe (Sohn and Hanne, 1992) and P and P4 (Goeke et ai, 1989) are shown together with theoretical results of a relativistic R-matrix calculation by Bartschat (19916). The parameters P5,Pe and the asymmetry parameters (fig. 9.9) are normalised to Pe = 1. The large values of these latter spin-dependent parameters show the importance of exchange and the spin—orbit interaction in the excitation of Hg (6 Pi) by electron impact. 

Note on collision strengths the vast majority of these values are computed, not experimental. This does not mean that they have zero uncertainty A recent example is given by the case of [S III] (Tayal Gupta 1999). This new 27-state R-matrix calculation resulted in changes of approximately 30% in the collision strengths for optical and IR forbidden transitions from earlier calculations. This shows that even for commonly-observed ions the atomic data is still in a state of flux. Observers should take into account the probable uncertainty in atomic data when estimating errors in abundances. 

Stewart, W. E., Multicomponent Mass Transfer in Turbulent Flow, AIChE J, 19, 398-400 (1973). Stewart, W. E. and Prober, R., Matrix Calculation of Multicomponent Mass Transfer in Isothermal... 

In Fig. 7, we show the cross section for photodetachment of Li via the S Skp channel over photon energies of approximately 5.04-5.16 and 5.29-5.46 eV. These ranges cover the regions below, and including, the Li(42p) and Li(52p) thresholds, respectively. Several Feshbach window resonances are observed to lie below these thresholds. In the figure the present measurements are compared with the result of a recent eigenchannel R-matrix calculation by Pan et al. [28]. The experimental resolution, which is estimated to be about 25 p,eV, is sufficiently high compared to the typical resonance widths that a direct comparison with theory can... 

Here, the index n represent the parameters for each resonance. Using this method we determined the parameters for resonances c and d in Fig. 7a. The measured positions and widths are shown in Table 1, along with corresponding values calculated by Lindroth [6]. There is a good agreement between the experiment and theory in this case. Lindroth s resonance parameters are derived directly from a complex rotation calculation. The R-matrix calculation of Pan et al. [28] did not explicitly yield the resonance parameters and therefore cannot be used for comparison. Since the Fano formula strictly only applies to total cross sections, the values of the Cj shape parameters are not entirely meaningful in the context of partial cross sections. This parameter is therefore omitted in the table. 

Fig. 1. Integral cross sections for elastic scattering of electrons by N2O. Short dashes, R-matrix calculation of Sarpal et al. (1996a, 1996b) long dashes, /1-matrix calculation of Morgan et al. (1997) solid line, SMC calculation of Winstead and McKoy (1998) squares, measurements of Johnstone and Newell (1993). The total scattering cross section measured by Szmytkowski etal. (1984) is also shown for comparison (crosses).

The results presented in Ref. 16 by Bocchetta and Gerratt and in this article [27] using non-orthogonal bases for R-matrix calculations are therefore most interesting for their implications for reactive... 

Dora, A., Tennyson, J., Bryjko, L., van Mourik, T. (2009). R-matrix calculation of low-energy electron collisions with uracil. The Journal of Chemical Physics, 130,164307. 

R-matrix calculation by Taylor and Burke, ref. 81. length and - - - velocity MBPT calculation by Carter and Kelly, ref. 83. Dots from previous measurement, described in ref, 84. 

The 3 parameter to describe the angular distribution of photoelectrons ejected from the 2s subshell of carbon has been calculated for the ionic states P, D, and by Chang and TaylorS5 using matrix elements obtained in R-matrix calculations. Their results, shown in Fig. 13, show considerable structure due to resonances. In this figure, the higher members of resonance series and minor series are not displayed. 

R-matrix calculations have also been carried out for the 2p ground state of atomic nitrogen by Le Dourneuf et al. ... 

R-matrix calculations have frequently included recouplings which leave the ion in an excited multiplet of the lowest configuration of the ion. There have been MBPT calculations for Fe 3d 4s 3d k or 3d 4pk which have resulted in an increase in the cross section near threshold by approximately 20%. There has also been a recent MBPT calculation by Ishihara et al for neon ls 2s 2p ls2s 2p 3s. Near threshold this process was calculated to reach a maximum of 5% of the single photoionization cross section and then drop with increasing energy for neon. ... 

A. Dora, J. Tennyson, L. Bryjko, and T. van Mourik, J. Chem. Phys., 130, 164307 1-8 (2009). R-Matrix Calculation of Low-Energy Electron Collisions with Uracil. 

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