On the Bethe approximation

Burgess, A.; Tully, J. A.

doi:10.1088/0022-3700/11/24/019

Cited by 86 publications

(95 citation statements)

References 12 publications

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“…7 of Aggarwal & Keenan (2008). For this reason we have calculated values of Ω up to an energy of 260 Ryd, as discussed in section 5 and hence in our work there is no need to invoke the high energy formulations of Burgess & Tully (1992), as undertaken by Liang et al (2010).…”

Section: Effective Collision Strengthsmentioning

confidence: 95%

“…For example, they included electron exchange only up to J = 12, and for J 13 adopted a coarse mesh of energy of ∼ 0.34 Ryd. More importantly, they performed calculations of Ω in a limited range of energy (∼ 90 Ryd), insufficient for the accurate determination of Υ up to Te = 4 × 10 8 K (∼ 2533 Ryd), although they did take into account the high energy expansion of Ω, based on the formulations suggested by Burgess & Tully (1992). Such compromises in the calculations may explain the large discrepancies in Υ noted by them with previous work.…”

Section: Introductionmentioning

confidence: 99%

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Energy levels, radiative rates and electron impact excitation rates for transitions in Fe xiv

Aggarwal

Keenan

2014

Monthly Notices of the Royal Astronomical Society

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Energies and lifetimes are reported for the lowest 136 levels of Fe XIV, belonging to the (1s 2 2s 2 2p 6 ) 3s 2 3p, 3s3p 2 , 3s 2 3d, 3p 3 , 3s3p3d, 3p 2 3d, 3s3d 2 , 3p3d 2 and 3s 2 4 configurations. Additionally, radiative rates, oscillator strengths and line strengths are calculated for all electric dipole (E1), magnetic dipole (M1), electric quadrupole (E2) and magnetic quadrupole (M2) transitions. Theoretical lifetimes determined from these radiative rates for most levels show satisfactory agreement with earlier calculations, as well as with measurements. Electron impact excitation collision strengths are also calculated with the Dirac atomic R-matrix code (DARC) over a wide energy range up to 260 Ryd. Furthermore, resonances have been resolved in a fine energy mesh to determine effective collision strengths, obtained after integrating the collision strengths over a Maxwellian distribution of electron velocities. Results are listed for all 9180 transitions among the 136 levels over a wide range of electron temperatures, up to 10 7.1 K. Comparisons are made with available results in the literature, and the accuracy of the present data is assessed.

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Section: Effective Collision Strengthsmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Energy levels, radiative rates and electron impact excitation rates for transitions in Fe xiv

Aggarwal

Keenan

2014

Monthly Notices of the Royal Astronomical Society

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“…This leads to significantly different behaviour of the cross-sections with energy, at least at high energy (e.g. Bransden & Joachain 2003;Burgess & Tully 1992). (21)), and g i is the statistical weight of the initial state i.…”

Section: Electronsmentioning

confidence: 99%

Mg line formation in late-type stellar atmospheres

Osorio

Barklem

Lind

et al. 2015

A&A

130

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Context. Magnesium is an element of significant astrophysical importance, often traced in late-type stars using lines of neutral magnesium, which is expected to be subject to departures from local thermodynamic equilibrium (LTE). The importance of Mg, together with the unique range of spectral features in late-type stars probing different parts of the atom, as well as its relative simplicity from an atomic physics point of view, makes it a prime target and test bed for detailed ab initio non-LTE modelling in stellar atmospheres. Previous non-LTE modelling of spectral line formation has, however, been subject to uncertainties due to lack of accurate data for inelastic collisions with electrons and hydrogen atoms. Aims. In this paper we build and test a Mg model atom for spectral line formation in late-type stars with new or recent inelastic collision data and no associated free parameters. We aim to reduce these uncertainties and thereby improve the accuracy of Mg non-LTE modelling in late-type stars.Methods. For the low-lying states of Mg i, electron collision data were calculated using the R-matrix method. Hydrogen collision data, including charge transfer processes, were taken from recent calculations by some of us. Calculations for collisional broadening by neutral hydrogen were also performed where data were missing. These calculations, together with data from the literature, were used to build a model atom. This model was then employed in the context of standard non-LTE modelling in 1D (including average 3D) model atmospheres in a small set of stellar atmosphere models. First, the modelling was tested by comparisons with observed spectra of benchmark stars with well-known parameters. Second, the spectral line behaviour and uncertainties were explored by extensive experiments in which sets of collisional data were changed or removed. Results. The modelled spectra agree well with observed spectra from benchmark stars, showing much better agreement with line profile shapes than with LTE modelling. The line-to-line scatter in the derived abundances shows some improvements compared to LTE (where the cores of strong lines must often be ignored), particularly when coupled with averaged 3D models. The observed Mg emission features at 7 and 12 μm in the spectra of the Sun and Arcturus, which are sensitive to the collision data, are reasonably well reproduced. Charge transfer with H is generally important as a thermalising mechanism in dwarfs, but less so in giants. Excitation due to collisions with H is found to be quite important in both giants and dwarfs. The R-matrix calculations for electron collisions also lead to significant differences compared to when approximate formulas are employed. The modelling predicts non-LTE abundance corrections ΔA(Mg) NLTE−LTE in dwarfs, both solar metallicity and metal-poor, to be very small (of order 0.01 dex), even smaller than found in previous studies. In giants, corrections vary greatly between lines, but can be as large as 0.4 dex. Conclusions. Our results emphasise ...

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“…These are obtained by considering appropriate total multiplicity and orbital angular momentum partial waves. However, in order to converge transitions at higher energies, we explicitly calculate partial waves up to J = 38 and use top-up procedures outlined in Burgess & Tully (1992) to account for further contribution to the total cross-section…”

Section: Electron-impact Excitationmentioning

confidence: 99%

“…Due to the long range nature of the Coulomb potential further contributions to the collision strengths arise from the higher partial waves, particularly for the dipole allowed lines. We compute these additional contributions using the Burgess & Tully (1992) sum rule as well as a geomteric series for the long-range nondipole transitions. Hence converged total collision strengths were accurately generated for all 42,486 transitions among the 292 fine-structure levels included in the collision calculation.…”

Section: Electron-impact Excitationmentioning

confidence: 99%

Photoionization of Co⁺and electron-impact excitation of Co^{2 +}using the DiracR-matrix method

Tyndall

Ramsbottom

Ballance

et al. 2016

Mon. Not. R. Astron. Soc.

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Modelling of massive stars and supernovae (SNe) plays a crucial role in understanding galaxies. From this modelling we can derive fundamental constraints on stellar evolution, mass-loss processes, mixing, and the products of nucleosynthesis. Proper account must be taken of all important processes that populate and depopulate the levels (collisional excitation, de-excitation, ionization, recombination, photoionization, bound-bound processes). For the analysis of Type Ia SNe and core collapse SNe (Types Ib, Ic and II) Fe group elements are particularly important. Unfortunately little data is currently available and most noticeably absent are the photoionization cross-sections for the Fe-peaks which have high abundances in SNe. Important interactions for both photoionization and electron-impact excitation are calculated using the relativistic Dirac Atomic R-matrix Codes (darc) for low ionization stages of cobalt. All results are calculated up to photon energies of 45 eV and electron energies up to 20 eV. The wavefunction representation of Co iii has been generated using grasp0 by including the dominant 3d 7 , 3d 6 [4s, 4p], 3p 4 3d 9 and 3p 6 3d 9 configurations, resulting in 292 fine structure levels. Electron-impact collision strengths and Maxwellian averaged effective collision strengths across a wide range of astrophysically relevant temperatures are computed for Co iii. In addition, statistically weighted level-resolved ground and metastable photoionization cross-sections are presented for Co ii and compared directly with existing work.

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On the Bethe approximation

Cited by 86 publications

References 12 publications

Energy levels, radiative rates and electron impact excitation rates for transitions in Fe xiv

Energy levels, radiative rates and electron impact excitation rates for transitions in Fe xiv

Mg line formation in late-type stellar atmospheres

Photoionization of Co⁺and electron-impact excitation of Co^{2 +}using the DiracR-matrix method

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On the Bethe approximation

Cited by 86 publications

References 12 publications

Energy levels, radiative rates and electron impact excitation rates for transitions in Fe xiv

Energy levels, radiative rates and electron impact excitation rates for transitions in Fe xiv

Mg line formation in late-type stellar atmospheres

Photoionization of Co+and electron-impact excitation of Co2 +using the DiracR-matrix method

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Photoionization of Co⁺and electron-impact excitation of Co^{2 +}using the DiracR-matrix method