Scholarly article on topic 'Configuration interaction effect on open M shell Fe and Ni LTE spectral opacities, Rosseland and Planck means'

Configuration interaction effect on open M shell Fe and Ni LTE spectral opacities, Rosseland and Planck means Academic research paper on "Earth and related environmental sciences"

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Academic research paper on topic "Configuration interaction effect on open M shell Fe and Ni LTE spectral opacities, Rosseland and Planck means"

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Configuration interaction effect on open M shell Fe and Ni LTE spectral opacities, Rosseland and Planck means

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Journal of Physics: Conference Series 717 (2016) 012017

doi:10.1088/1742-6596/717/1/012017

Configuration interaction effect on open M shell Fe and Ni LTE spectral opacities, Rosseland and Planck means

D Gilles1, M Busquet2, F Gilleron3, M Klapisch4 and J-C Pain3

1CEA, DSM, IRFU, F-91191 Gif-sur-Yvette, Cedex, France 2Research Support Instruments, Lanham, MD 20706, USA 3 CEA, DAM, DIF, F-91297 Arpajon, France 4Berkeley Research Associates, Beltsville, MD 21042, USA

E-mail: dominique.gilles@cea.fr

Abstract. We have recently shown that iron and nickel open M-shell opacity spectra, up to An = 2 are very sensitive to Configuration Interaction (CI) treatments at temperature around 15 eV and for various densities. To do so we had compared extensive CI calculations obtained with two opacity codes HULLAC-v9 and SCO-RCG. In this work we extend these comparisons to a first evaluation of CI effects on Rosseland and Planck means.

1. Introduction

HULLAC-v9 [1, 2] and SCO-RCG [3, 4] detailed opacity codes can now provide precise spectral opacities for many applications like comparisons with experimental spectra and astrophysical studies [4, 5]. We shall discuss in this work an example of low temperature (kT = 15.3 eV) - low density (ne = 3 10-17 cm-3) plasma condition typical of stellar envelopes [5]. In such example a precise evaluation of the spectrum, and of the associated Rosseland (KR) and Planck (KP) means, supposes a careful evaluation of the billion of open M-shell transitions together with full Configuration Interaction treatment [6]. This is impossible in practise and only partial CI is included in recent improved opacity tables [7]. In a previous work we explored CI effect using HULLAC-v9 until convergence over the set of configurations [6]. We have shown that full CI treatment is really important for the first open M-shell transitions (n = 3, An = 0, 1, 2) by comparing "full CI" and "CI in one Non Relativistic Configuration (NRC)". But it is not practically possible to include higher excited levels (n > 5) using full CI treatment. A complete detailed description of the spectrum and of CI effect on the associated KR and KP requires mixed CI treatments and validation of the results are ongoing.

In this work we have taken advantage of interplaying comparisons [6] between the large possibilities and complementarities of HULLAC-v9 and SCO-RCG codes to discuss full CI influence on KR and KP means. The latter code is able to produce complete and precise LTE spectra, Rosseland and Planck means assuming CI in one NRC and the former can evaluate main full CI effects on the first M-shell transitions. On the example chosen above, we shall discuss and validate a method to provide corrections to KR (and KP) by using comparisons between HULLAC-v9 full CI and CIinNRC results and SCO-RCG ones. The Stark broadening of ion lines is now implemented using simple Dimitrijevic

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9th International Conference on Inertial Fusion Sciences and Applications (IFSA 2015) IOP Publishing

Journal of Physics: Conference Series 717 (2016) 012017 doi:10.1088/1742-6596/717/1/012017

& al. estimates [8] in both codes, but this effect is very small for such low density and will not be discussed in this paper.

2. Main features of the des opacity codes

2.1. The SCO-RCG code. The detailed opacity code SCO-RCG [3, 4, 6] is devoted to the diagnostics and interpretation of spectroscopy experiments in LTE plasmas. The data required for the calculation of the detailed transition arrays (Slater, spin-orbit and dipolar integrals) are obtained from the superconfiguration code SCO, providing in this way a consistent description of the plasma screening effects on the wave functions. Then, the level energies and the lines (position and strength) are computed by an adapted RCG routine of Cowan. The extended list of configurations or super-configurations is generated automatically according to several criterions (on Boltzmann probability, number of successive excitations,...). DLA calculations are performed only for pairs of configurations giving rise to less than 800 000 lines. In other cases, transition arrays are represented statistically by Gaussian profiles in the UTA or SOSA formalisms. The strength of the hybrid approach is that we take into account many satellite lines and highly excited states, using an extension of the PRTA (Partially Resolved Transition Array) model, which enables us to replace many statistical transition arrays by small-scale DLA calculations. The SCO-RCG code, which includes many satellite lines and highly excited states, provides precise opacities, required for astrophysics, inertial confinement fusion, and for the interpretation of laser and Z-pinch experimental spectra. SCO-RCG iron spectral opacity is illustrated in Fig. 1, corresponding to the stellar envelope plasma condition of interest (15.3 eV, 3.2 1017 cm-3), showing the numerous open M-shell transitions contributing to Rosseland and Planck means for 1 < u = hv / kT < 20 (see definitions on Fig. 1). To compute 1/KR we split the spectral range in 3 domains. (a): below u < 0.7 (mainly f-f which gives a small contribution of 5 10-5), (b): 0.7 < u < 10, where Kbb is dominant and can be solely used as it contributes to 96% of the integral, (c): above u=10, where line and b-f contributions are negligible (3 10-6). Same decomposition is applied to KP.

K = K bb-i- K br+ K "-t- K

_v_v__v v v

(M E IO7

v% W i O IO6 IO5

~o o IO4

it IO3

O O IO2

Fig 1: Iron SCO-RCG spectral f-f (blue dotted-dashed), b-f (red long dashed) and total opacities (full black line) at 15.3 eV and 3.2 10 17 cm-3 (< Z > = 8.5). KR and KP means definitions and values are reported on the figure.

2.2. The HULLAC-v9 code. This code is an integrated code for calculating atomic structure and cross sections for collisional and radiative atomic processes, in a jj coupling scheme [1, 2, 6] and references inside). In the Detailed Level description mode it is possible to take into account CI effects inside user defined groups of configurations (GroC). The diagonalization of eigenvectors for all levels of same J

Journal of Physics: Conference Series 717 (2016) 012017

doi:10.1088/1742-6596/717/1/012017

(in one charge state) is performed in each GroC. To be named "full or exact", CI treatment requires the inclusion of the whole set of fine structure levels in the same GroC, what means there will be one GroC per charge state. The keyword CIinNRC in the code generates coefficients of the Hamiltonian only between Relativistic Configurations pertaining to the same parent Non Relativistic Configuration (RCM), whereas CI lifts this restriction. The size of the matrices to be diagonalized obviously and dramatically increases with An. Following previous study conclusions our CI comparisons are performed over most intense and most sensitive to CI An < 2 transitions. More details on the validation are given in [2, 6]. Stark broadening of ion lines is now implemented using [8], together with Doppler and instrumental gaussian. Fig. 2 shows a comparison and a good agreement between SCO-RCG (all transitions) and HULLAC-v9 (assuming "CI in one NRC" and only n = 3, An < 2 transitions) over all the energy range of interest. This is true also for nickel (not illustrated) for same conditions.

Fig. 2: Good agreement between SCO-RCG (all transitions) and HULLAC-v9 (assuming "CI in one NRC" n = 3, An < 2 transitions) spectral opacity for 0.7 < u < 13 and same conditions as Fig. 1. A Gaussian broadening of 0.01 eV is applied to make the figure readable.

3. Evaluation of CI effect using HULLAC-v9 code.

In preceding sections we have shown that An < 2 b-b contributions are sensitive to CI and mainly contribute to KR (and KP) changes. Thus we can now continue and restrict our comparisons to HULLAC full CI and HULLAC CIinNRC b-b An < 2 contributions (Fig. 3 a, b). As we assume LTE, total opacity is just the opacity of different ionic species contributions, weighted by the populations. For our case we get: Fe VIII (0.03), Fe IX (0.41), Fe X (0.52), Fe XI (0.04). On Fig. 3 we have compared the two calculations for Fe VIII, spectral integrand (3a) and integrated over A hv = 0.1 eV (3b). Fig. 3b reveals at which energies the integrals are most sensitive to CI. KR is reduced by 38% because of CI. To obain KR correction for any other density ones just needs to use the appropriated ionic populations. KP linear means is less sensitive to CI (19.5%) and present a quite constant reduction for each individual charge states, 17% (Fe VIII), 19 % (Fe IX), 20 % (Fe X) and 18 % (Fe XI). Full CI and CIinNRC atomic data (energies, cross sections,...) have been stored for the different Fe (and Nickel not illustrated here) ions. We shall repeat this work for other temperatures in the range 10-30 eV to obtain quantitative corrections (ion, T, p) for all stellar envelopes conditions of interest [5]. For larger T we expect inclusion of more excited transitions to be required. These extensive

Journal of Physics: Conference Series 717 (2016) 012017

doi:10.1088/1742-6596/717/1/012017

studies are ongoing to calculate full CI and CIinNRC spectra using the atomic HULLAC-v9 data already calculated [1] and to characterize (T, p) regions of importance.

Fig. 3 a, b: Comparisons between iron HULLAC full CI and HULLAC CIinNRC b-b (An < 2) 1/ Kr contributions: (a) spectral integrand, (b) same after integration over A hv = 0.1 eV for clarity.

4. Conclusion.

In a CI treatment both the CI effects and the number of configurations play a role, but the difficulty increases with the value of the principal quantum number of the upper shell of the transitions. Thus extensive detailed comparisons between SCO-RCG and HULLAC-v9 (including nickel opacities not illustrated in this paper) have been very instructive and useful for understanding the sensitivity of the opacity to CI, to the inclusion of highly excited transitions and to determine the spectral region of importance in the method proposed here. In this example full CI treatment up to An < 2 transitions is enough and make change in the b-b contribution to Rosseland means of about 38% (and around 20% for KP). HULLAC-v9 and SCO-RCG have been upgraded to take into account Stark effects. As expected Stark broadening effect is small compared to Doppler effect for low density - low temperature application. After this first comparison on a typical stellar envelope condition, we shall use HULLAC-v9 CI and CIinNRC atomic data [6] to investigate more conditions (p-T) in the future and we shall also include Stark broadening in our corrections.

References

[1] Busquet M, Bar-Shalom A, Klapisch, Oreg J 2006 J. Phys. IV 133 973.

[2] Busquet M, Klapisch and M Gilles 2013 D EPJ Web of Conferences 59 14004; Gilles D, Turck-Chieze S, Busquet M & al 2013 EPJ Web of Conferences 59 14003.

[3] Pain J-C and Gilleron F 2015 High Energy Density Phys. 15 30.

[4] Pain J-C and Gilleron to be published in 9th IFSA 2015 conference proceedings.

[5] Gilles D, Tuck-Chieze S, G Loisel & al 2011 High Energy Density Phys. 7 312; Gilles D, Tuck-Chieze S, Busquet M, Thais F & al 2013 EAS publication series 58 51; Turck-Chieze S, Gilles D, Le Pennec M, Blenski T & al 2013 High Energy Density Phys. 9 473.

[6] Gilles D, Busquet M, Klapisch M, Gilleron F, and Pain J-C 2015 High Energy Density Phys. 16 1.

[7] New OPLIB (http://aphysics2.lanl.gov/opacity/lanl/); OPAL (https:// http://opalopacity.llnl.gov/).

[8] Dimitrijevic M S and Konjevic N 1980 J. Quant. Spectrosc. Radiat. Transfer 24 451.