Paper presented by Sterling et al. at the IAU Symposium 283, Planetary Nebulae: an Eye to the Future, 25-29 July 2011, Tenerife, Spain.

1. Advances in Atomic Data for Neutron-Capture Elements
N. C. Sterling1, M. C. Witthoeft2, P. C. Stancil3, D. A. Esteves4, R. C. Bilodeau5,6, R. L. Porter3, & A. Aguilar3
(1: Michigan State U., 2: NASA/GSFC, 3: U. Georgia, 4: U. Colorado, 5: LBNL/ALS, 6: Western Michigan U.)
ABSTRACT
Neutron(n)-capture elements (atomic number Z>30), which can be produced in planetary nebulae (PNe) progenitor stars via s-process nucleosynthesis, have been detected in nearly 100 PNe. This demonstrates that nebular spectroscopy is a
potentially powerful tool for studying the production and chemical evolution of trans-iron elements. However, significant challenges must be addressed before this goal can be achieved. One of the most substantial hurdles is the lack of
atomic data for n-capture elements, particularly that needed to solve for their ionization equilibrium (and hence to convert ionic abundances to elemental abundances). To address this need, we have computed multi-configuration distorted-
wave photoionization (PI) cross sections and radiative recombination (RR) and dielectronic recombination (DR) rate coefficients for the first six ions of Se and Kr. The calculations were benchmarked against experimental PI cross section
measurements conducted at the Advanced Light Source synchrotron radiation facility. We estimate the internal uncertainties to be 30--50% for PI cross sections, ≲10% for RR, and from 20% up to two orders of magnitude for DR rate
coefficients. In addition, we computed charge transfer (CT) rate coefficients for ions of six n-capture elements using multi-channel Landau Zener and Demkov codes. We have begun incorporating these data into the photoionization code
Cloudy to derive ionization correction factors for Se and Kr, and will test the sensitivity of abundance determinations to atomic data uncertainties via Monte Carlo simulations. These efforts will enable the accurate determination of nebular
Se and Kr abundances, allowing robust investigations of s-process enrichments in PNe.
MOTIVATION
In spite of their low cosmic abundances, trans-iron elements are sensitive probes of the nucleosynthetic
histories of astrophysical objects and the chemical evolution of the Universe (e.g., Sneden et al. 2008). Much of
our knowledge of the synthesis of these elements (via slow or rapid n-capture nucleosynthesis ! the s-process
and r-process) is based on the interpretation of abundances derived from stellar spectra. Nebular spectroscopy
provides access to several n-capture elements that are not detectable in stellar spectra, and enables investigations
of classes of stars and stages of evolution in which stellar photospheres are obscured by heavy mass loss (e.g.,
intermediate-mass AGB stars, M = 4!8 M⊙). These elements are of particular interest in PNe, since they can be
produced by s-process nucleosynthesis during the thermally-pulsing AGB stage of evolution.
Typically only one or two ions of a given trans-iron element are detected in individual nebulae. To derive
elemental abundances, one must therefore estimate the abundances of unobserved ions. This is most robustly
accomplished by numerical simulations of the nebular ionization balance, but the accuracy of such models
strongly depends on the availability of accurate atomic data for processes that control the ionization balance of
elements. In photoionized nebulae such as PNe, these data include photoionization (PI) cross sections, and rate
coefficients for radiative recombination (RR), dielectronic recombination, and charge transfer (CT). These data
are unknown for the overwhelming majority of n-capture element ions. Sterling et al. (2007) showed that
inaccurate data for these processes can lead to abundance uncertainties of factors of two or higher.
Figures 4-5. Comparison of RR (dotted lines), DR (dashed lines), and total Figure 6. Total rate coefficients for CT
recombination (solid lines) rate coefficients for Se and Kr ions. Note that recombination of X+ (dash-dot-dot-dot-
ATOMIC DATA CALCULATIONS indicated ions are the target species (i.e., before recombination). dash curves), X2+ (dash-dot-dash curves),
X3+ (dotted curves), X4+ (solid curves), and
We have computed PI cross sections and RR and DR rate coefficients for the first six ions of Se and Kr X5+ (dashed curves), where X is the
(Sterling & Witthoeft 2011; Sterling 2011), and similar calculations are underway for Xe. We employed the element indicated in each panel.
atomic structure code AUTOSTRUCTURE (Badnell 1986), which efficiently computes multi-configuration
distorted-wave PI cross sections and radiative and autoionization rates, and accounts for relativistic effects via For five-times ionized species, our CT rate coefficients are lower limits, due to the incomplete energy level
Breit-Pauli formalism and semi-relativistic radial functions. Total and partial final state-resolved RR and DR rate listings of NIST. We also computed CT ionization rate coefficients for neutral species of these six elements.
coefficients were determined over the temperature range (101!107)z2 K, where z is the charge, from the direct and
resonant portion of the PI cross sections (respectively) using detailed balance. We focused on "n=0 core EXPERIMENTAL PI CROSS SECTIONS
excitations for DR, since these dominate DR at the low temperatures of photoionized nebulae. In order to benchmark our AUTOSTRUCTURE calculations, we experimentally
Photoionization cross sections of ground state Se and Kr ions are shown in Fig. 1. Figs. 2 and 3 measured absolute PI cross sections of several Se and Xe ions, and utilized existing
compare the calculated cross sections to experimental measurements (see next section). Because these measurements of Kr ions (Lu et al. 2006a,b). These measurements were conducted at the
are distorted-wave calculations (as opposed to R-matrix), the experimental resonance positions and Advanced Light Source (ALS) synchrotron radiation facility in Berkeley, California, using
strengths are not accurately reproduced. Our goal is to best reproduce the direct cross sections, which the ion-photon merged beams (IPB) endstation (Fig. 7; Covington et al. 2002) on Beamline
agree with experiment to within 30-50%. 10.0.1. Figure 7 (left). IPB Apparatus
• Ions produced in electron-cyclotron resonance (ECR) source
• Accelerated by a potential
• Desired charge/mass state selected with analyzing magnet
• Ion beam merged with photon beam (photon energies
controlled with spherical grating monochromator)
• Demerging magnet directs photoions to detector
• Interaction region – absolute PI cross-section measurements
Photoion yields as a function of energy were determined by setting the bias voltage in the interaction region (I.R.)
to zero, maximizing the merging path. To place these yields on an absolute scale, a nonzero bias voltage was applied
to the I.R., energy-tagging the photoions produced therein. By determining the overlap of the photon and ion beams
in the I. R., absolute cross sections were determined at discrete energies, and used to normalize the photoion yields to
an absolute scale. We have measured the absolute PI cross sections of Se+ (Sterling et al. 2011; Esteves et al. 2011a),
Se2+, Se3+ and Se5+ (Esteves et al. 2011b), Xe+, and Xe2+ near their ionization thresholds to accuracies of 20-30%
(Figs. 8-10). These measurements are invaluable for constraining theoretical PI cross sections, leading to
improvements in the accuracy of our calculated results of up to a factor of two (Sterling 2011).
Figures 2-3. Comparison of calculated (solid
lines) and experimental (dashed lines) PI cross
Figure 1. Calculated ground state PI cross sections sections for Se+ (top) and Kr+ (bottom)
of Se and Kr ions near their ionization thresholds.
Figs. 4 and 5 show the RR (dotted lines) and DR (dashed lines) rate coefficients for the first six Se and Kr ions.
With the exception of Kr+, DR is the dominant recombination mechanism for these Se and Kr ions near 104 K; the
DR rate coefficient can exceed that of RR by up to two orders of magnitude.
Uncertainties in the PI cross sections and RR rate coefficients were estimated by using three different Figures 7-12. Experimental absolute PI cross sections measured at the ALS for a sample of Se and Xe ions. Circles
configuration-interaction (CI) expansions for each ion, testing the sensitivity of the results to the orbital scaling with error bars indicate absolute measurements at discrete energies, to which the photoionization spectra are normalized.
parameters, and through comparison to experimental PI cross section measurements. These tests show that the
direct PI cross sections have typical uncertainties of ~30-50%, while the RR rate coefficients (near 104 K) are IMPLEMENTATION AND FUTURE DIRECTIONS
uncertain by <10% except for singly-ionized species. The data are most sensitive to the adopted CI expansion. We have begun incorporating the new atomic data into the photoionization code Cloudy (Ferland et al. 1998).
Following Sterling et al. (2007), we will compute a grid of models to determine corrections for the abundances of
In the case of DR, uncertainties are dominated by the unknown energies of near-threshold autoionizing states. unobserved Se and Kr ions in ionized nebulae. In addition, we will use Cloudy to test the effects that atomic data
These energies have not been spectroscopically measured, and are extremely challenging to determine uncertainties have on derived elemental abundances. This quantitative analysis will clarify the ionic systems and
theoretically. It is not possible to determine theoretically whether these states lie just above threshold (and can atomic processes that require further attention in future investigations. These results will be applied to optical
contribute to DR), or just below. In our calculations, we shifted the continuum relative to the near-threshold (Sterling et al. 2009) and near-infrared (Sterling & Dinerstein 2008) PN spectra to determine robust n-capture element
resonances by an amount equal to the largest difference in theoretical vs. experimental energies, in order to test abundances and study details of s-process nucleosynthesis and convective mixing in PN progenitor stars.
the sensitivity of our results to this effect. These tests revealed uncertainties in the DR rate coefficients near While Se and Kr are the two most widely detected n-capture elements in PNe, several other trans-iron elements
104 K ranging from ~30% up to 2 orders of magnitude, where the uncertainties are largest for near-neutral states. have also been detected (e.g., Ge, Br, Rb, and Xe). We are currently computing PI, RR, and DR data for Xe ions, and
plan to extend our atomic database to Br and Rb in the near future (experimental PI cross section measurements have
The reason that DR is so dominant compared to RR is that for such complex (N shell) systems, the density of already been performed for select Br ions).
resonances near the ionization threshold is very high, compared to lighter species. Uncertainties in these
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