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.)

ABSTRACTNeutron(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.

ATOMIC DATA CALCULATIONS We have computed PI cross sections and RR and DR rate coefficients for the first six ions of Se and Kr (Sterling & Witthoeft 2011; Sterling 2011), and similar calculations are underway for Xe. We employed the 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 Breit-Pauli formalism and semi-relativistic radial functions. Total and partial final state-resolved RR and DR rate 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 excitations for DR, since these dominate DR at the low temperatures of photoionized nebulae.

REFERENCESBadnell, N. R. 1986, J. Phys. B, 19, 3827Butler, S. E., & Dalgarno, A. 1980, ApJ, 241, 838Covington, A. M., et al. 2002, Phys. Rev. A, 66, 062710Esteves, D. A., et al. 2011, Phys. Rev. A, in pressEsteves, D. A., et al. 2011, submittedFerland, G. J. 1998, PASP, 110, 761Janev, R. K., et al. 1983, Phys. Rev. A, 28, 1293Lu, M., et al. 2006a, Phys. Rev. A, 74, 012703Lu, M., et al. 2006b, Phys. Rev. A, 74, 062701

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).

Sneden, C., et al. 2008, ARA&A, 46, 241Sterling, N. C., et al. 2007, ApJS, 169, 37Sterling, N. C., & Dinerstein 2008, ApJS, 174, 158Sterling, N. C., et al. 2009, PASA, 26, 339Sterling, N. C., et al. 2011, J. Phys. B, 44, 025701Sterling, N. C. 2011, A&A, in pressSterling, N. C., & Stancil, P. C. 2011, A&A, submittedSterling, N. C., & Witthoeft, M. C. 2011, A&A, 529, A147Swartz, D. 1994, ApJ, 428, 267

Photoionization cross sections of ground state Se and Kr ions are shown in Fig. 1. Figs. 2 and 3 compare the calculated cross sections to experimental measurements (see next section). Because these are distorted-wave calculations (as opposed to R-matrix), the experimental resonance positions and strengths are not accurately reproduced. Our goal is to best reproduce the direct cross sections, which agree with experiment to within 30-50%.

Figure 1. Calculated ground state PI cross sections of Se and Kr ions near their ionization thresholds.

IMPLEMENTATION AND FUTURE DIRECTIONS 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 unobserved Se and Kr ions in ionized nebulae. In addition, we will use Cloudy to test the effects that atomic data uncertainties have on derived elemental abundances. This quantitative analysis will clarify the ionic systems and atomic processes that require further attention in future investigations. These results will be applied to optical (Sterling et al. 2009) and near-infrared (Sterling & Dinerstein 2008) PN spectra to determine robust n-capture element abundances and study details of s-process nucleosynthesis and convective mixing in PN progenitor stars. While Se and Kr are the two most widely detected n-capture elements in PNe, several other trans-iron elements 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 already been performed for select Br ions).

Figures 7-12. Experimental absolute PI cross sections measured at the ALS for a sample of Se and Xe ions. Circles with error bars indicate absolute measurements at discrete energies, to which the photoionization spectra are normalized.

Figures 2-3. Comparison of calculated (solid lines) and experimental (dashed lines) PI cross sections for Se+ (top) and Kr+ (bottom)

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 configuration-interaction (CI) expansions for each ion, testing the sensitivity of the results to the orbital scaling 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 uncertain by <10% except for singly-ionized species. The data are most sensitive to the adopted CI expansion.

In the case of DR, uncertainties are dominated by the unknown energies of near-threshold autoionizing states. These energies have not been spectroscopically measured, and are extremely challenging to determine theoretically. It is not possible to determine theoretically whether these states lie just above threshold (and can contribute to DR), or just below. In our calculations, we shifted the continuum relative to the near-threshold resonances by an amount equal to the largest difference in theoretical vs. experimental energies, in order to test the sensitivity of our results to this effect. These tests revealed uncertainties in the DR rate coefficients near 104 K ranging from ~30% up to 2 orders of magnitude, where the uncertainties are largest for near-neutral states.

The reason that DR is so dominant compared to RR is that for such complex (N shell) systems, the density of resonances near the ionization threshold is very high, compared to lighter species. Uncertainties in these resonance positions can therefore lead to large uncertainties in the DR rate coefficients. Thus, DR uncertainties are likely to be significant for other heavy element ions (e.g., Fe-peak elements). CT requires a different treatment, as it is a quasi-molecular problem. With a multichannel Landau-Zener code (Butler & Dalgarno 1980; Janev et al. 1983), we computed CT rate coefficients for collisions of the form Xq+ + H ! X(q-1)+ + H+ + #E (q=2-5). Singly-charged ions cannot be treated in this approximation since the products do not interact via a Coulomb potential (and hence the diabatic potentials do not cross). For those systems, we used the Demkov approximation (Swartz 1994). CT rate coefficients for low-charge ions of the n-capture elements Ge, Se, Br, Kr, Rb, and Xe (Sterling & Stancil 2011) are illustrated in Figure 6.

EXPERIMENTAL PI CROSS SECTIONS In order to benchmark our AUTOSTRUCTURE calculations, we experimentally measured absolute PI cross sections of several Se and Xe ions, and utilized existing measurements of Kr ions (Lu et al. 2006a,b). These measurements were conducted at the Advanced Light Source (ALS) synchrotron radiation facility in Berkeley, California, using the ion-photon merged beams (IPB) endstation (Fig. 7; Covington et al. 2002) on Beamline 10.0.1.

Figures 4-5. Comparison of RR (dotted lines), DR (dashed lines), and total recombination (solid lines) rate coefficients for Se and Kr ions. Note that indicated ions are the target species (i.e., before recombination).

Figure 6. Total rate coefficients for CT recombination of X+ (dash-dot-dot-dot-

dash curves), X2+ (dash-dot-dash curves), X3+ (dotted curves), X4+ (solid curves), and

X5+ (dashed curves), where X is the element indicated in each panel.

For five-times ionized species, our CT rate coefficients are lower limits, due to the incomplete energy level listings of NIST. We also computed CT ionization rate coefficients for neutral species of these six elements.