Issue 
A&A
Volume 536, December 2011



Article Number  A51  
Number of page(s)  8  
Section  Atomic, molecular, and nuclear data  
DOI  https://doi.org/10.1051/00046361/201117348  
Published online  06 December 2011 
Atomic data of Zn I for the investigation of element abundances^{⋆}
^{1}
Department of Physics, College of ScienceNational University of Defense Technology, 410073 Changsha, Hunan, PR China
email: jiaolongzeng@hotmail.com
^{2}
National Astronomical Observatories, Chinese Academy of Sciences, 100012 Beijing, PR China
Received: 26 May 2011
Accepted: 9 September 2011
Aims. We calculate the energy levels, oscillator strengths, and photoionization crosssections of Zn I to provide atomic data for the study of element abundances in astrophysics.
Methods. The calculations are carried out by using the Rmatrix method in the LScoupling scheme. The lowest 12 terms of Zn II are utilized as target states and extensive configuration interaction is included to properly delineate the quantum states of Zn II and Zn I.
Results. The 3443 oscillatorstrength values are calculated in both length and velocity forms, for the dipoleallowed transitions between 235 bound states of Zn I. The photoionization crosssection of each bound state is presented in a photon energy range from the first threshold to about 1.5 Ry. Some resonance structures are identified in the photoionization crosssections.
Conclusions. A set of atomic data to derive the spectral characteristics of neutral zinc is obtained. Comparisons are made with available experimental and other theoretical results.
Key words: stars: abundances / atomic data
The complete set of atomic data is only available at the CDS via anonymous ftp to cdsarc.ustrasbg.fr (130.79.128.5) or via http://cdsarc.ustrasbg.fr/vizbin/qcat?J/A+A/536/A51
© ESO, 2011
1. Introduction
Accurate determination of the abundance of zinc is important to investigate the chemical evolution of both damped Lyα systems (Pettini et al. 1997) and our Galaxy (Allen et al. 2011; Bihain et al. 2004). Bisterzo et al. (2004) determined the Zn abundances for stars of different stellar populations and metallicities based on high resolution spectra. Using the most widely available stellar nucleosynthesis expectations, they found that the abundance of zinc is central to inferring its astrophysical origin. It has been recognized that it is important to consider the effects of nonlocal thermodynamic equilibrium (NLTE) when determining element abundances (Asplund 2005). Research has shown that NLTE can strongly affect the abundances of Na, Mg, Al, Si, K, and Ca (Andrievsky et al. 2007, 2008, 2010; Gehren et al. 2004, 2006; Mashonkina et al. 2008; Shi et al. 2008) and these effects are sensitive to the accuracy of the atomic data used in the NLTE modeling. An adequate atomic model requires a complete set of atomic data, and the development of such a model is a difficult task for Zn owing to its complex atomic structure (Mishenina et al. 2002). To the best of our knowledge, the only published study of the effects of NLTE of Zn abundance is Takeda et al. (2005), who used the photoionization crosssections derived from hydrogenic approximation. There is therefore an urgent need to obtain a complete set of accurate atomic data for Zn.
Energy levels, oscillator strengths, and photoionization crosssections are the basic atomic parameters. The energy levels of Zn I were published by Moore (1971) and comprehensively summarized by Sugar & Musgrove (1995), whereas the oscillator strengths and the photoionization crosssections of Zn I are not widely available in the literature.
Experimental studies of the oscillator strengths of Zn I were addressed by Landman & Novick (1964) and Lurio et al. (1964), who measured the lifetime of the excited state 3d^{10}4s4p . The lifetimes of more quantum states including 3d^{10}4s4p were measured by Martinson et al. (1979) and Zerne et al. (1994). Kerkhoff et al. (1980) measured the oscillator strengths for transitions of 3d^{10}4sns ^{3}S–3d^{10}4smp and 3d^{10}4sn′d ^{3}D–3d^{10}4smp (n = 5 − 7,n′ = 4 − 6,m = 4,5). From the theoretical point of view, Hibbert (1989) calculated the oscillator strength of the resonance transition 3d^{10}4s^{2}^{1}S–3d^{10}4s4p using model potentials. The oscillator strength of the same transition was discussed by Brage & Froese Fischer (1992) using a multiconfiguration HartreeFock (MCHF) approach that considered the core polarization effects. Glowacki & Migdalek (2006) and Chen & Cheng (2010) carried out relativistic configuration interaction (CI) calculations for the transition rates of 3d^{10}4s^{2}–3d^{10}4s4p and 3d^{10}4s^{2}–3d^{10}4s4p .
Most investigations of the photoionization of Zn I have focused on the ground state 3d^{10}4s^{2}^{1}S. Marr & Austin (1969) and Harrison et al. (1969) measured the photoionization crosssection of Zn I in the photon energy range of 0.69–1.22 and 0.73–3.69 Ry, respectively. The dshell absorption spectrum was presented and analyzed by Sommer et al. (1987) using synchrotron radiation as the background source. Photoionization crosssections for the 4s, 3d, 3p, 3s subshells of Zn I were calculated by Fliflet & Kelly (1974, 1976) using manybody perturbation theory. Bartschat (1987) calculated the photoionization crosssection of the ground state 3d^{10}4s^{2}^{1}S for Zn I by using the semirelativistic Rmatrix method based on the BreitPauli Hamiltonian, while Stener & Decleva (1997) presented timedependent local density approximation (TDLDA) calculations for the photoionization of the ground state. Froese Fischer & Zatsarinny (2007) calculated the photoionization of the 4s4p excited states using the MCHF approach and the Bspline Rmatrix method.
The atomic data presented above, either experimental or theoretical, are insufficient for building a practical NLTE model for the investigation of the Zn abundance, as such a model would need a complete and consistent set of atomic data involving a large number of quantum states. In this work, we aim to provide a complete set of atomic data including the energy levels, oscillator strengths, and photoionization crosssections for Zn I. The present calculations are carried out using the Rmatrix program^{1}, which is a modified version of the Belfast atomic Rmatrix program RMATRX1 (Berrington et al. 1995). Extensive CI is taken into account to ensure that accurate atomic data can be obtained.
2. Theoretical methods
The Rmatrix method is a kind of closecoupling approach to the analysis of electronatom and photonatom interactions, which was described in great detail by Burke et al. (1971) and Berrington et al. (1987). The outline of this method is briefly presented in the following, where LScoupling is assumed. In the internal region, the wave functions of the (N + 1)electron system are depicted as linear combinations of the energyindependent basis states ψ_{k} that are expanded in the form (1)where Â is the antisymmetrization operator that takes the exchange effects between the target electrons and the (N + 1)th electron into account, and i is the channel symbol. The term X_{m} stands for the spatial (r_{m}) and the spin (σ_{m}) coordinates of the mth electron. The Φ_{i} are channel functions consisting of CI wavefunctions for the residual ion coupled with spinangle functions for the (N + 1)th electron to give an eigenstate of definite total orbital angular momentum L and total spin S. The functions u_{ij}(r) in the first term on the right hand side of Eq. (1), which are normally obtained from appropriate equations and boundary conditions, form the basis sets for the continuum wavefunctions of the (N + 1)th electron. The {φ_{j}} in the second term on the right hand side of Eq. (1) are (N + 1)electron bound states that are eigenstates with the same L and S, and they are included to allow for electron correlation effects. In the external region, the exchange effects between the target electrons and the (N + 1)th electron have been ignored and the radial functions F_{i}(r) of the (N + 1)th electron can be obtained by directly integrating the radial equations. Matching the two regions at the Rmatrix radius provides a scattering matrix and the wave functions of the (N + 1)electron system, hence the dipole transition probabilities.
The oneelectron orbitals of bound states from which the {φ_{j}} are constructed are represented as linear combinations of Slatertype orbitals (2)where the parameters C_{jnl} and ζ_{jnl} are determined variationally by optimizing the energies of specific LScoupled states. In practice, the Slatertype coefficients C_{jnl} are replaced by Clementitype coefficients G_{jnl} as (3)
In this work, we employed 12 orbitals of Zn II. The orbitals 1s, 2s, 2p, 3s, 3p, 3d, 4s were chosen to be HF functions given by Clementi & Roetti (1974) for the ground state 3d^{10}4s ^{2}S of Zn II. However, 3d and 4s were adjusted by minimizing a linear combination of the ground state and 3d^{9}4s^{2}^{2}D with the CIV3 computer code (Hibbert 1975). The orbitals 4p, 4d, 5s, 5p were obtained by optimizing linear combinations of the energies of the corresponding 3d^{10}nl (occupying a weight of 99.6%) and 3d^{9}4sn′l′ (the same LS term as 3d^{10}nl occupying a weight of 0.4%) states, respectively. The only pseudo orbital was obtained by optimizing the state of 3d^{9}4s^{2}^{2}D. The relevant parameters of the valence orbital radial functions are listed in Table 1.
Orbital parameters of the radial functions obtained with the CIV3 code for Zn II.
The Rmatrix radius was chosen to be 36.0 a.u. to ensure that the wavefunctions of bound states were completely wrapped within the Rmatrix sphere. As for the construction of the continuum states, the number of the continuum basis functions u_{ij}(r) was set to be 75. The 12 lowest terms of Zn II were utilized as target states, whose energy levels are listed in Table 2.
Energy levels (in Ry) for the target states of Zn II in different scales of configuration interaction.
To adequately describe the target states, extensive CI was included in the present work. To show the CI effects on the energy levels of the target states, we present three sets of calculations in Table 2, which are represented by cases A, B, and C, respectively. In case A, a single electron excitation is allowed from 3d and 4s subshells of the ground configuration 3d^{10}4s excluding subshell. Explicitly, configurations of 3d^{10}4s, 3d^{10}4p, 3d^{10}4d, 3d^{10}5s, 3d^{10}5p, 3d^{9}4s^{2}, 3d^{9}4s4p, 3d^{9}4s4d, 3d^{9}4s5s, and 3d^{9}4s5p were included in the calculation. In case B, in addition to configurations included in case A, two electron excitations are allowed from 3d and 4s subshells of the configuration 3d^{9}4s^{2}, excluding subshell. Therefore, in addition to configurations included in case A, the following configurations were taken into account: 3d^{9}4p^{2}, 3d^{9}4p4d, 3d^{9}4p5s, 3d^{9}4p5p, 3d^{9}4d^{2}, 3d^{9}4d5s, 3d^{9}4d5p, 3d^{9}5s^{2}, 3d^{9}5s5p, 3d^{9}5p^{2}, 3d^{8}4s^{2}4p, 3d^{8}4s^{2}4d, 3d^{8}4s^{2}5s, 3d^{8}4s^{2}5p, 3d^{8}4s4p^{2}, 3d^{8}4s4p4d, 3d^{8}4s4p5s, 3d^{8}4s4p5p, 3d^{8}4s4d^{2}, 3d^{8}4s4d5s, 3d^{8}4s4d5p, 3d^{8}4s5s^{2}, 3d^{8}4s5s5p, 3d^{8}4s5p^{2}, 3d^{7}4s^{2}4p^{2}, 3d^{7}4s^{2}4p4d, 3d^{7}4s^{2}4p5s, 3d^{7}4s^{2}4p5p, 3d^{7}4s^{2}4d^{2}, 3d^{7}4s^{2}4d5s, 3d^{7}4s^{2}4d5p, 3d^{7}4s^{2}5s^{2}, 3d^{7}4s^{2}5s5p, and 3d^{7}4s^{2}5p^{2}. In case C, two electron excitations are allowed from either the 3d or 4s subshells of the configuration 3d^{9}4s^{2}, including excitations to the subshell, and five additional configurations are included to describe the target states. In addition to the configurations included in cases A and B, the following configurations were included in case C: 3d^{10}5d, 3d^{9}4s5d, 3d^{9}4p5d, 3d^{9}4d5d, 3d^{9}5s5d, 3d^{9}5p5d, 3d^{9}5d^{2}, 3d^{8}4s^{2}5d, 3d^{8}4s4p5d, 3d^{8}4s4d5d, 3d^{8}4s5s5d, 3d^{8}4s5p5d, 3d^{8}4s5d^{2}, 3d^{8}4p^{2}5d, 3d^{8}4p4d5d, 3d^{8}4p5s5d, 3d^{8}4p5p5d, 3d^{8}4p5d^{2}, 3d^{7}4s^{2}4p5d, 3d^{7}4s^{2}4d5d, 3d^{7}4s^{2}5s5d, 3d^{7}4s^{2}5p5d, and 3d^{7}4s^{2}5d^{2}.
In Table 2, we also give the experimental energy levels compiled by Sugar & Musgrove (1995). One can find that the energies of the target states become closer and closer to the experimental results as the CI scale increases from case A to C. In the following, all results on the energy levels, oscillator strengths, and photoionization crosssections were obtained by using the CI in case C.
3. Results and discussions
Using the method described above, we calculated the energy levels of the bound states, boundbound oscillator strengths, and photoionization crosssections of Zn I.
3.1. Bound states of Zn I
We obtained 235 bound states of different symmetries (characterized by total orbital angular momentum and spin and parity) in this work. The energy levels of some of the lowest bound states and several high Rydberg states are listed in Table 3, together with the experimental data (Sugar & Musgrove 1995). From the inspection of Table 2, one can see that the calculated energies of the target states are a little lower than the experimental results, except for the term of 3d^{9}4s^{2}^{2}D. This shows that the energy of the ground term 3d^{10}4s ^{2}S was slightly overestimated in the calculation. Such an overestimate is due to the complexity of atomic structure of Zn. To better describe 3d^{10}4s ^{2}S and 3d^{9}4s^{2}^{2}D, one has to include electron correlations with three and four electron excitations from orbital 3d and higher orbitals, such as that of n = 6. Nevertheless such a larger scale of CI is untractable. In addition, relativistic effects may play a role in describing atomic structure. As a result, the energy of the ground term 3d^{10}4s^{2}^{1}S of Zn I was overestimated. The calculated ionization energy of Zn I is 0.66614 Ry. To make a more helpful comparison with the experiment, we set the energy of the ground term 3d^{10}4s^{2}^{1}S of Zn I to 0.02432 Ry in Table 3, which is the difference between the calculated and experimental value (0.69046 Ry). In this way, most of the calculated energy levels are in closer agreement with the experimental data.
Energy levels (in Ry) of bound states for Zn I.
Several high Rydberg states given in Table 3 show the correct order of energy even at the principal quantum numbers n = 18, 19, and 20. For the states with high principal quantum number n, the energies tend to be degenerate. For example, the energies of 3d^{10}4s8g ^{3}G (0.67481 Ry), 3d^{10}4s8h ^{3}H° (0.67483 Ry), and 3d^{10}4s8i ^{3}I (0.67484 Ry) are very close and nearly degenerate. Such a conclusion is consistent with the basic theory of atomic structure and spectra (Cowan 1981). The treatment of this degeneracy of Rydberg states is a great challenge of the theory. One must be very careful to assign the correct state order in the calculations. The energies of a Rydberg series become closer to the experimental values as the principal quantum number n increases, which can be found from 3d^{10}4snp ^{1}P° and 3d^{10}4snd ^{1}D (n = 8,10,14,18 − 20) of the Rydberg series. This indicates that our method is effective for high Rydberg states.
3.2. Oscillator strengths
For the zinc atom, the observed lines are mainly concentrated into boundbound transitions between configurations of the Rydberg series 3d^{10}4snl (n = 4 − 7, l = 0,1,2) (Ralchenko et al. 2010). In Table 4, we compare our calculated weighted oscillator strengths (gfvalues) for some dipole allowed transitions with experimental and other theoretical results in the literature. The online data provided by Kurucz^{2} are also listed, which were mostly derived from the theoretical work of Warner (1968), in only a few of cases from experiments. Experimental values are given between the finestructure levels instead of LScoupled terms, hence we give the gfvalues according to LS terms wherever possible. The symbol “*” denotes that the experimental data do not contain any contribution to the final states of J_{f} = 1, as a result the experimental data are smaller in value than our theoretical results. Most gfvalues in length form in Table 4 have a relative difference of smaller than 20% with experimental data. For the transition of 4s4p ^{1}P°–4s6s ^{1}S, the relative difference between gfvalues in length form of this work and that of Warner is 50%. For this transition, the oscillator strength is very small and thus sensitive to the wavefunctions and CI included in the calculation. Warner carried out his calculation based on the scaled ThomasFermiDirac (STFD) wavefunctions, which differs from those adopted in the present work.
As an illustrative example, we give the weighted oscillator strengths of transitions between the Rydberg series of 3d^{10}4snd ^{3}D and 3d^{10}4sn′f of Zn I in Table 5. Some gfvalues in Table 5 are negative, because the initial and final terms are reversed. Taking transition series 4s4d − 4snf, 4s5d − 4smf, 4s4f − 4snd and 4s5f − 4smd (n = 4 − 12, m = 5 − 12) as examples, one can find that as the principal quantum number n increases, the oscillator strengths of a Rydberg series generally decrease quite fast. This can be understood qualitatively from the general trends of oscillator strengths (Cowan 1981). For a Rydberg series of transition, among other factors such as transition energies and angular momentum, the oscillator strengths and the effective quantum numbers n^{∗} have the approximate relation (4)and this relation stands reasonably for higher principal quantum number n_{j}.
From the inspection of Tables 4 and 5, generally good agreements are found between the length and velocity forms of our oscillator strengths. In Table 5, the relative differences between the length and velocity forms are smaller than 7%. In Table 4, such a relative difference is smaller than 30% (majority of which are smaller than 10%) except for transitions of ^{1}S–. For the transitions of 4s^{2} ^{1}S–4s4p ^{1}P° and 4s4p ^{1}P°–4s5s ^{1}S, the length form of oscillator strengths agree better with the experiments, hence the length form is more reliable. To evaluate the quality of the calculated oscillator strengths as a whole, we show the velocity form versus the length form of absolute gfvalues in Fig. 1 for the boundbound transitions whose absolute gfvalues are greater than 0.001 in all of the 3443 dipoleallowed transitions. Since the data cover five orders of magnitude, we adopted the logarithm coordinates for both the length and velocity forms. For thousands of calculated gfvalues, nearly all of them are centered at the line corresponding to equality between the two forms, especially for larger gfvalues. Such a generally good agreement between the velocity and length forms of the oscillator strengths is an indication of quality for the present calculation, although scope remains for some improvement in the accuracy of the results.
gfvalues compared with experimental data and other theoretical results for Zn I.
Fig. 1 Velocity vs. length forms for the oscillator strengths of Zn I. 

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Fig. 2 Photoionization crosssection for the ground state 3d^{10}4s^{2} ^{1}S of Zn I. The solid line represents the crosssection in the present work. The dotted line represents the theoretical result carried out by Bartschat (1987). The dashed line and the filled circles represent the experimental data from Marr & Austin (1969) and Harrison (1969), respectively. The inset at the top left corner is the crosssection near threshold shown on an expanded scale. 

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gfvalues for the transition series 3d^{10}4snd ^{3}D–3d^{10}4sn′f ^{3}F° of Zn I.
3.3. Photoionization crosssections
In stellar atmospheres, photoionization of neutral species are crucial because they are photoionizationdominated atoms (Asplund 2005). Photoionization crosssections are much more important for the ground and several lowest excited states. In the following, we present in detail the photoionization crosssections of the ground state 3d^{10}4s^{2} ^{1}S, the first excited state 3d^{10}4s4p ^{3}P°, the second excited state 3d^{10}4s4p ^{1}P°, and the third excited state 3d^{10}4s5s ^{3}S for Zn I, although the photoionization crosssections of all bound states were performed in a photon energy range from the first threshold to about 1.5 Ry in this work. Furthermore, the Rydberg series of 3d^{10}4sns (n = 5 − 8) ^{3}S are presented to show the general trend of a Rydberg series.
Figure 2 shows the photoionization crosssection for the ground state of Zn I in a solid line. To compare with the experimental results, we show the experimental data from Marr & Austin (1969) and Harrison et al. (1969) as a dashed line and filled circles, respectively. The crosssection near the threshold is shown on an expanded scale at the top left corner, and is shifted by 0.02432 Ry, which is the difference between the calculated ionization potential of the ground state and the experimental value shown in Table 3. In the energy range of the 3d^{9}4s^{2}4p resonance, Marr & Austin’s experiment exhibited three resonance peaks, a weak resonance at about 0.82 Ry of the photon energy and the double maximum near 0.87 Ry. The authors labeled the weak resonance at 0.82 Ry as , and the double maximum as resonances and . Nevertheless, there is clearly inconsistency among the energy levels of Zn I (Sugar & Musgrove 1995), because the energy levels of , , and are 0.82221, 0.86761, and 0.87292 Ry, respectively. Moreover, the transition probability of the dipole allowed transition should be stronger than the dipole forbidden transitions and . Fortunately, Bartschat (1987) analyzed these resonances with a semirelativistic Rmatrix method, which enabled them to classify the weak resonance at 0.82 Ry as , and to establish that the double maximum near 0.87 Ry originated from the interference of the strong resonance with the weak resonance that in turn produced a minimum located in the center of the strong resonance peak. The photoionization crosssection obtained by Bartschat is indicated by a dotted line in Fig. 2. The resonances of , , and are not shown as the maximal crosssections of these resonances were unknown from Fig. 1 given by Bartschat. Since the LScoupling scheme is used in this work, the present approach cannot reproduce the spin forbidden transitions from the ground term 3d^{10}4s^{2} ^{1}S to 3d^{9}4s^{2}4p ^{3}P° and 3d^{9}4s^{2}4p ^{3}D° autoionization states.
Fig. 3 Photoionization crosssections for the first excited state 3d^{10}4s4p ^{3}P° of Zn I. The partial wave crosssections of ^{3}S, ^{3}P and ^{3}D are displayed in a), b), and c), respectively, and the total crosssection is displayed in d). The solid lines represent the length forms of crosssections, and the dashed lines represent velocity forms. 

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For the photoionization of the first excited state 3d^{10}4s4p ^{3}P° of Zn I, there are three allowed final channels ^{3}S, ^{3}P and ^{3}D according to the dipole selection rule. The partial waves ^{3}S and ^{3}D contain a contribution from the first ionization threshold 0.40268 Ry, while the energetically lowest ionization channel of partial wave ^{3}P opens from the second ionization threshold 3d^{10}4p ^{2}P° (0.84082 Ry). Figure 3 shows these partialwave crosssections and the total crosssection of 3d^{10}4s4p ^{3}P°, where the partialwave crosssections of ^{3}S, ^{3}P, and ^{3}D are displayed in the subpictures (a), (b), and (c) respectively, and the total crosssection is displayed in (d). Solid lines in Fig. 3 represent the length forms of the crosssections, while dashed lines represent the velocity form, and the two forms closely agree with each other. It can be seen that the ^{3}P partial crosssection clearly contains a contribution from the photon energy of 0.9 Ry. In Figs. 3a and 3c, the first autoionization resonances of partial waves ^{3}S and ^{3}D are produced by the configuration 3d^{10}4p5p, not by the configuration 3d^{10}4p^{2}, because two equivalent electrons in the 4p subshell cannot form the triplet symmetries ^{3}D and ^{3}S according to the Pauli exclusion principle. Figure 3c also shows a broad and strong resonance, which should be caused by 3d^{9}4s4p^{2} ^{3}D, whose positions are in the energy range of the resonances 3d^{9}4s^{2}nd ^{3}D (n = 4,5). These resonances of the partial ^{3}D are much stronger than any other partial symmetries ^{3}S and ^{3}P in the shown photon energy range.
Figures 4a and 4b show the partial photoionization crosssections of ^{1}S and ^{1}D for the second excited state 3d^{10}4s4p ^{1}P° of Zn I. As the first excited triplet state 3d^{10}4s4p ^{3}P°, the ^{1}S and ^{1}D partialwave photoionization crosssections for the second excited state contain a contribution from the first ionization threshold 0.25705 Ry, while the energetically lowest ionization channel of the partial wave ^{1}P opens from the second ionization threshold 3d^{10}4p ^{2}P° (0.69519 Ry) and its partial crosssection is lower than 0.01 Mb until the photon energy exceeds 0.86 Ry. Therefore, we did not give the partial crosssection of ^{1}P symmetry. Solid and dashed lines represent the length and velocity forms of photoionization crosssections, respectively. It is quite clear that the first resonances of ^{1}D and ^{1}S partial waves for the photoionization crosssections of 3d^{10}4s4p ^{1}P° are both produced by the configuration 3d^{10}4p^{2}.
From the inspection of Fig. 4, it can be seen that the autoionization resonances of 3d^{10}4p^{2} ^{1}S and ^{1}D have completely different characteristics. The former is narrow with an autoionization width being about 0.004 Ry and the peak crosssection of nearly 300 Mb, while the latter is a giant resonance with a width exceeding 0.1 Ry. To distinguish more clearly the resonance of 3d^{10}4p^{2} ^{1}S, the crosssection near the resonance are redrawn in the inset of Fig. 4a on a logarithmic scale. These two resonances were carefully investigated by Froese Fischer & Zatsarinny (2007) using both the MCHF and Bspine Rmatrix methods and their results are shown in Fig. 4 in dotted lines. To enable a clearer comparison, their results have been shifted by 0.007 Ry toward lower photon energy. One can see that there is generally good agreement between our own and their results near the two resonances.
Fig. 4 ^{1}S and ^{1}D partial photoionization crosssections of 3d^{10}4s4p ^{1}P° for Zn I. Solid and dashed lines represent the length and velocity forms of crosssections, and the dotted lines represent the theoretical results carried out by Froese Fischer & Zatsarinny (2007). The inset in a) is the crosssection near the resonance of 3d^{10}4p^{2} ^{1}S on a logarithmic scale. 

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Fig. 5 Photoionization crosssections of the Rydberg series 3d^{10}4sns ^{3}S (n = 5–8 from the top down). 

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Photoionization crosssections of the Rydberg series 3d^{10}4sns ^{3}S (n = 5, 6, 7, and 8) are displayed in Fig. 5. One can see that with the increase in the principal quantum number n, the ionization potential decreases, and the crosssection in the threshold increases, but it falls off fast as photon energy increases near the threshold. This is consistent with the basic theory of atomic structure (Cowan 1981). For photoionization of the Rydberg state with a high principal quantum number n, the crosssection near the threshold tends to be hydrogenic according to (5)where ε_{n} is the threshold ionization energy for the shell n, and ε_{p} is the photon energy. In addition, the peak value of the same resonance decreases from the top down for 3d^{9}4s^{2}4p, 3d^{10}4p5s, and 3d^{9}4s^{2}5p autoionization states, yet for higher n autoionized states such as 3d^{10}4pns and 3d^{10}4pnd , the strongest photoionization crosssection occurs for the respective state of 3d^{10}4sns ^{3}S, where the principal quantum number n is identical to that of the autoionized states. This conclusion is similar to the boundbound transitions, as shown in Table 5, which considers the transitions of 3d^{10}4snd ^{3}D–3d^{10}4sn′f ^{3}F° of Zn I as an example to illustrate such characteristics. For transitions from the state of 4s4d ^{3}D, the value of the oscillator strengths decreases with increasing Rydberg series of 3d^{10}4sn′f ^{3}F°, while for transitions from the initial state of 4s5d ^{3}D, the maximal oscillator strengths occurs for 3d^{10}4s5f ^{3}F°, not for 3d^{10}4s4f ^{3}F°.
Some autoionization resonances are identified and labeled in Figs. 2–5 and the resonance positions are listed in Table 6. The energically lowest autoionized state corresponds to 3d^{10}4p^{2}^{1}D and the second lowest to 3d^{10}4p^{2}^{1}S. As discussed in the above, 3d^{10}4p^{2}^{1}D is a giant resonance with the autoionizing width exceeding 0.1 Ry. This giant resonance will surely play an important role in the NLTE modeling of element abundance determination not only owing to its large photoionization crosssection, but also to its low photon energy.
In conclusion, a complete set of atomic data including the energies of bound states, oscillator strengths of electric dipole transitions between these bound states, and the photoionization crosssections of all bound states of Zn I were obtained by a closecoupling approach implemented using the Rmatrix method. The complete set of atomic data are available upon request and at the CDS. To achieve a clearer representation of the target and N + 1 electronic states, we included adequate electron correlations in the calculation. Detailed comparisons are made with available experimental and theoretical results in the literature. For the oscillator strengths and photoionization crosssections, generally good agreement is found between the length and velocity forms. Some resonances shown in the photoionization crosssections are identified. The energically lowest autoionized state 3d^{10}4p^{2} ^{1}D and the second lowest one 3d^{10}4p^{2} ^{1}S may play an important role in the NLTE modeling of element abundance determination. The former one is a giant resonance with autoionizing width exceeding 0.1 Ry and the latter contains strong absorption of the incident radiation.
Energy levels of autoionization states for Zn I obtained from analyzing the resonance structures shown in photoionization crosssections (Figs. 2–5).
Acknowledgments
This work was supported by the National Natural Science Foundation of China under Grants Nos. 10878024, 10774191, and 10734140, and the National Basic Research Program of China (973 Program) under Grant No. 2007CB815105.
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All Tables
Orbital parameters of the radial functions obtained with the CIV3 code for Zn II.
Energy levels (in Ry) for the target states of Zn II in different scales of configuration interaction.
gfvalues compared with experimental data and other theoretical results for Zn I.
gfvalues for the transition series 3d^{10}4snd ^{3}D–3d^{10}4sn′f ^{3}F° of Zn I.
Energy levels of autoionization states for Zn I obtained from analyzing the resonance structures shown in photoionization crosssections (Figs. 2–5).
All Figures
Fig. 1 Velocity vs. length forms for the oscillator strengths of Zn I. 

Open with DEXTER  
In the text 
Fig. 2 Photoionization crosssection for the ground state 3d^{10}4s^{2} ^{1}S of Zn I. The solid line represents the crosssection in the present work. The dotted line represents the theoretical result carried out by Bartschat (1987). The dashed line and the filled circles represent the experimental data from Marr & Austin (1969) and Harrison (1969), respectively. The inset at the top left corner is the crosssection near threshold shown on an expanded scale. 

Open with DEXTER  
In the text 
Fig. 3 Photoionization crosssections for the first excited state 3d^{10}4s4p ^{3}P° of Zn I. The partial wave crosssections of ^{3}S, ^{3}P and ^{3}D are displayed in a), b), and c), respectively, and the total crosssection is displayed in d). The solid lines represent the length forms of crosssections, and the dashed lines represent velocity forms. 

Open with DEXTER  
In the text 
Fig. 4 ^{1}S and ^{1}D partial photoionization crosssections of 3d^{10}4s4p ^{1}P° for Zn I. Solid and dashed lines represent the length and velocity forms of crosssections, and the dotted lines represent the theoretical results carried out by Froese Fischer & Zatsarinny (2007). The inset in a) is the crosssection near the resonance of 3d^{10}4p^{2} ^{1}S on a logarithmic scale. 

Open with DEXTER  
In the text 
Fig. 5 Photoionization crosssections of the Rydberg series 3d^{10}4sns ^{3}S (n = 5–8 from the top down). 

Open with DEXTER  
In the text 
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