3 The atomic data for minor elements

3.1 Lithium isoelectronic sequence

The Lithium-like ions atomic structure is simpler than other sequences and there are no metastable levels. This causes the Li-like spectral lines to be density insensitive and very useful for differential emission measure studies. The Lithium-like spectrum is dominated by the strong 2s ²S_1/2 - 2p ²P_1/2,3/2 doublet, which has been extensively observed and studied in the past two decades in all the spectra of the most abundant elements.

The minor elements ²S - ²P doublets have been detected in several observations, both in active region and flare conditions. Na IX has been detected in active and quiet Sun (Vernazza & Reeves 1978; Doyle 1983) and falls in the spectral range covered by both SUMER and CDS spectrograph, where it has been detected in limb and disk spectra (Landi et al. 1998; Feldman et al. 1997). Lines from P XIII to Co XXV have been observed by several authors in active and flaring Sun (Kelly & Palumbo 1973; Sandlin et al. 1976; Widing & Purcell 1976; Dere 1978).

McWhirter (1994) reviewed the existing literature for Lithium-like ions and found that the electron excitation data available seem to be very accurate. Since we are going to include in this database the ions of minor elements heavier than Oxygen, following the suggestions of McWhirter (1994) we adopt the theoretical data calculated by Zhang et al. (1990). The authors provide complete data for all the minor ions. Configurations up to 5d are considered, corresponding to 20 fine structure energy levels. Additional collisional data are also available for the 5f transitions but no radiative transition probabilities have been found in literature so these levels have been omitted. Relativistic distorted wave collision strengths are provided for 6 electron energies, together with the electric dipole oscillator strengths. Some additional oscillator strengths come from Martin et al. (1993). The observed energy levels are taken from the NIST database (Martin et al. 1995). For the heavier ions only the energies of the lowest configurations have been measured so wavelengths for transitions coming from higher levels have been calculated with the theoretical energy levels found in Zhang et al. (1990).

3.2 Beryllium isoelectronic sequence

Beryllium like ions have been studied extensively in literature both for differential emission measure determination and for plasma diagnostics, since in their atomic structure some metastable levels are present. The Be-like spectrum is dominated by the strong resonance transition 2s^{2 1}S₀ - 2s2p ¹P₁ giving rise to some of the most prominent lines in solar and stellar spectra. In the literature some Be-like minor elements lines have been observed (Sandlin et al. 1976; Dere 1978; Vernazza & Reeves 1978; Doyle 1983; Feldman et al. 1987; Thomas & Neupert 1994) in active and flaring Sun. Moreover the Na VIII 2s^{2 1}S₀ - 2s2p ¹P₁ line at 411.17 Å is observed by the Coronal Diagnostic Spectrometer (CDS) on SOHO (Landi et al. 1998) and several other minor elements lines are detectable by CDS (Brooks et al. 1998). Beryllium-like minor elements lines have been detected also by the Solar UV Measurement of Emitted Radiation (SUMER) on SOHO (Feldman et al. 1997).

Be-like minor elements electron excitation literature is richer than other sequences and has been reviewed by Berrington (1994). It has therefore been possible to insert in the Arcetri spectral code complete data for all the minor ions. Both close coupling R-Matrix and distorted wave calculations are available in literature, and following the suggestions in Berrington (1994) we have adopted the close coupling data when possible, and used distorted wave results only where CC data were unavailable. Maxwellian averaged collision strengths from Keenan et al. (1986) have been adopted for Na VIII, while the values of Keenan (1988) have been used for P XII, Cl XIV and K XVI. Both these works provide analytical fits to the effective collision strengths that allow to calculate their values for a wide range of electron temperature around the maximum abundance temperature of each ion. The relativistic distorted wave collision strengths of Zhang & Sampson (1992) have been taken for the remaining heavier minor elements; they provide relativistic distorted wave collision strengths for all the possible transitions in the adopted atomic model, evaluated for six values of the electron energy. The atomic model includes the n=2 configurations (2s², 2s2p, 2p²) corresponding to 10 fine structure levels. Experimental energy levels have been taken from Edlen (1983). Allowed oscillator strengths are taken from Zhang and Sampson (1992), while forbidden radiative transition probabilities come from Muhlethaler & Nussbaumer (1976) and Bhatia et al. (1986). No radiative transition probability is available for level 2s2p ³P₀.

3.3 Boron isoelectronic sequence

The Boron-like spectra have been proved extremely useful for density diagnostic in a variety of plasma conditions and have been studied extensively in literature. Nevertheless their spectra do not present very strong and prominent lines as the Li, Be, Na and Mg-like ions and so in the past lines from the Boron-like minor elements have been observed very seldom (Vernazza & Reeves 1978; Doyle 1983; Thomas & Neupert 1994). Na VII lines fall in the CDS spectral range and have been observed around 350 Å blending Mg V lines (Brooks et al. 1998) and are expected in the range 486 - 490 Å. Boron-like minor elements lines have been detected by the Solar UV Measurement of Emitted Radiation (SUMER) on SOHO (Feldman et al. 1997).

The Boron-like electron excitation rates have been reviewed by Sampson et al. (1994). It appears that the minor ions have been neglected in the literature and the only complete datasets available are those by Zhang & Sampson (1994a) (n=2 transitions), Zhang & Sampson (1994b) and Sampson et al. (1986) (n=2 to n=3 transitions). Zhang et al. (1994) calculated close coupling LS coupled effective collision strengths for all the n=2 transitions of the most abundant elements as part of the iron project (Hummer et al. 1993). Unfortunately they did not cover the minor elements, and therefore their high quality calculation can only be used for interpolation purposes. An additional problem is that effective collision strengths are reported only between LS coupled levels, while the Arcetri spectral code includes only fine structure data.

In the arcetri spectral code we have included only the n=2 transitions. The configurations 2s²2p, 2s2p² and 2p³ have been considered, corresponding to 15 energy levels whose experimental energies were taken from the NIST database (Martin et al. 1995) and Edlen (1981). Allowed transitions oscillator strengths come from Zhang et al. (1994a), while forbidden and intercombination ones are taken from Flower & Nussbaumer (1975). Zhang et al. (1994a) provide also relativistic distorted wave collision strengths for 6 electron energies for all the possible transitions between the levels included in the atomic model; these collision strengths have been adopted in the Arcetri code.

3.4 Carbon isoelectronic sequence

The atomic structure of Carbon-like ions shows several metastable levels and this produces a rather strong density sensitivity of the emitted lines in a variety of plasma conditions, from quiet Sun (Na VI to Si IX) to active region (Mg VII to S XI) and flares (higher ions). For this reason C-like ions have been widely studied in the past for density diagnostics purposes.

As for the Boron-like ions, the absence of very strong and dominating lines in the C-like spectrum has been an obstacle to the detection of C-like minor ions lines; however a few have been observed by Vernazza & Reeves (1978); Doyle (1983) and Thomas & Neupert (1994). Some lines fall in the CDS spectral range, but their weakness and the blending with stronger lines have been an obstacle to their detection and identification. Carbon-like minor elements lines have been detected by the solar UV measurement of emitted radiation (SUMER) on SOHO (Feldman et al. 1997).

The atomic data available for the Carbon-like ions have been reviewed by Monsignori Fossi & Landini (1994c), although their assessment is limited only to the most abundant ions from O III to Fe XXI. They found that there were differences between distorted wave and close coupling R-matrix results; the discrepancies were mainly due to differences in the target wave functions used in the calculation and to the possibility of taking into account the resonance contributions to the effective collision strengths with the close coupling method. They recommended the use of close coupling results when possible. Nevertheless C-like minor ions collision strengths literature is very poor. Lennon & Burke (1994) calculated close coupling effective collision strengths for transitions between the ground configuration levels, including also the 2s2p^{3 5}S term for all the ions from N II to S XI. Zhang & Sampson (1996) calculated relativistic distorted wave collision strengths for all the ions with 9 $\le$ Z $\le 54$ for all the n=2 to n=2 transitions. Therefore, following the recommendation of Monsignori Fossi & Landini (1994c) we adopted the close coupling data from Lennon & Burke (1994) for Na VI and the distorted wave results for all the remaining transitions and ions. We have preferred distorted wave data to close coupling results in the case of Al VIII and P X because Lennon & Burke (1994) provide effective collision strengths only up to 10⁵ K, while the temperature of maximum abundance of these two ions is respectively 10^5.9 K and 10^6.3 K. Since we are most interested in the temperature range around the maximum abundance temperature of each ion we felt that Zhang & Sampson results were more reliable for our purposes.

The adopted atomic model includes three configurations (2s²2p², 2s2p³ and 2p⁴) corresponding to 20 fine structure levels, whose experimental energies are taken from the NIST database (Martin et al. 1995); additional energy levels come from the compilation of Edlen (1985). Allowed transition oscillator strengths are taken from Zhang & Sampson (1996) and Bhatia et al. (1987a). There are some discrepancies between these data and the results of Fawcett (1987), and differences of $\simeq$ 20 - 30% have been found in the A values. Ground configuration radiative transition probabilities for the minor ions have been calculated by several authors (Nussbaumer & Rusca 1979; Froese Fischer & Saha 1985; Bhatia et al. 1987a; Bhatia & Kastner 1993a; Bhatia & Doschek 1993a; Bhatia & Doschek 1995a; Galavis et al. 1997). A comparison between these calculations has shown a general good agreement although some more consistent differences arise for transitions ³P₀-¹D₂ and ³P₂-¹S₀. In the present work data from Galavis et al. (1997) have been adopted.

All the collisional data are from Zhang & Sampson (1996); they provide relativistic distorted wave collision strengths for all the possible transitions in the adopted atomic model calculated for 6 values of the electron energy. For Na VI, the Lennon & Burke (1994) close coupling effective collision strengths have been adopted. A comparison between these two datasets shows that some differences are found for low temperature values, due probably to the effect of resonances.

3.5 Nitrogen isoelectronic sequence

Nitrogen-like ions show a rather strong density sensitivity for a variety of solar plasma conditions and for this reason have been extensively used for density diagnostic. The N-like spectra do not give rise to very strong lines, and for this reason Nitrogen like minor elements lines have seldom been observed. We find some relatively weak lines of the lighter minor elements in the spectra of SERTS (Thomas & Neupert 1994), SUMER (Feldman et al. 1997), while some lines from Cr XVIII have been observed around 15 Å by McKenzie & Landecker (1982), which also point out the importance of chromium as plasma diagnostic for hot plasmas.

The electron-ion collision literature of the nitrogen isoelectronic sequence is rather poor and the same problem is found for the radiative transition probabilities. Kato (1994) has reviewed the existing N-like literature and found that some calculations have been perfomed only for Na V, Ti XVI, Mn XIX and Zn XXIV. The Na V calculation are very old (earlier than 1970) and the Zn XXIV distorted wave calculation by Bhatia et al. (1989) is carried on for only one incident electron energy, giving in this way additional uncertainties in the evaluation of the Maxwellian-averaged collision strength.

For this reason for most of the minor elements it has been necessary to interpolate the existing data for the most abundant elements in order to obtain both the radiative transition probabilities and the effective collision strengths of the minor elements. The data used for these interpolation come from Bhatia and Mason (1980a) (Mg VI to Ca XIV) and Bhatia & Mason (1980b) (Fe XX). New calculations for Mg VI has been recently performed by Bhatia & Young (1997), who find excellent agreement between their results and Bhatia & Mason (1980a). Co XXI and Ni XXII collisional data have not been interpolated because of the great uncertainties in the values of the Zn XXIV effective collision strengths. The accuracy of the interpolation results is rather poor, since some irregularities of the effective collision strengths along the isoelectronic sequence are found for several transitions. For this reason further studies on the Nitrogen-like electron-ion collision strengths are required.

The adopted atomic model for N-like minor elements includes two configurations (2s²2p³ and 2s2p⁴) corresponding to 13 fine structure energy levels. The values of the energy levels are taken from Edlen (1984) and NIST (Martin et al. 1995). All radiative and collisional transition probabilities have been interpolated for all the ground transitions and the transitions between the two adopted configurations. Only Ti XVI, Mn XIX and Zn XXIV data have not been interpolated. The distorted wave calculations of Bhatia et al. (1989) have been adopted for Zn XXIV only for the two considered configurations, although data for additional configurations are available. The atomic data for Ti XVI and Mn XIX are taken from the distorted wave calculations of Bhatia et al. (1980) and Bhatia (1982) respectively. These papers report radiative transition probabilities and collision strengths for all the ground configuration and for 2s²2p³ - 2s2p⁴ transitions; the collision strengths have been calculated for three values of the incident electron energy.

3.6 Oxygen isoelectronic sequence

The Oxygen-like less abundant ions give rise to relatively weak lines on the EUV spectral range and for this reason they have not been observed in the past. Only some lines of the highly ionized Cr XVII have been observed by McKenzie & Landecker (1982). Nevertheless lines for the lighter ions of the sequence are observable by the CDS spectrometer on board on SOHO and some identifications of these lines are suggested by Brooks et al. (1998).

The lack of observed Oxygen-like minor ions lines has caused these ions to be neglected in literature. Lang & Summers (1994) reviewed the existing electron excitation data available; from their compilation it comes out that only Na IV, Al VI and P VIII (calculations earlier than 1970) and the highly ionised Ti XV and Mn XVIII (Bhatia et al. 1980 and Bhatia 1982) have been studied using the distorted wave approximation, while no data is available for the other ions. The Iron Project has partially covered the gaps providing close coupling calculations for collisional induced transitions between the ground levels of all the Oxygen-like ions from F II to Ar XI (Butler & Zeippen 1994). To our knowledge, no collision strengths calculations are available for transitions between the ground and the excited configurations for the minor elements.

The adopted atomic model for Oxygen-like ions includes three configurations ($\rm 2s^22p^4$,$\rm 2s2p^5$ and $\rm 2p^6$) corresponding to 10 fine structure levels. The experimental energy levels of Edlen (1983) are used for calculating the transition wavelengths. The radiative transition probabilities come from different sources. The ground transitions data have been taken from Galavis et al. (1997), while data for the allowed $\rm 2s^22p^4 - 2s2p^5$ and $\rm 2s2p^5-2p^6$ transitions come from Fawcett (1986a). Vilkas et al. (1994) also have calculated electric dipole transition probabilities for the Oxygen-like ions from Ne to Fe, including several minor ions, but their values do not well agree neither with the Fawcett (1986a) data nor with the radiative data of the CHIANTI database for the most abundant elements (Bhatia et al. 1979; Lolergue et al. 1985). Ti XV and Mn XVIII radiative data come from Bhatia et al. (1980) and Bhatia (1982). The Arcetri spectral code adopts the Iron Project collisional data for the ground transitions of the minor elements Na IV, Al VI and P VIII. Collisional data for all the other transitions have been interpolated along the isoelectronic sequence, with the only exception of Ti XV and Mn XVIII whose collision strengths are taken from the distorted wave calculations of Bhatia et al. (1980) and Bhatia (1982). Since data for elements heavier than Fe were not available, it has not been possible to interpolate any data for Co XX, Ni XXI and Zn XXIII which therefore are not included in the Arcetri spectral code.

3.7 Fluorine isoelectronic sequence

The Fluorine-like minor ions give rise to very weak lines and therefore to our knowledge there are no direct observations of their lines in astrophysical plasmas, with the only exception of Cr XVI (Acton 1985; McKenzie & Landecker 1982). F-like minor ions lines are potentially detectable by the CDS spectrometer from Na III to P VII.

Because of their weakness, very few calculations are available in literature providing minor ions electron excitation rates: Bhatia 1994 has reviewed the Fluorine isoelectronic sequence electron excitation data; only very old Coulomb-Born calculations by Blaha (1968, 1969) are mentioned. Moreover no data are available at all for Al IV and Co XIX, and only Ti XIV and Mn XVII have been studied more extensively with the distorted wave approximation (Bhatia et al. 1980; Bhatia 1982); furthermore, only LS coupling results are available from the close coupling calculation of Mohan et al. (1989).

In the present work we have adopted a two configurations atomic model (2s²2p⁵ and 2s2p⁶), including three fine structure energy levels. The experimental energies are taken from the NIST database (Martin et al. 1995), while all the electron excitation effective collision strengths have been interpolated using the existing data of the most abundant elements included in the CHIANTI database. Ti XIV and Mn XVII data instead come from Bhatia et al. (1980), Bhatia (1982). In order to check the quality of the interpolation method, we have also interpolated collisional data for Ti and Mn, and comparisons have been made between our results and the existing LS coupling literature for these two ions, showing reasonable agreement.

3.8 Sodium isoelectronic sequence

The Sodium-like spectrum is dominated by the two very strong 3s ²S_1/2 - 3p ³P_1/2,3/2 lines which give rise to some of the brightest lines observed from visible to UV and EUV spectral ranges. The strength of these features have permitted the observation of all the Na-like minor elements from P V to Zn XX (Burton 1970; Doyle 1983; Vernazza & Reeves 1978; Dere 1978; Thomas & Neupert 1994) in a variety of solar conditions. Several of these lines are included in the CDS and SUMER spectral ranges and have been observed (Feldman et al. 1997). These lines are density insensitive and can be used for differential emission measure studies (Landi & Landini 1998).

Sodium-like ions literature is relatively rich, nevertheless the great majority of them deals only with the most abundant ions of the sequence and only few studies cover also the minor ions. In the present work we have adopted the radiative and collisional data coming from Zhang & Sampson (1990). The adopted atomic model includes 11 configurations (3s, 3p, 3d 4s, 4p, 4d, 4f, 5s, 5p, 5d, 5f) corresponding to 19 fine structure energy levels. Allowed radiative and collisional transition probabilities are taken from Zhang & Sampson 1990; they provide relativistic distorted wave collision strengths for 6 values of the incident electron energy. The experimental energies are taken from the NIST database (Martin et al. 1995).

3.9 Magnesium isoelectronic sequence

The Magnesium sequence is dominated by the very strong 3s^{2 1}S₀ - 3s3p ¹P₁ transition giving rise to some of the most prominent lines in EUV and UV spectra. For this reason also the minor elements lines have been observed in astrophysical plasmas (Dere 1978; Vernazza & Reeves 1978; Thomas & Neupert 1994; Feldman et al. 1997; Brooks et al. 1998).

Nevertheless, Mg-like minor elements literature is very poor and data are quite uncertain. Only Cr XIII has been studied by Christensen et al. (1986), which provide distorted wave collision strengths for 3 incident electron energies. To our knowledge there are no other sources for collisional data. A further problem with the Magnesium like ions is the difficulty to reliably interpolate Christensen et al. (1986) data since the collision strengths show irregular behaviour for several transitions. For this reason we have preferred not to calculate minor elements data by interpolation, recommending further work on this subject.

The Cr XIII adopted atomic model is the same as the CHIANTI Mg-like abundant ions: 5 configurations are included corresponding to 16 fine structure energy levels. Radiative transition probabilities and experimental level energies are also taken from Christensen et al. (1986).

3.10 Fe III

Fe III lines have been observed in the past decades in many different astrophysical objects and have been extensively analysed by several authors. In the recent past Ekberg (1993) carried on a very careful analysis of the Fe III spectrum using a laboratory light source, identifying a very large number of lines ($\simeq 3200$), many of which were observed for the first time; moreover the SUMER instrument on board SOHO has recorded many Fe III allowed transitions (Feldman et al. 1997).

All these observations have recently raised the interest into theoretical calculations of the Fe III atomic data and radiative and collisional transition probabilities despite the difficulties caused by the complexity of this ion. Both radiative and collisional transition probabilities have been studied in the Iron Project (Hummer et al. 1993) which represent the most accurate and extensive calculations performed on Fe III. Ab initio calculations of radiative transition probabilities have been performed by Nahar & Pradhan (1996), including electric dipole transitions between the three lowest configurations, and quadrupole and magnetic dipole transitions probabilities among the ground configuration levels. The authors found some differences between their calculation and the semiempirical calculations made in the past (Kurucz & Peytremann 1975; Biemont 1976; Fawcett 1989 and Ekberg 1993). Also Quinet (1996) has calculated radiative transition probabilities between the ground levels; a comparison with the Nahar & Pradhan (1996) results show a reasonable good agreement although sometimes discrepancies larger than 30% are found.

The most recent calculations of collisional data have been performed by Zhang (1996) and Berrington et al. (1991). The former represents a large scale calculation which covers 219 fine structure levels among the three lowest configurations using a non relativistic close coupling approximation. Berrington et al. (1991) data included relativistic effects calculations but studied only some ground configuration transitions. Zhang & Pradhan (1995) show that the relativistic effects should be negligible and that a non relativistic fine structure calculation should be accurate, provided that an extensive eigenfunction basis set is used. For this reason we adopt the Zhang (1996) collisional data in the Arcetri spectral code.

Unfortunately, no radiative transition probabilities are available for $\rm 3d^6$ - 3d⁵4s transitions and among the $\rm 3d^54s$ levels. Thus several metastable levels of the $\rm 3d^54s$ configuration have no radiative transition probability available. This would lead to greatly overestimate the population of these levels and to alter the population balance of the ion. For this reason this configuration has not been included in our Fe III model. Since the energies of the $\rm 3d^54s$ configuration are close to those of the ground levels, it is possible that in coronal conditions the level populations for the $\rm 3d^54s$configuration are high enough to affect the total level population of Fe III, and therefore the omission of this configuration may be a limitation to the present model for Fe III.

The adopted atomic model for Fe III includes the two configurations $\rm 3d^6$ and part of the $\rm 3d^54p$, corresponding to 131 fine structure levels. The experimental energy levels come from Sugar & Corliss (1985) and Ekberg (1993); no value is available for the level $\rm 3d^54p$⁵D₃, and therefore its energy has been interpolated from the available energies of the $\rm 3d^54p$ ⁵D multiplet. Radiative data for both forbidden and allowed transition probabilities come from Nahar & Pradhan (1996), while Maxwellian-averaged collision strengths for transitions between all levels of the adopted atomic model come from Zhang (1996), which provides values of the Maxwellian-averaged collision strengths for 20 values of the electron temperature $T_{\rm e}$between 10³ to 10⁵ K.