Current Status and Developments of the Atomic Database on Rare-Earths at Mons University (DREAM)

: The main purpose of the Database on Rare Earths At Mons University (DREAM) is to provide the scientific community with updated spectroscopic parameters related to lanthanide atoms ( Z = 57–71) in their lowest ionization stages. The radiative parameters (oscillator strengths and transitions probabilities) listed in the database have been obtained over the past 20 years by the Atomic Physics and Astrophysics group of Mons University, Belgium, thanks to a systematic and extensive use of the pseudo-relativistic Hartree–Fock (HFR) method modified for taking core-polarization and core-penetration effects into account. Most of these theoretical results have been validated by the good agreement obtained when comparing computed radiative lifetimes and accurate experimental values measured by the time-resolved laser-induced fluorescence technique. In the present paper, we report on the current status and developments of the database that gathers radiative parameters for more than 72000 spectral lines in neutral, singly-, doubly-, and triply-ionized lanthanides.


Introduction
The atomic structures and radiative properties characterizing the lowest ionization stages of lanthanide elements, from La (Z = 57) to Lu (Z = 71), have been the subject of many experimental and theoretical investigations during the last years. At our last consultation (January 2020), the NIST atomic spectra bibliographic database [1] counted 1816 references on energy levels and 480 references on radiative transition rates related to the first four spectra (I -IV) of lanthanide atoms. The cumulative numbers of relevant papers published over the last decades are reported in Figures  1 and 2, respectively. These figures are the result of a steady increase of publications since the 1950s, demonstrating the growing interest for the atomic data characterizing such heavy atomic species. This is mainly due to the fact that the remarkably rich spectra arising from lanthanide ions provide an essential source of information for the development of other fields, mainly in astrophysics and the lighting industry (see, e.g., [2][3][4][5][6]). Cumulative number of available references related to atomic energy levels for neutral, singly-, doubly-and triply-ionized lanthanides taken from the NIST bibliographic database [1].

Figure 2.
Cumulative number of available references related to radiative parameters (oscillator strengths and transition probabilities) for neutral, singly-, doubly-and triply-ionized lanthanides taken from the NIST bibliographic database [1].
In astrophysics, many lines of neutral, singly-and doubly-ionized lanthanides have been identified in the high-resolution spectra of chemically peculiar stars. The most striking example is probably the roAp star HD 101065, better known as the Przybylski's star, in which the observation of hundreds of lanthanide lines allowed to deduce abundances in these elements of several orders of magnitude greater than the solar values (see, e.g., [7][8][9]). The lanthanides are particularly important because they form a group of contiguous elements in which patterns of abundance may be observed and investigated in connection with stellar nucleosynthesis and chemical fractionation [10].
Another important astrophysical application of lanthanide elements concerns the new hot topic of neutron star mergers. Indeed, the ejecta from neutron star mergers produce an electromagnetic signal that can be used, together with the detection of gravitational waves, to locate the source and to study the physics of these mergers. The r-process nucleosynthesis in these ejecta may lead to radioactively powered transients called kilonovae. The timescale and peak luminosity of these transients depend on the composition of the ejecta, which determines the local heating rate from nuclear decays and the opacity which can drastically be increased by lanthanides, as mentioned in [11][12][13]. The largest remaining uncertainty in kilonova emission relates to missing information about the wavelength dependent opacity of the ejecta, mostly because of the lack of relevant atomic data for the lowest ionization stages of lanthanides [14,15].
Because of their unusual luminescent properties, triply ionized lanthanide atoms also play an important role in photonics, laser physics, biotechnology, medical diagnostics, and lighting industry, see, e.g., [16][17][18][19]. All of these ions, except La IV, are characterized by a ground electronic configuration of the type [Xe]4f k with k varying from 1 (Ce IV) to 14 (Lu IV) which is largely responsible for their interesting photophysical properties such as long-lived luminescence and sharp absorption and emission lines. Reliable information about the atomic structures and radiative parameters of triply charged lanthanide ions is therefore essential for analyzing and understanding their light emission.
For all these reasons, about 20 years ago, we started systematic and detailed investigations of + four spectra of lanthanide elements. In the present paper, we briefly remind how these radiative parameters were determined, we present an overview of the current status and developments of DREAM, and we give some remarkable examples of use of the data available in this database.

Atomic structure and radiative rate calculations
The lowest ionization stages of lanthanide atoms are generally characterized by strongly interacting low lying configurations of the type 4f k , 4f k-1 nl, 4f k-2 nln'l' and 4f k-3 nln'l'n"l". Moreover, the well-known collapse of the 4f orbital occurring at lanthanum is enhanced when the number of 4f electrons increases which makes the atomic structure calculations very difficult, as described in [6]. In all the lanthanide species considered in our theoretical investigations, the same computational approach was used, namely the one based on the pseudo-relativistic Hartree-Fock (HFR) method originally introduced by Cowan [20], and modified for taking core-polarization effects into account, giving rise to the so-called HFR+CPOL approach. In this latter, described in detail in many of our previous papers (see, e.g., [21][22][23]), the largest part of the intravalence correlation is represented within a configuration interaction scheme, i.e., by explicitly including a set of electronic configurations in the physical model, while core-valence correlation is approximated by a core-polarization (CPOL) model potential depending on two parameters, namely the dipole polarizability, αd, of the ionic core, for which numerical values can be found in the literature (see, e.g., [24,25]), and the cut-off radius, rc, that is arbitrarily chosen as a measure of the size of the ionic core. In practice, this latter parameter is usually chosen to be equal to the HFR mean value <r> for the outermost ionic core orbital. In order to allow for a more accurate treatment of core-valence interactions, we added a further correction to account for the penetration of the core by the valence electrons, according to the formalism developed by Hameed and coworkers [26,27].
In addition, for each atomic system, the radial parameters corresponding to the configuration average energies (Eav), the monoconfiguration (F k , G k ) and configuration interaction (R k ) Slater integrals, the spin-orbit parameters (ζnl) and, if needed, the effective interaction parameters (α, β, γ) [20] were adjusted in a semi-empirical least-squares fit to reduce as much as possible the differences between the calculated energy levels and the available experimental values. This approach, although strongly dependent upon the quantity and the quality of the observed energy levels, allowed us to optimize the eigenvalues and eigenstates, and thus the computed wavelengths, radiative lifetimes, transition probabilities and oscillator strengths for most of the lanthanide elements considered in our work. However, in some cases, the number of available experimental energy levels was found to be too limited to perform a satisfactory fit. This can be illustrated by considering the two specific examples of Pr I [28] and Pr II [29]. In Pr I, according to the NIST compilation [1], among the 8421 possible levels belonging to the lowest odd-and even-parity configurations, namely 4f 3 6s 2 , 4f 3 5d6s, 4f 2 5d6s6p, 4f 2 6s 2 6p, 4f 2 5d 2 6p, 4f 2 5d6s 2 , 4f 2 5d 2 6s, 4f 3 6s6p and 4f 3 5d6p, only 410 have been determined experimentally, with unambiguous labelling. In Pr II, for the low-lying even-parity configurations 4f 4 , 4f 3 6p, 4f 2 5d 2 , 4f 2 5d6s and 4f 2 6s 2 , only 55 levels are listed in the NIST compilation on a total of 1033 possible levels. In such cases, the scarcity of experimentally established energy levels obviously makes it completely unthinkable a reliable leastsquares fitting procedure of the calculated eigenvalues of the Hamiltonian, thus highlighting the need for new basic spectral analyses in the laboratory, especially for neutral and singly ionized lanthanide atoms.
The results we have obtained so far concerning the theoretical determination of radiative data for lanthanide atoms, in their first four ionization stages, are listed in Table 1, together with the corresponding references in which the details of computations can be found.

Comparisons with experimental data
In view of their complexity, modelling the atomic structures and computing the radiative parameters in neutral and lowly ionized lanthanides represent a difficult task so that it is necessary to assess the quality of the results obtained through comparisons with laboratory measurements. In order to estimate the reliability of the theoretical models considered in our work, a large number of experimental investigations were also carried out over the past 20 years. More precisely, for many lanthanide ions, atomic lifetime measurements were carried out using time-resolved laser-inducedfluorescence (TR-LIF) spectroscopy, mainly with the instrumental setup developed at the Lund Laser Centre, Sweden. It is well known that this technique has many advantages including the elimination of cascade problems through different types of selective excitation, such as one-step, two-step or two-photon excitation, and the use of various laser dyes. The accessible lifetimes range generally from 1 ns to several hundreds of ns, with uncertainties of a few percent in the large majority of cases. This technique, described in many papers, see, e.g., [30,31], is based of the production of free atoms and ions within a plasma created by laser ablation in which a laser pulse of a few ns duration irradiates a metallic foil placed in a vacuum chamber. The expanding laserproduced plasma is then crossed by another laser whose wavelength allows to selectively populate the considered level. The fluorescence generated is collected by a fused-silica lens, and then appropriately filtered by a monochromator, to be finally detected by a microchannel-plate photomultiplier tube. The decay curves are analyzed and the lifetimes are extracted by a leastsquares fit of a single exponential decay, convoluted to the data by the measured laser pulse, if necessary, i.e., in the case of lifetime values similar to the laser pulse duration.
In our common work with the Lund Laser Centre, we managed to measure the radiative lifetimes for a total of 324 energy levels belonging to La I, La III, Ce II, Ce IV, Pr I, Pr II, Pr III, Nd I, Nd II, Nd III, Sm II, Sm III, Eu III, Tb III, Dy III, Ho III, Er II, Er III, Tm III, Yb II, Yb III, Lu I, Lu II, and Lu III lanthanide ions. These experimental measurements, for which the corresponding references are quoted in Table 1, were systematically compared with the lifetime values deduced from our calculations. In most cases, an agreement within a few percent was found except for a limited number of cases that could generally be explained by large mixings occuring in the level compositions, by the fragmentary knowledge of the energy level schemes for some ions or by dubious level assignments in the published experimental level values. In fact, for the whole set of lanthanide ions considered in our work, we found a mean ratio between the calculated and the experimental lifetimes, τ (CALC) / τ (EXP), equal to 0.98 ± 0.23, where the uncertainty corresponds to the standard deviation of the mean. All the details of these comparisons can be found in the papers referred to in the DREAM database and in Table 1, while a general overview is shown in Figure 3 where the ratio τ (CALC) / τ (EXP) is plotted against τ (CALC) for all the levels of lanthanide elements for which the radiative lifetimes were experimentally determined in our work. Note that atomic lifetime measurements were also performed for several lanthanide ions using the same TR-LIF experimental technique in other laboratories, mainly at Jilin University (Changshun, China) and Wisconsin University (Madison, USA). In some instances, these measurements were compared with our calculations, giving also rise to a good overall agreement. An example of such an agreement is shown in Figure 2 of our recent paper dedicated to neutral lanthanum [32], this figure illustrating the comparison between our computed HFR+CPOL radiative lifetimes and the TR-LIF experimental values measured at Madison [33]. In this case, the mean ratio τ (CALC) / τ (EXP) was found to be equal to 0.94 ± 0.22 for 70 La I energy levels from 15000 to 32140 cm -1 .
In addition, experimental transition probabilities and oscillator strengths were published, mainly by the Jilin and Wisconsin groups, for some lowly charged lanthanide ions. These results were generally obtained by combining accurate TR-LIF radiative lifetimes with branching fraction measurements performed in emission spectra collected using grating or Fourier transform spectrometers. In Table 2, we give a comparison between the oscillator strengths extracted from the DREAM database and the available experimental results for four specific lanthanide ions, i.e. Sm III [34], Eu III [35], Tm III [36], and Yb III [37]. As it can be seen, the agreement between both sets of gfvalues is very good, the average deviation being found to be within 34% when considering the 135 transitions of Table 2 with calculated log gf-values larger than -2, this deviation being even reduced to 14% when considering only the 78 strongest lines with log gf-values greater than -1. An overview of this comparison is illustrated in Figure 4. This is further confirmation that the DREAM data are trustworthy, especially for the most intense transitions.  [34], Eu III [35], Tm III [36], and Yb III [37].

Current status and developments of the DREAM database
The DREAM database contains information concerning the wavelengths, the oscillator strengths and the transition probabilities for spectral lines of neutral, singly-, doubly-and triply ionized lanthanides. The different available spectra are classified in order of increasing Z-values, and for a given Z, according to the ionization degree. For each line in a specific spectrum, the tables show, respectively : -The wavelength (in Å) deduced from the experimental energy levels. These wavelengths are given in air above 2000 Å and in vacuum below that limit. -The lower level of the transition represented by its experimental value (in cm −1 ), its parity ((e) for even and (o) for odd) and its J-value. Level energies (rounded values), are taken from the NIST compilations [1] and from subsequent publications. -The upper level of the transition presented in the same way as for the lower level.
-The calculated oscillator strength, log gf, where g = 2J + 1 is the statistical weight of the lower level of the transition. In general, only transitions for which log gf > −4.0 are reported in the tables. -The calculated transition probability, gA in s −1 , where g = 2J + 1 is the statistical weight of the upper level of the transition. -The cancellation factor, CF, as defined by Cowan [20]. Small values of this factor (typically CF < 0.05) indicate transitions affected by severe cancellation effects and should therefore be taken with some care. The details about the computational procedures are given in the different publications corresponding to the atomic systems considered and appearing at the top of each table. For some ions, experimental oscillator strengths and transition probabilities or normalized log gf-and gAvalues using measured lifetimes are given. In these cases, EXPT or NORM appears in the last column of the tables.
At present, more than 72000 spectral lines are listed in the DREAM database. They concern La I, La III, Ce II, Ce III, Pr II, Pr III, Pr IV, Nd II, Nd III, Nd IV, Sm II, Sm III, Eu III, Gd III, Tb III, Dy III, Ho III, Er II, Er III, Tm II, Tm III, Tm IV, Yb II, Yb III, Yb IV, Lu I, Lu II, and Lu III. This represents about 75 times more lines with transition probabilities than those currently available for the same ions in the NIST database [1]. For each of these ions, the exact number of lines reported in the DREAM database is given in Table 3 while a sample of data, corresponding to Lu II, is shown in Table 4.
It is also interesting to mention that a rather small number of computed transition rates reported in the DREAM database were found to be affected by strong cancellation effects (with CF < 0.05), indicating that the associated oscillator strengths could be unreliable [20]. Moreover we note that a large majority of these 'uncertain' transitions correspond to the weaker ones, with log gfvalues generally smaller than -2. This is illustrated in Figure 5 where the CF-factors are plotted as a function of log gf for all Ce II and Pr III lines listed in the DREAM database. A complete list of all the papers we have published regarding our theoretical and experimental investigations of lanthanide elements is also given in the database.

Some examples of uses of atomic data from DREAM
Since the creation of DREAM in 1999 [23], the database has been quoted several dozens times in the literature and the data compiled therein have been extensively used in different astrophysical studies. For instance, the important impact of this database on various astrophysical issues was already discussed by Jorissen [38] while its key role in the great improvement of the abundance patterns of neutron capture elements for metal poor stars was highlighted by Ryabchikova & Mashonkina [39] and Monier [40]. As stated in [39], the atmospheric modelling of the famous Przybylski's star (HD 101065), whose spectrum consists totally of lanthanide lines with a small number of other lines, became possible thanks to the use of oscillator strengths taken from the DREAM database. Let us also mention that, to ensure greater visibility, most of the DREAM data were incorporated into larger databases such as the Vienna Atomic Line Database (VALD) [41] and the Virtual Atomic and Molecular Data Center (VAMDC) [42].
Another remarkable usefulness of this database concerns the line at 6708.1 Å which was previously identified in some heavily s-process enriched post-AGB stars as being due to lithium, despite the redward shift of about 0.2 Å compared to other photospheric lines. This shift was then explained by hypothetical line formation in infalling circumstellar gas or photospheric downdrafts. Using the available atomic data from DREAM, this line could be safely identified as not being due to Li but coming from a Ce II transition at 6708.099 Å, the cerium abundance derived from this single line being comparable to the one deduced from other Ce II lines in the spectra [43]. Moreover, no inclusion of a significant amount of lithium at photospheric wavelength was needed in the synthesis of three highly s-process enriched stars, namely IRAS 05341+0852, IRAS 06530-0213, and IRAS 05113+1347, allowing to conclude that there was no evidence for in situ Li production and thus no need to invoke special non-standard mixing during the AGB evolution to explain the supposed high abundance of this fragile element in these stars. Using the DREAM database, a succesful systematic search for lines of elements beyond the baryum-peak could also be carried out in spectra of various s-process enriched post-AGB stars, leading, for the first time, to the determination of high abundances of elements heavier than europium, such as Gd, Yb and Lu, in these objects [44].
The use of oscillator strengths compiled in the DREAM database also allowed to identify new lanthanide lines in many different high-resolution astrophysical spectra and to deduce reliable abundances of rare earth elements (sometimes up to several orders of magnitude higher than the solar values in the case of various chemically peculiar stars), see, e.g., [45][46][47][48][49][50][51][52][53][54][55][56]. To give just one noteworthy specific example, we will mention the recent multicolour photometric investigation of the eclipsing binary system HD 66051 [53] carried out using, among other data, the spectroscopic parameters of the second and third spectra of lanthanides taken from the DREAM database. Thanks to a detailed analysis of the abundance patterns, the authors came to the conclusion that the primary component of this uncommon system is a slowly rotating late B-type star with a highly peculiar composition reminiscent of the singular HgMn related star HD 65949, where most of the heavy elements, in particular the lanthanides, are overabundant, while the secondary component is estimated to be a slowly rotating A-type star. As stated in [53], the unique configuration of HD 66051 opens up intriguing possibilities for future research, which might eventually and significantly contribute to the understanding of such diverse phenomena as atmospheric structure, mass transfer, magnetic fields, photometric variability and the origin of chemical anomalies observed in HgMn stars and related objects.
Finally, let us also mention the use of the atomic data compiled in the DREAM database in the context of neutron star mergers, as for example in two recent works published by Tanaka et al. [57,58]. In the first one, the authors performed radiative transfer simulations for neutron star merger ejecta powered by radioactive energy of r-process nuclei including, for the first time, all the r-process elements from gallium to U, thus including in particular the data for lanthanide elements available in the DREAM database. They could show that the opacity of the neutron star ejecta was higher than previously expected by a factor of about 100 due to many transitions of r-process elements. In the second study, three-dimensional, time-dependent, multi-frequency Monte Carlo radiative transfer simulations were performed for radioactively powered emission from black hole -neutron star mergers by taking into account the wavelength-dependent opacities of r-process elements using relevant atomic data among which those available in the DREAM database. This study allowed the authors to deduce a noteworthy property whereby, when the tidally disrupted black hole -neutron star merger ejecta are confined to a small solid angle, the emission tends to be bluer than that from neutron star -neutron star merger ejecta for a given total luminosity, which makes it possible to distinguish black hole -neutron star merger events from neutron star -neutron star merger events by multi-band observations of the radioactively powered emission. Such observations can also provide information on the progenitors of gravitational wave sources and the nature of compact objects merging.

Conclusions
The DREAM database currently contains radiative parameters (wavelengths, oscillator strengths, transition probabilities) for about 72700 spectral lines belonging to 28 different lanthanide atoms and ions. The large majority of the transition rates were obtained using the relativistic Hartree-Fock method including core-polarization and core-penetration effects and were validated by the good agreement obtained when comparing computed radiative lifetimes and accurate experimental values measured by the time-resolved laser-induced fluorescence technique. The reliability of the results reported in the database was also confirmed by the good agreement observed between the tabulated data and the most accurate experimental radiative lifetimes and/or transition probabilities recently published for some lanthanide ions. The DREAM database is certainly the most comprehensive at present available for spectroscopic parameters related to the lowest ionization stages of lanthanide elements and it is expected that it will be updated in the light of the new atomic structure calculations we intend to perform in the future for these species of great interest in many different scientific fields. However, new detailed semi-empirical calculations are largely compromised by the obvious lack of fundamental experimental data, in particular with regard to energy levels belonging to neutral and singly ionized lanthanides for which basic spectroscopic term analyses are urgently requested. Accurate branching fraction measurements, obtained using Fourier transform spectroscopy for example, would also be of great interest in order to provide, when combined with the available radiative lifetimes, new experimental transition probabilities in the many ions where such data have not yet been published. This would allow to further refine the estimation of uncertainties related to the calculated radiative parameters tabulated in the DREAM database.   [34]. d Experimental oscillator strengths, log gf, taken from Tian et al. [35]. e Experimental oscillator strengths, log gf, taken from Yu et al. [36]. f Experimental oscillator strengths, log gf, taken from Öberg and Lundberg [37].