Atomic emission lines

Most of the lines we see in LIBS spectra are atomic emission lines that are result of the energy level differences between the free electron shells of atom in question.

In hot plasma the outermost electron jumps on higher energy levels, and when it returns back to a lower energy atomic orbital is when a light emission occurs.

There are also molecular emission lines for some specific molecules that we can see in LIBS spectrum, which are presented shortly in chapter on molecular LIBS examples

Linelists

There is no fully comprehensive list of all atomic emission lines. Some of the best atomic line datasets are are:

• NIST ASD Atomic Spectral Database at https://www.nist.gov/pml/atomic-spectra-database. At least 293550 lines according to my own extraction of their database. NIST has a LIBS specific NIST LIBS interface which is often a nice starting point for LIBS analysis.

• Kurucz

Robert L. Kurucz passed away in March 2025 https://www.keefefuneralhome.com/memorials/robert-l-kurucz/5559934/. He had dedicated much to understand stars and in doing that computed models and spectra and datasets of billions of spectral lines. We are very thankful for his work. linelists at http://kurucz.harvard.edu/linelists.html. 2.31 million "good" lines and 850million predicted lines. They are freely available for download.

• VALD Vienna Atomic Line Database at https://vald.astro.uu.se/. According to Pakhomov et al.

Pakhomov, Y., Piskunov, N. and Ryabchikova, T. (2017) ‘VALD3: current developments’. arXiv. Available at: https://doi.org/10.48550/arXiv.1710.10854. in 2015 VALD offered 1.2 million "good" lines with accurate wavelengths and 250 million predicted, but it's been updated since and includes Kurucz datasets so the total number of lines presently(in 2025) in VALD is certainly more. VALD can be used after a quick email registration which is open for everyone.

So we have millions or hundreds of millions of known emission lines, depending if we consider the predicted lines as known. These huge numbers make it clear how atomic transitions and emissions is not an easy problem to comprehensively describe.

Only a tiny fraction of these lines will be significant in our analysis, but to find out which ones we want to use the most complete datasets. For LIBS we only need to consider the low ionization levels, mostly base state and first ionization, so that helps us trim the dataset down a lot.

The VALD and Kurucz datasets have separate collections for hyperfine splitting of atomic lines. Pakhomov, Yu.V., Ryabchikova, T.A. and Piskunov, N.E. (2019) ‘Hyperfine Splitting in the VALD Database of Spectral-line Parameters’, Astronomy Reports, 63(12), pp. 1010–1021. Available at: https://doi.org/10.1134/S1063772919120047".

Atomic line datasets processing

A request from VALD gives us a table of atomic lines, for example (Nickel atomic lines):

For our purpose of calculating atomic emissions we only need the element, ionization, wavenumber, "log gf" an E_up values so we only take those columns and get the following kind of table:

Nickel atomic lines:

The relative intensities of atomic lines(at same ion level and plasma parameters) from the same upper state is given by $10^{loggf} \cdot wn^2$, which we derive in section XX. And the populations of these states in a given temperature is calculated by Boltzmann equation and the populations of different ions by Saha equation. Combining these three we can calculate expected line intensities.

Kurucz and NIST ASD, and VALD datasets have the same information but instead using NIST ASD gives Einstein coefficients $A_{ki}$ instead of loggf values.

Why does an atom have its specific lines?

kinda poetically

Electrons are standing waves bound to an atom. The different energy levels are different possible harmonics of these standing waves around an atom. Giving more energy to the electron cloud will tune up an electron to a higher frequency and thus change the music. But the conductor of the orchestra is cheap and only wants to hear the energetically lowest possible frequencies and so all solo electrons playing their own tune will eventually fall back in to their designated place where they fill every harmonic one by one from the lowest energy upwards.

Explained

Every atom or ion has electrons around it in a set of specific energy levels (electron shells) filling up starting from lowest energy i.e. most tightly bound electrons. Above highest energy electron is a set of empty potential shells where an electron could be. On the highest of these low levels we have what we call an optical electron that will jump up if we give it energy via heat or radiation. The optical electron returning back down to its proper place can happen through all the possible paths. The energy differences from these jumps back down is what makes up the atomic line emissions we see.

If the available free energy levels for the optical electron of an atom are few and far between we get a simple easy to read spectrum with only few lines such as with hydrogen or lithium. And conversely if there are lots of of energy levels close to each other, such as with iron or other transition metals, we see a messy spectrum of thousands of lines.

Some example atom energy levels and transitions between them illustrated. Note that the possible transitions which is same as the number of atomic lines grows as a factorial of available energy level.

NOTES

What is "log gf"?

It is calculated log_10 g*f,

where:

• $g$ is the statistical weight of the lower energy level, and $f$ is the oscillator strength of the transition.

from this value together with plasma parameters we can calculate the relative intensities of the atomic lines.