Rare gases : calculating absorption by oscillator strength

[Ecthe]

Hello,

I have some papers (I can give references if needed) giving the oscillator strength of rare gases for a given energy bandwidth and from those values, I would like to calculate their absorption in those bandwidth. However, I am a little bit lost in how to do it. I looked a bit around and found lots of references on how to do it but I am still confused.

For exemple, in http://gausssum.sourceforge.net/GaussSum_UVVis_Convolution.pdf, the answer I need seems to be the equation 9. But with only data on the oscillator strength, how can I found ${\Delta}_{1/2}{\nu}'$ or ${\nu}'_{i{\rightarrow}f}$ ?

I am not saying that the reference I used as an exemple is a good starting point and I would be glad to have a solid book reference for that.

Thanks in advance and looking foreward for some help.

PS: please forgive my english mistake, I am not fully comfortable in writting it.

 

[eljose79]

Hello,

Thank you for your question. Calculating the absorption of rare gases from oscillator strength values can be a bit complex, but I can provide some guidance and resources to help you.

Firstly, let's define some terms. The oscillator strength (f) is a dimensionless quantity that measures the strength of an electronic transition between two energy levels. The bandwidth (Δν) is the range of frequencies over which the absorption is being measured. The half-width (Δ1/2ν') is the width of a line at half of its maximum intensity, and the transition frequency (ν'i→f) is the frequency at which the transition occurs.

To calculate the absorption, you will need to use the equation:

A = f * N * σ * Δν

where A is the absorption, N is the number density of the absorbing species, and σ is the absorption cross-section. The absorption cross-section can be calculated using the following equation:

σ = (8π^3me^2/3hc)(ν'i→f)^2fΔ1/2ν'

where me is the electron mass and h is Planck's constant.

To find the values for Δ1/2ν' and ν'i→f, you will need to consult a database or literature source that provides this information for the specific rare gases you are studying. One resource that may be helpful is the NIST Atomic Spectra Database (https://www.nist.gov/pml/atomic-spectra-database). This database provides detailed information on energy levels, transition frequencies, and oscillator strengths for various elements.

Additionally, I recommend consulting a textbook on atomic spectroscopy, such as "Atomic Spectra and Atomic Structure" by Gerhard Herzberg or "Atomic Spectra and Radiative Transitions" by Walter Greiner. These books provide a more comprehensive understanding of the theory and calculations involved in atomic spectroscopy.

I hope this information helps you in your research. Best of luck!