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https://github.com/nategphillips/spectra

A simulation of the Schumann-Runge bands of molecular oxygen written in Python.
https://github.com/nategphillips/spectra

python spectroscopy

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A simulation of the Schumann-Runge bands of molecular oxygen written in Python.

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README 

        
# spectra



> *Last Updated: 6 June 2024*



A simulation of the Schumann-Runge bands of molecular oxygen written in Python.



## Background



This is a simple tool for computing and displaying the spectrum of molecular oxygen for the $B^3\Sigma_u^- - X^3\Sigma_g^-$ transition. The vibrating rotator approximation is used, with up to fourth-order corrections being applied to the vibrational term value.



Diatomic constants are obtained directly from the [NIST database](https://webbook.nist.gov/cgi/cbook.cgi?ID=C7782447&Mask=1000#Diatomic). General theory and notation are explained in the included document.



Included within this tool for comparison are:



- Experimental data from the [Harvard CFA molecular database](https://lweb.cfa.harvard.edu/amp/ampdata/cfamols.html)

- Simulated data from [PGOPHER](https://pgopher.chm.bris.ac.uk/Help/makeo2.htm)

- Tabulated data from [HITRAN](https://hitran.org/lbl/3?36=on)

- Simulated data from [Cosby 1993](https://ntrs.nasa.gov/citations/19930050666)



## Features



This tool includes features for:



- Population density based on the Boltzmann distribution and total partition function

- Simulating the effects of triplet splitting



The plots can be displayed as:



- Quantized spectral line positions

- Convolved lineshapes given a measurement temperature and pressure to better match experimental data

- Comparisons with experimental or simulated data



Convolutions include the effects of:



- Thermal doppler broadening (Gaussian)

- Pressure broadening (Lorentzian)

- Natural broadening (Lorentzian)

- Predissociation broadening (Lorentzian)



The effects are all computed and convolved into an overall Voigt profile.



Since this tool only simulates the Schumann-Runge bands of $\text{O}_2^{16}$, neither the molecule nor the electronic transition can be changed. Vibrational transitions up to around $v=15$ are supported with the included Franck-Condon factor tables, but the constants currently used are only valid to around $v\approx9$. The maximum rotational quantum number is $N=35$, which is limited by the predissociation broadening data used.



## Example Spectrum



An example spectrum of $\text{O}_2^{16}$ using:



- $(v',v'')=(2,0)$

- $N_\text{max}=35$

- $T=300$ $\text{K}$

- $p=101325$ $\text{Pa}$



Convolved lineshapes are simulated and plotted against sample data from the [Harvard CFA database](https://lweb.cfa.harvard.edu/amp/ampdata/o2pub92/o2wb2x0.xsc).



![Example Spectrum](img/example.webp)



## Roadmap



There is quite a bit of functionality I'd still like to add in the future, such as:



- [x] Predissociation linewidth broadening in the Lorentzian convolution

- [x] Addition of Franck-Condon factors to allow for the computation of two or more vibrational transitions at once

- [x] Add support for including the effects of laser-induced fluorescence (LIF) spectroscopy

- [ ] Add correct predissociation rates for all vibrational and rotational quantum numbers

  - Currently using data that is only valid for $v' = 0$

- [ ] Compute the number of photons emitted by a given band for LIF