# Stark broadening and Voigt fitting

I have LIBS spectral data acquired with a CT spectrometer of resolution 0.4nm. I fitted the Voigt profile into the spectral peak at $\lambda_0$. The lorentz $\Delta \lambda_L$ and the gaussian $\Delta \lambda_G$ were calculated. I also used a UV lamp to obtain the instrumental parameters ($\Delta \lambda^a_L$ and $\Delta \lambda^a_G$) using a narrow peak and Voigt profile fitting as well.

How can I obtain the corrected $\Delta \lambda_{Stark}$?

• Can you discuss more about how you measured the instrument broadening (both Lorentzian and Gaussian)? – iwantmyphd Apr 18 '16 at 18:19

## 1 Answer

There are several broadening mechanisms, and you have to know how they "add" together. Since a Voigt profile is the convolution of a Gaussian and Lorentzian profile, you rightly calculated both widths rather than just the overall width of the Voigt peak. For the Lorentzian portion, the width is the arithmetic sum of the individual widths:

$\Delta \lambda_{L} = \Delta\lambda_{Nat}+\Delta\lambda_{VDW}+\Delta\lambda_{Stark}+\Delta\lambda_{Res}+\Delta\lambda_{Inst}$

and for the Gaussian portion it is the square root of the sum of the squares:

$\Delta \lambda_{G} = \sqrt{ \Delta\lambda_{Inst}^{2} + \Delta\lambda_{Dopp}^{2} }$

and the sum of them is:

$\Delta \lambda_{V} = \frac{ \Delta \lambda_{L}}{2} + \sqrt{ \frac{\Delta\lambda_{L}^{2}}{4} + \Delta\lambda_{G}^{2} }$

Stark broadening, along with Natural broadening, Resonance broadening, van der Waals broadening, and the Lorentzian part of the instrumental broadening, are all added together. Since you know the instrumental broadening, you can subtract that. I assume you can find or calculate the Natural line width from data tables. That leaves Resonance and van der Waals broadening that need to be subtracted out to get just Stark broadening. Otherwise, the best you can do is to say that Stark broadening is within a range of values; zero if Stark broadening were not present at all, and the remaining width if you subtracted Natural and instrumental, and then assumed there was no van der Waals or Resonance.