# Line-shape asymmetry in undergraduate Hydrogen-Deuterium experiment

I'm working as an LA (undergraduate TA) for an undergraduate physics laboratory experiment where students test the Bohr model and use reduced mass to determine the approximate mass of the neutron.

In the experiment, a discharge tube is filled with a mixture of H and D gas, and the data that come from the spectrometer (Ocean Optics HR-2000 with an optical resolution of about 0.04 nm) look fairly defined. However there's an asymmetry in the peak (the peaks are skewed to the left slightly), and this is bothering me a little bit. The results that students get from fitting gaussians to the peaks are pretty good in terms of agreeing with the literature but the models themselves don't get great reduced chi-square values.

Where could the asymmetry come from? Doppler and natural lifetime broadening are symmetric and should yield a Voigt profile, which is symmetric. These contributions are also much smaller than the instrument resolution.

Using the optical resolution as the standard deviation of a gaussian instrument error function, I fit these peaks with a model taking fine-structure into account (fine-structure is about half the size of the instrument error). This, however yields some very poor confidence intervals in the fit and still does not fix the high chi-squared value.

The only things left that I can think of are instrument error (which I think could be asymmetric) or (grasping at straws here) something kind of complicated like a fano resonance.

What could this be? Is there any reason to think that the peak line shape of H$_\alpha$ should be skewed?

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Now this is a good question. A picture or plot would be make it even better. I think the inherent shape of the peak is actually a Lorentzian rather than a Gaussian, but that won't give you the observed asymmetry. Another place to look would be in the behavior of your instruments. In any case, very interesting. – dmckee Jun 22 '13 at 17:05
Actually, poking around the link I gave for the Lorentzian suggests yoo may actually have a Voigt lineshape. Might be worth looking at. – dmckee Jun 22 '13 at 17:22
Thanks for the prompt reply! So my belief in using gaussians is based on the thought that the doppler broadening dominates the natural lifetime broadening. Doppler should have a contribution on the order of $\sqrt{k_BT/m_{H_2}} \lambda_0$, much larger than the natural lifetime broadening effect (of order $10^{-4}$ angstroms). In the limit where the Lorentzian looks like a delta relative to the doppler broadening, the voigt function approaches the gaussian. – Dawson Baker Jun 22 '13 at 19:46