The hydrogen emission spectra and the corresponding anti-hydrogen emission spectra are expected to exhibit similar patterns due to their similar atomic structures. However, subtle differences can arise due to the influence of quantum effects, such as the Lamb shift, which is a small correction to the energy levels of the atom.
The Lamb shift arises from the interaction between the electron in the atom and the surrounding vacuum fluctuations of the electromagnetic field. It causes a slight deviation from the theoretical predictions based solely on classical electromagnetism. The Lamb shift has been experimentally verified in hydrogen, and it agrees well with theoretical predictions.
Regarding anti-hydrogen, experiments conducted at CERN (the European Organization for Nuclear Research) have focused on studying its properties, including its emission spectra. The ALPHA experiment at CERN has made measurements of the 1S-2S transition in anti-hydrogen, which is analogous to the hydrogen Lamb shift. So far, the results indicate that the anti-hydrogen Lamb shift is consistent with the hydrogen Lamb shift within the experimental uncertainties.
It is important to note that precision measurements of anti-hydrogen properties are challenging due to the technical difficulties involved in producing and manipulating antimatter. The current experimental data on the Lamb shift in anti-hydrogen is still limited, and further studies are needed to improve our understanding and reduce the uncertainties.
In summary, based on the available data, there is no evidence pointing to statistically significant differences in the Lamb shift between hydrogen and anti-hydrogen emission spectra. However, ongoing research and future experiments will continue to shed light on this topic and refine our understanding of antimatter physics.