Hydrogen and Helium

Hydrogen and helium are essentially impossible to detect by a lab-based XPS. Helium is not normally present as a solid and even when present (implanted) in a solid its 1s orbital has a very small cross-section for photoemission. Hydrogen also has an extremely small photoelectron cross-section and suffers from having to share its only electron in forming compounds, which then resides in a valence-like orbital.

Recent work [1] using a synchrotron based ambient pressure (AP) XPS has shown that it is possible to detect these elements with these specialized instruments.  A lower energy, high flux X-ray source increases the cross-section for H and He dramatically, and ambient pressure apparatus are needed to handle these gas phase elements.  Note that lab based AP-XPS cannot detect these elements - the synchrotron source is essential for this type of work.

Reference:
[1] J.-Q. Zhong, M. Wang, W.H. Hoffmann, M.A. van Spronsen, D. Lu, J.A. Boscoboinik, Appl. Phys. Lett. 112 (2018) 091602.