# Splitting of atomic orbitals due to Stark effect

I am performing graduate level research on ZEKE Photoelectron Spectroscopy and central to this form of spectroscopy is Rydberg states and the Stark effect. The Stark effect is caused by an electric field polarizing the species, thereby inducing a non-zero dipole moment. This causes degenerate states to split. However, say for the hydrogen atom's $$n = 2$$ state, there is 4-fold degeneracy: $$\mathrm{2s}$$, $$\mathrm{2p}_x$$, $$\mathrm{2p}_y$$, and $$\mathrm{2p}_z$$. When an external electric field is applied to the system, two spectral lines, each red and blue-shifted, are observed for the $$\mathrm{2s}$$ and $$\mathrm{2p}_x$$ orbitals. Each has an azimuthal quantum number equal to $$0$$.

Why are only these orbitals shifted? I do not understand why each of these orbitals are split; is it because each is centered on the $$z$$-axis? Is what I described only apply to the linear Stark effect, and the $$\mathrm{2p}_x$$ and $$\mathrm{2p}_y$$ orbitals are shifted according to the quadratic Stark effect? If so, what is the difference between the linear and quadratic Stark effects?

I have read several research papers about the matter, but I don't have a strong understanding of math involved in quantum mechanics. Typically, when the author explains the Stark effect using Dirac notation, I quickly become confused.

• Presumably, your grad level studies are under the supervision of whomever is supporting the research, so ask them to recommend suitable reference publications. This is something research mentors/advisors/directors are happy to do: they want you to succeed. And taking a course or two might help with such things as the Dirac notation! Best of success!
– Ed V
Apr 20 '21 at 18:11
• A proper understanding will require some quantum mechanics (especially angular momentum). A good reference for the Stark effect in Rydberg states is Gallagher's book. Note also that there are several things happening here as well: the levels split and there are transitions between the levels that are governed by selection rules.
– Paul
Apr 20 '21 at 18:36