Why is spin-orbit coupling neglected in Helium atom?

Click For Summary

Discussion Overview

The discussion centers on the role of spin-orbit coupling in the helium atom, particularly why it is often neglected in analyses compared to other effects like spin-spin coupling. Participants explore the implications of this neglect on the fine structure of helium's spectral lines.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant notes that while spin-orbit coupling is small in helium, it is still present, unlike in hydrogen where it is more significant.
  • Another participant explains that spin-orbit coupling is a relativistic effect that is less pronounced in lighter atoms like helium due to weaker nuclear attraction, which does not accelerate electrons to relativistic speeds.
  • A different viewpoint questions the absence of spin-orbit coupling in helium, pointing out that hydrogen, which is lighter, does exhibit fine structure due to this interaction.
  • One participant suggests that the analytical treatment of spin-orbit coupling in hydrogen is feasible, while for multi-electron atoms like helium, it is more complex and often omitted in introductory texts.
  • There is a discussion about the implications of neglecting spin-orbit coupling, particularly regarding the fine structure of helium's spectral lines, with one participant asserting that without it, there would be no observable splitting of energy levels.
  • Another participant raises confusion about the Grotrian diagram, noting that while the J value is included, the absence of vertical separation suggests a lack of observable fine structure.
  • One participant argues that including spin-orbit coupling would necessitate accounting for additional corrections, such as nuclear spin and Lamb's shift, which complicates the analysis.
  • Reference to external resources, such as the NIST database, is made to illustrate the small magnitude of spin-orbit splitting in helium compared to other energy level differences.

Areas of Agreement / Disagreement

Participants express differing views on the significance of spin-orbit coupling in helium, with some arguing it can be neglected while others emphasize its presence and implications for fine structure. The discussion remains unresolved regarding the extent to which spin-orbit coupling affects helium's spectral lines.

Contextual Notes

Participants highlight the complexity of accurately incorporating spin-orbit coupling in multi-electron systems and the potential for additional corrections that complicate the analysis. The discussion reflects uncertainty about the implications of these factors on the observed spectral lines of helium.

misko
Messages
46
Reaction score
0
I was looking at grotrian diagrams for helium and I see that there is no splitting of energy levels due to spin-orbit coupling. In my book it is said that spin-orbit coupling in helium is small and can be neglected but no further explanation is given. At the same time we do spin-spin coupling between electrons in He which obviously is not negligible.

If there is no spin-orbit coupling then there is no fine structure in helium spectral lines like in alkali metals, right? So why is that we can neglect spin-orbit coupling in He?
 
Physics news on Phys.org
Spin-orbit coupling is the first-order portion of relativistic effect in atoms or molecules. For light atoms such as He, the nuclear attraction is not so strong to cause the electrons to move in relativistic speed, hence the relativistic effect is small and in turn the spin-orbit coupling is also small.
In contrast, spin-spin coupling is independent of relativistic motion because it's solely governed by Pauli exclusion principle - any system with more than one identical particles will show up to some extent the effect of Pauli principle.
 
But we have spin-orbit interaction taken into account for hydrogen atom fine structure and hydrogen is even lighter than helium.

Here http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/hydfin.html they say:

When the familiar red spectral line of the hydrogen spectrum is examined at very high resolution, it is found to be a closely-spaced doublet. This splitting is called fine structure and was one of the first experimental evidences for electron spin.
hfin1.gif

The small splitting of the spectral line is attributed to an interaction between the electron spin S and the orbital angular momentum L. It is called the spin-orbit interaction.
 
It's not like the spin-orbit effect He completely vanishes, it's there but very small (still larger than hydrogen I think). The good thing with hydrogen is that the spin-orbit coupling can be analytically incorporated perturbatively as well as exactly through the Dirac equation. The same thing in any other atom with more than one electron is almost imposible to do. That's why in most introductory books on atoms and molecules the author never bothers to account for spin-orbit effect analytically.
 
  • Like
Likes   Reactions: misko
So to sum it up, if there is no spin-orbit coupling (or we neglect it) then there is no fine structure in He?
By fine structure I mean spectral lines split in more than one component (with no external magnetic field present) if we look at it with high enough resolution.

For example on this Grotrian diagram for He https://www.physics.byu.edu/faculty/christensen/Physics%20428/FTI/Helium%20Grotrian%20Diagram%27.htm
there is no vertical separation between terms 3D0,1,2 on the right (triplet) side of diagram. Does it mean that for example any transition from 33D0,1,2 to say 23P0,1,2 gives just one line? Like all D terms have same energy no matter value of J.

Please correct me if my understanding is wrong, here is my logic: if there is spin-orbit coupling then there is split of energy levels which gives line splitting (small but observable). So if there is no spin-orbit coupling there is no fine structure?

However on this diagram they included J value in term symbol (low right corner) which means that they did perform LS spin-orbit coupling but still they didn't draw separation of energy levels. Confused...
 
misko said:
So to sum it up, if there is no spin-orbit coupling (or we neglect it) then there is no fine structure in He?
Yes.
misko said:
there is no vertical separation between terms 3D0,1,2 on the right (triplet) side of diagram. Does it mean that for example any transition from 33D0,1,2 to say 23P0,1,2 gives just one line?
Yes.
misko said:
So if there is no spin-orbit coupling there is no fine structure?
Yes.
misko said:
However on this diagram they included J value in term symbol (low right corner) which means that they did perform LS spin-orbit coupling but still they didn't draw separation of energy levels. Confused...
If they shall include spin-orbit, then there is no reason to exclude nuclear spin. In turn, if they do include nuclear spin, they should also take the radio wave level Lamb's shift. And if they include Lamb's shift, the gravitational effect should not be left behind.
It will be an endless of an addition of correction terms. The reason why that diagram does not include spin-orbit is just because it's too small to be of significant importance for the topic being discussed.
Take a look at this database from NIST http://physics.nist.gov/PhysRefData/Handbook/Tables/heliumtable5.htm and see how small the splitting for 3P0,1,2 levels is compared to the difference between this level with 1S.
 
  • Like
Likes   Reactions: misko

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 0 ·
Replies
0
Views
904
  • · Replies 1 ·
Replies
1
Views
2K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
Replies
6
Views
4K
  • · Replies 1 ·
Replies
1
Views
18K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 2 ·
Replies
2
Views
5K