Asking a question Has anyone tried to incorporate the electrons magnetic dipole moment into the atomic orbital theory?, I was curious whether anyone has attempted to relate the intrinsic property of the magnetic moment of the electron to the above-mentioned properties of spin.

In the extremely detailed answer (thanks to the author, who took the time despite the pointlessness of such a question) it is clarified that

The effects are weak, and they are secondary to all sorts of other interactions that happen in atoms,...

Also, in case you're wondering just how weak: this paper calculates the energy shifts coming from electron spin-spin coupling for a range of two-electron systems. The largest is in helium, for which the coupling energy is of the order of $\sim 7 \:\mathrm{cm}^{-1}$, or about $0.86\:\rm meV$, as compared to typical characteristic energies of $\sim 20\:\rm eV$, some five orders of magnitude higher, for that system.

Now there is a new question about Electron to electron interaction.

There is a critical distance

$$d_\text{crit}=\sqrt\frac{3\epsilon_0\mu_0\hbar^2}{2m^2}=\sqrt{\frac{3}{2}}\frac{\hbar c}{m}=\sqrt{\frac{3}{2}}\overline\lambda_C,$$

where $\overline\lambda_C$ is the reduced Compton wavelength of the electron, at which the two forces are equal in magnitude.

Since the Compton wavelength is a standard measure of where quantum effects start to be important, this classical analysis can't be taken too seriously. But it indicates that spin-spin interactions are important at short distances.

I wonder how these two points of view can be related.


They can be related by the fact that the Bohr radius of hydrogen is $1/\alpha\approx 137$ times larger than the reduced Compton wavelength of the electron. (Here $\alpha$ is the fine-structure constant. For helium, divide by 2 to get 68.5.) At this large a separation between the proton and electron, the magnetic interaction that I calculated is small compared to the electrostatic interaction.

  • $\begingroup$ May you expand your answer to the electron-electron interactions in atoms? $\endgroup$ – HolgerFiedler Aug 19 at 6:18
  • $\begingroup$ That's a messy subject that I don't want to get into. $\endgroup$ – G. Smith Aug 19 at 6:21
  • $\begingroup$ Why it is a messy subject. Will I get an answer asking this on PSE? $\endgroup$ – HolgerFiedler Aug 19 at 6:32
  • $\begingroup$ intuitively it is all due that there are no magnetic monopoles, and the magnetic dipoles are a higher order effect, whereas the Bohr orbits come from first order effects. $\endgroup$ – anna v Aug 19 at 6:49
  • $\begingroup$ @annav So there is no chance to calculate the interactions of a model of electrons magnetic dipoles - say for Ne - numercally? $\endgroup$ – HolgerFiedler Aug 19 at 7:28

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