0
$\begingroup$

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.

$\endgroup$
2
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.