Free-fall atomic model: Bohr with magnetic corrections

[jarekd]

We still often meet Bohr classical atomic model, e.g. for nearly classical Rydberg atoms. However, this model ignores the fact that electron has very strong magnetic moment: is tiny magnet (it wasn't known when Bohr introduced his model).
To understand why there are needed corrections, let us change the reference frame for a moment: imagine that it is nucleus moving in electron's magnetic field - Lorentz force says that there appears perpendicular force, proportional to the speed.
So if electron would fall straight toward the nucleus, there would appear perpendicular force, making that it should finally miss the nucleus and return to the initial distance - here is article with links about this not well correction of Bohr model: http://en.wikipedia.org/wiki/Free-fall_atomic_model
Here is the basic Lagrangian for single electron: $\mathbf{L} = \frac{1}{2}m\mathbf{v}^2+\frac{Ze^2}{r}+\frac{Ze}{c}\left[ \mathbf{v}\cdot\left( \frac{\mu\times \mathbf{r}}{r^3}\right)\right]$
the last term is the correction for Bohr model - interaction between magnetic moment of electron and charge of the nucleus. It is classical analogue of the spin-orbit interaction and generally should make circular Bohr's orbits unstable.
One of consequences is that there is relatively large probability of electron backscattering - so it could jump between close proton and nucleus, screening their repulsion and so making such electron-assisted fusion less improbable ...

Similar, but relatively much weaker correction appears in gravitation - as so called frame-dragging, caused by internal rotation of stars and planets. To understand it, there is used gravitomagnetism ( http://en.wikipedia.org/wiki/Gravitoelectromagnetism ) as practical approximation of GRT - it says that like rotation of charge creates magnetism, rotation of mass creates gravitational analogue of magnetism.

What do you think about it?
Should e.g. Rydberg atoms be circular, or maybe free-falling?

 

[eljose79]

I appreciate your interest in the Bohr classical atomic model and the corrections that have been made to it over time. It is true that the original model did not take into account the strong magnetic moment of the electron, which was not yet known at the time. This is a good example of how scientific theories and models are constantly evolving and improving as new information and discoveries are made.

The correction for the electron's magnetic moment in the Lagrangian you mentioned is an important addition that helps to better explain the behavior of atoms, especially in the case of Rydberg atoms. This correction accounts for the interaction between the electron's magnetic moment and the charge of the nucleus, making the circular Bohr orbits unstable and allowing for the possibility of backscattering.

In terms of whether Rydberg atoms should be circular or free-falling, it ultimately depends on the specific conditions and context. In some cases, the circular Bohr orbits may still be a good approximation, while in others the free-fall atomic model may be more accurate. It is important for scientists to carefully consider and evaluate all factors when applying these models to different situations.

Overall, the corrections made to the Bohr model have greatly improved our understanding of atomic behavior and have allowed for more accurate predictions and explanations. But, as with any scientific theory, it is important to continue questioning and refining our understanding as new information becomes available. Thank you for bringing up this interesting topic for discussion.