Imagine a photon hits a hydrogen ion and is absorbed, how do the nucleon of the hydrogen knows and start to accelerate? Any difference between this and hydrogen ion in a electric field?
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The hydrogen ion is just a proton (assuming we are taking about $\,^1H_1$ here).
The first process that you have described is not technically possible. See proof in the footnote before. The closest you can come is a Compton scattering which is just a fancy term for the process where a photon hits a proton and another photon is emitted with a different frequency while the proton's momentum and energy is changed as a result.
The second process has to be between two charged particles with the two exchanging virtual photons in the process.
The biggest difference is in the nature of particles involved. The former involves three particles --one incoming real photon, one proton, and one outgoing real photon. In the latter, you have one proton, one other charged particle of your choice, and some virtual photons.
Footnote:
We operate in a frame where the proton is initially at rest. Let's say that the incident photon has a momentum $p_{\nu}$. After the collision, the proton has a final momentum $p_p$. Now, conservation of momentum implies $p_{\nu} = p_p$. But conservation of energy implies $m_pc^2 + p_{\nu}c = \sqrt{m_p^2c^4 + p_p^2c^2}$. The two equations are not compatible with each other. Here $m_p$ is the mass of proton.
