I Can atoms absorb photons with energy higher than transition energy?

[Haorong Wu]

TL;DR Summary

Can atoms absorb photons with energy higher than transition energy?

Suppose a atom has two energy levels $\hbar \omega _ a$, and $\hbar \omega _b$, and let $\hbar \omega _0 =\hbar \omega _b -\hbar \omega _a$. Also, there is a phton with enerigy of $\hbar \omega$.

If $\hbar \omega =\hbar \omega _0$, then a atom in level $\hbar \omega _ a$ can absorb this photon and jump into level $\hbar \omega _b$.

What if $\hbar \omega =\hbar \omega _0 + \epsilon$, where $\epsilon \gt 0$ ? Where would the additional energy $\epsilon$ be?

Would it become part of the energy of the atom which has just absorbed the photon, or would it become a new photon with energy $\hbar \omega '= \epsilon$?

 

[PeterDonis]

What if $\hbar \omega =\hbar \omega _0 + \epsilon$, where $\epsilon \gt 0$ ?

Then the atom cannot absorb the photon. At least, that's the case for an atom alone in free space.

If the atom is inside a solid, then it might be able to absorb the photon, if there are vibration modes of the solid or other degrees of freedom that can take the extra energy $\epsilon$. Note that these degrees of freedom will be quantized as well, so this will only work for particular values of $\epsilon$, not all values.

 

[PeterDonis]

would it become a new photon with energy $\hbar \omega '= \epsilon$?

Not for an atom alone in free space, since the atom can't absorb the photon in the first place.

For an atom in a solid, if there are extra degrees of freedom available with the right energy spectrum, then the extra energy $\epsilon$ that got absorbed into those extra degrees of freedom could be re-emitted as another photon, yes.

 

[Haorong Wu]

Not for an atom alone in free space, since the atom can't absorb the photon in the first place.

For an atom in a solid, if there are extra degrees of freedom available with the right energy spectrum, then the extra energy $\epsilon$ that got absorbed into those extra degrees of freedom could be re-emitted as another photon, yes.

Thanks, PeterDonis. Great answers!

 

[PeterDonis]

Thanks

You're welcome!