## Free particle spectrum?

Err......no.
For simplicity, let's consider the total absorption of a photon by an electron in the lab frame, where the electron is initially at rest. For a photon of energy Eγ = pc and momentum p = Eγ/c , the final total energy of the recoiling electron would be

Ee= m0c2 + Eγ.

But the momentum of the recoiling electron would be p = Eγ/c,

leading to a total energy of

[Ee]2= [m0c2]2 + [pc]2= [m0c2]2 + [Eγ]2

These two equations are irreconcilably different, because energy and momentum cannot both be conserved..

Bob S

 Is the electron a composite particle?
 No, not yet at least. See the LBL Particle Data Group listing: http://pdg.lbl.gov/2002/s003.pdf Bob S
 So, that's the essential difference between your and my derivation. The electron's rest mass cannot change, since it is truly an elementary particle. However, composite particles (such as atoms, molecules, nuclei and even hadrons) have a complicated internal structure described by so called "internal degrees of freedom". The rest mass of a bound system is always smaller than the sum of the rest masses of its constituents, the difference being called mass defect $\Delta m$ and being connected to a quantity called binding energy of the system $B = \Delta m c^{2}$. This is why the whole energy of the photon can be absorbed by the composite particle. In order that we compensate for the momentum of the particle (at any given energy, massless particle have the highest possible momentum, so this is the "worst case scenario"), we better give the composite particle an equal by magnitude and opposite in direction momentum and, thus even more energy is available. Now comes the paradox. The whole amount of the photon energy + kinetic energy of the particle are supposed to increase the rest energy of the particle. This is only possible if the rest mass of the particle decreases. If you remember, the rest mass was smaller than the sum of the rest masses of the constituents and the difference (by definition positive) was called mass defect. Increasing the rest mass of the particle is equivalent to decreasing the mass defect, which, in turn is directly proportional to the binding energy of the system. We can only do this until the binding energy becomes zero. Then, the composite system becomes unbounded and it disintegrates into its constituent parts.
 (Bob S and Dickfore):Wow. But light does interact with an electron. It does get polarized-angular momentum gets exchanged.Why can't the electron gain mass along with the energy, or lose angular momentum, at least temporarily.

 Quote by george simpso (Bob S and Dickfore):Wow. But light does interact with an electron. It does get polarized-angular momentum gets exchanged.Why can't the electron gain mass along with the energy, or lose angular momentum, at least temporarily.
Please provide evidence for a process where a free electron absorbs a photon.

 Dickfore: Your request puts me back to where I was when I logged in to "free particle spectrum" For starters check out http://farside.ph.utexas.edu/teachin...s//node85.html. Next google "free electron laser" and "Absorption spectra of electrons in plasmas". There are a lot of experiments and calculation supporting absorption of a photon by an electron. For what it's worth, google "free electro absorb a photon" you'll get >200,000 responces. But, query "free electron cannot absorb a photon", and ther are ~100,000.( more data/opinions pro than con ). I think the evidence supports free electron absorption of a photon, but perhaps the collective physics wisdom does not. So, what do you come up with?

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 Quote by Dickfore One can view this increase in rest mass as excitation of the intrinsic degrees of freedom of the particle by an energy $\Delta \epsilon = \Delta M \, c^{2}$. We see that this dependence is a continuous function, so the absorbtion spectrum of the photon depends only on the excitation spectrum of the particle. Notice that the translational degrees of freedom where not limited and, therefore, they are not quantized.
Not sure what your point is exactly, but these excitations of intrinsic degrees of freedom can not include excitations of translational degrees of the composite particle, since that would violate the requirement that the final particle momentum be zero in this frame.

So you are only allowed to excite the other degrees of freedom: rotational, vibrational, and interaction terms (which are all quantized).

 Quote by george simpso ... "Absorption spectra of electrons in plasmas". There are a lot of experiments and calculation supporting absorption of a photon by an electron. ...
Electrons in plasmas are free? Google "collective modes in plasmas"
 Quote by Gokul43201 Not sure what your point is exactly, but these excitations of intrinsic degrees of freedom can not include excitations of translational degrees of the composite particle, since that would violate the requirement that the final particle momentum be zero in this frame. So you are only allowed to excite the other degrees of freedom: rotational, vibrational, and interaction terms (which are all quantized).
Exactly what I was saying and those contribute to the rest mass of a composite object.

 Recognitions: Science Advisor Free electrons can absorb EM radiation via inverse Bremsstrahlung absorption, the catch being that it can only occur in the vicinity of atoms. Claude.

 Quote by Claude Bile Free electrons can absorb EM radiation via inverse Bremsstrahlung absorption, the catch being that it can only occur in the vicinity of atoms. Claude.
So, how are they free if they are in the vicinity of atoms?

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 Quote by Dickfore So, how are they free if they are in the vicinity of atoms?
Free as in not bound to a nucleus. Conduction band electrons in a condensed dielectric for example.

Claude.

 Quote by Claude Bile Free as in not bound to a nucleus. Conduction band electrons in a condensed dielectric for example. Claude.
What is the meaning of this 'band' you are using?

(Posted by Dickfore:)
So, how are they free if they are in the vicinity of atoms?
 Quote by Claude Bile Free as in not bound to a nucleus. Conduction band electrons in a condensed dielectric for example.
The difference between the photoelectric effect, in which the photon's total energy is absorbed by the electron, and Thomson scattering on free electrons, is that a little recoil momentum is absorbed by the recoiling atom or atomic lattice. Conduction electrons are not free electrons; the work function to remove a conduction electron is >= 3 eV.

Bob S

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