# Photoelectric Effect via QED?

• A
Chapter 5 of this book:

https://www.amazon.com/dp/0750633719/?tag=pfamazon01-20

as one can see in the table of contents preview, discusses the photoelectric effect starting from the first principles of quantum field theory developed in the earlier chapters.

I can't find another qft book which discusses the photoelectric effect, or anything from chapter 5 really. For example one cannot find much material in a book like Peskin and Schroeder which discusses material from chapter 5.

I am wondering why this is so - what is the point of chapter 5, and what makes it different to what qft books usually discuss, such as Compton scattering, Bremsstrahlung etc...?

My guess is that chapters 4 and 5 are discussing bound state problems (Schweber makes the comment that scattering cannot account for bound state problems), and so I am simply facing the same question brought up in:
• "With regard to phenomena, I recall wondering, as a student, why some of the fundamental things I studied in NRQM seemed to disappear in QFT. One of these was bound state phenomena, such as the hydrogen atom. None of the introductory QFT texts I looked at even mentioned, let alone treated, it. It turns out that QFT can, indeed, handle bound states, but elementary courses typically don’t go there. Neither will we, as time is precious, and other areas of study will turn out to be more fruitful. Those other areas comprise scattering (including inelastic scattering where particles transmute types), deducing particular experimental results, and vacuum energy. "
• http://www.quantumfieldtheory.info/website_Chap01.pdf
This seems to make sense, e.g. the photoelectric effect does seem to be a bound state problem where an atom emits a photon into the continuous spectrum.

However if you actually look through chapter 5, they don't bring up bound states anywhere except a comment in a problem, and begin by discussing an electron emitting a photon in a given 'external field', but they don't treat the EM field as an external classical field since everything is done with second quantization, and they re-derive formulas like dipole radiation from a second quantization perspective, and seem to simply use formulas from perturbation theory.

Thus, what is going on in chapter 5, and how does it naturally relate to the discussion one would find in, say, Peskin and Schroeder?

Thanks!

Demystifier

ZapperZ
Staff Emeritus
The problem here is that in the standard photoelectric effect (i.e. UV light impinges on a metal surface), the initial state is not really a "bound state" other than the presence of the work function. The initial state here is a continuous energy and momentum states in the metal's conduction band.

So your intuition that this is similar to "... an atom emits a photon into the continuous spectrum ... " is not quite right, because it does not involve an atom, but rather a many-body state made up of a conglomerate of atoms, resulting in the conduction band.

A very detailed treatment of the photoelectric effect that is covered within a more general treatment can be found under the Photoemission phenomenon (the book by Huffner is one such example). It isn't a straightforward process, especially if one considers the Spicer Three-Step model of photoemission. This alone makes it rather different than a simple atomic process.

Zz.

dextercioby
Thanks for the reference - the reason I said "... an atom emits a photon into the continuous spectrum ... " is based on what they say in the beginning of section §56:

"In §49-52 we have discussed radiative transitions (with emission or absorption of a photon) between atomic levels of the discrete spectrum. The photoelectric effect differs from such a photon absorption process only in that the final state belongs to the continuous spectrum. The cross-section for the photoelectric effect can be calculated in an exact analytical form for the hydrogen atom and for a hydrogen-like ion"

and the earlier sections referred to are all called "Radiation from atoms: ...", where they discuss (in the beginning of §49): "The energies of the outer electrons (which take part in optical radiative transitions)".

Hence my guess that they treat the initial atom as a bound state (and set up the theory for the outer-most electrons to be involved in the photoelectric effect).

However, the whole point of view of chapter 5 and how it relates to, say, Peskin and Schroeder is extremely confusing, so I have no sense of why they set up the photoelectric effect solution the way they do.

ZapperZ
Staff Emeritus
Then what they are doing is describing photoionization, instead of photoelectric effect.

The spectrum of photoelectron energies due to photoionization is distinctly different than the photoelectric effect. While in many situations people tend to lump these two phenomena together, to me, it is rather sloppy considering that each of them already have a designated label.

It is why I tried to make myself explicitly clear of what *I* meant as the photoelectric effect (UV light impinges on a METAL surface), because there are many other photoemission phenomena that extend well beyond that narrow scenario (example: x-ray photoemission, which probes the core-level states of a solid rather than the conduction or valence band).

Zz.

bhobba and dextercioby
My guess is they would argue that the ionization process is the *real* photoelectric effect

I will definitely consider the subtleties after I figure out the whole point of what they are doing, thanks for the help thus far, perspective of these chapters is pretty confusing compared to a book like P&S.

Thanks

This is simply bizarre.

Apparently chapter 5 of that book is actually all about first order qed processes (!!!), i.e. the first term in the perturbation expansion with the QED Lagrangian.

Of course nearly every QFT book states or proves that this is impossible, including another book called Quantum Electrodynamics by the same author Berestetskii who says in it's chapter 5:
• However, it can be easily shown that the matrix elements of $S$ vanish if the electron taking part in the process is free
and then shows that first order processes for QED are impossible due to conservation of energy.

He later says:
• In order for the conservation laws to be satisfied the participation of a third body is necessary. Absorption or emission of a photon can occur only as a result of a "triple collision" in which the interaction of the electron with the "third" body plays an essential role. In a number of important cases this interaction can be described with the aid of the concept of an external field appearing in the Hamiltonian for the electron. The operator of the electron-positron field can be expanded in terms of the eigenfunctions of this Hamiltonian, and the concept of the electron state will in such a case automatically take into account the interaction of the electron with other bodies. We shall say that such electron states are not free. Such an approach enables us to study the processes of emission and absorption of a photon by means of the first order scattering matrix, since its elements between electron states that are not free are, generally speaking, different from zero.
Note he does not say the states are bound states.

The crazy non-trivial thing is the addition of an extra external field - I even mentioned an 'external field' in my original post!

Of course the book in the OP actually does mention these very important subtleties way later in a one-line footnote in chapter 9 in a way one could very very easily miss, but it makes perfect sense once you recognize the point it's trying to make, knew there was something deep here...

I wonder how general this is.

atyy