Electron can't Absorb 2 Photons in a Row

[Talanum46]

For an electron absorbing photons twice in a row we have the following spin states:

before the interaction:

e: s = -1/2 h_bar

gamma: s = 1 h_bar

after the first interaction

e: s = 1/2 h_bar

since the LS s must sum to the RS s.

after the second interaction:

e: s = 3/2 h_bar,

which is impossible.

What am I doing wrong?

[Talanum46]

So after the first interaction the photon supposedly changed it's handedness, but the electrons Isospin wouldn't have changed and Wikipedia says Isospin of left and right handed electrons are different.

[OceanBreeze]

After the first interaction, the electron's spin increased from -1/2 to +1/2 and the photon's spin is gone.

The second interaction can be the reverse of the first; the electron's spin can be changed back from + 1/2 to -1/2 and the photon's spin is gone.

Spin interactions can be additive or subtractive.

The photon's spin can also go into the electron's orbital angular momentum leaving the electron's spin unchanged.

[Talanum46]

At the second interaction the photon spin value must be -1 h_bar, but its spin quantum number is still 1 h_bar. So you're telling me spin quantum number of a system does not add together.

Also: C-Parity is not conserved in both interactions.

To change a left handed electron into a right handed one, one needs to change the Isospin as well: photons don't do this.

Edited December 11, 2024 by Talanum46

[OceanBreeze]

I wrote my first answer going on memory alone, which I probably should not do.

If memory serves me right, spin interactions can be additive or subtractive.

The photon can have spin  1 or in some esoteric cases spin 0 which we will not consider.

The electron can have spin of + 1/2 or - 1/2.

First Interaction:

Before: electron spin is – 1/2, photon spin 1.

After: The photon gets absorbed we need not consider it.

The electron has a spin-up reaction from – 1/2  to + 1/2

Particle spin is conserved.

Second Interaction:

Before: electron spin is + 1/2, photon spin 1

After: The photon is absorbed

The electron has a spin-down reaction from + 1/2  to – 1/2.

Particle spin is conserved!

The last statement is not intuitive and perhaps a bit of esoteric knowledge.

 Like every other member, I must back up my claim when it is controversial.

Unfortunately, I can only find  very few sources that even mention additive versus subtractive spin interactions.

Here is one:  Section 5.4: “It is not self-ev­i­dent, but spin val­ues can be ad­di­tive or sub­trac­tive within the con­fines of their dis­crete al­low­able val­ues”

 

Here is your original question answered by a Physicist with a PhD.

“When an electron (spin +1/2) absorbs a photon of spin +1, does it get spin 3/2?”

 

“No. The intrinsic angular momentum (spin) of an electron is always 1/2, but its extrinsic (orbital) angular momentum can be any integer value.

When adding angular momenta, including spin, (lets call them j1 and j2) the resultant angular momentum can be any integer increment between (and including) |j1−j2| and j1+j2.

Here, presuming no orbital angular momenta initially, combining 1/2 and 1 the resultant can be either 1/2 or 3/2.

There are two places that the spin of the photon can go. One is that it can change the projection of the electron spin from -1/2 to +1/2 (or vice versa), leaving the resultant angular momentum (the electron spin) as 1/2. Second, it can change the orbital angular momentum by 1.”

 

The part in bold seems to agree with what I answered, only better stated. I am a marine engineer, not a particle physicist but I try my best to give accurate responses to posts. To add to the confusion, I will add this: A photon cannot interact with a free electron, it can only interact with an electron bound to an atom. That is why the photon spin can be conserved by adding to the orbital angular momentum of the atom, leaving the electron spin unchanged.

For more detailed information, you will need to do your own research.