What is the role of spin in electron K-capture?

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Discussion Overview

The discussion revolves around the role of spin in the process of electron K-capture, exploring the transformation of particles and the conservation laws involved. Participants examine the interactions between elementary particles, particularly focusing on the relationship between spin and momentum in quantum mechanics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant describes K-capture as a process where a proton captures an electron, resulting in the proton becoming a neutron and producing an electron neutrino, questioning the behavior of the electron in this context.
  • Another participant suggests that the electron emits a W- boson, which facilitates the transformation of the proton into a neutron by changing a u quark into a d quark, and recommends looking into Feynman diagrams for further understanding.
  • A participant expresses a new understanding that elementary particles can interact and change forms while preserving certain symmetries, specifically asking for confirmation regarding this idea.
  • It is noted that various conservation laws must be upheld during these interactions, including electric charge, color charge, spin, lepton number, and baryon number, with a distinction made about CP and CPT symmetries.
  • One participant inquires about the relationship between spin and momentum, specifically questioning whether spin orientation is independent of the particle's velocity or momentum direction.
  • Another participant clarifies that spin is unrelated to linear momentum, comparing it to a spinning top that can spin independently of its trajectory, while introducing the concept of helicity as the relevant projection of spin in the direction of motion.

Areas of Agreement / Disagreement

Participants express varying views on the relationship between spin and momentum, with some asserting independence while others clarify specific aspects of their relationship. The discussion does not reach a consensus on the implications of spin in K-capture.

Contextual Notes

There are unresolved questions regarding the nature of particle interactions and transformations, particularly concerning the role of spin and its relationship to momentum, as well as the implications of conservation laws in these processes.

MikeGomez
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If I understand correctly, when a proton captures an electron through K-capture, the proton is changed to a neutron and an electron neutrino is created in the process.

The electron is an elementary particle, and yet the newly created neutron is composed of quarks, which are elementary also. What happened to the electron? It seems as though the electron does not behave as an ‘elementary’ particle in this process. What am I missing?
 
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One way to look at this process is that the electron emits a W- boson. This particle carries away the electron's negative charge and so emitting this particle essentially changes the electron into a neutrino. The W- boson is then absorbed by a u quark, which changes the u quark into a d quark. Since the proton is uud and the neutron is udd, this changes the proton into a neutron. Try googling electron capture and looking at the Feynman diagrams.
 
I see. So my new understanding is that the elementary particles (of the standard model) can interact and change forms. The interactions/transformations must preserve symmetry (CP or CPT).

Correct?
 
There are multiple things which must be conserved in the interactions, including electric charge, color charge, spin, lepton number, and baryon number. There are some interactions that violate CP symmetry, but it appears that CPT symmetry is always preserved.
 
Thanks phyzguy.

Regarding spin, is it related to momentum? I don't mean the angular momentum of the particle, I mean the directional momentum. Is the spin orientation independent of the particle's velocity and/or momentum direction, or is there a strict relationship?
 
No, spin has nothing to do with linear momentum. It is not dissimilar to taking a spinning top and throwing it (in space); the top can spin any which way just fine. Of course this is quantum mechanics so when you measure the spin relative to some axis it will be quantised. There is however an important quantity called helicity which is the projection of spin in the direction of motion, which perhaps is what you are thinking of.
 

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