Radioactive capture of proton and neutron

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Discussion Overview

The discussion revolves around the process of neutron and proton fusion to form a deuteron and a photon, specifically focusing on the energy of the emitted photon and the application of conservation laws in this context. The scope includes theoretical considerations and mathematical reasoning related to nuclear physics.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant proposes using conservation of energy to find the energy of the photon emitted in the reaction n + p → d + γ.
  • Another participant confirms that energy is conserved and mentions that momentum is also conserved, noting that photons carry momentum.
  • A question is raised about whether the relationship Eγ = (En + Ep) - Ed is valid for calculating the photon energy.
  • It is suggested that the process is relatively straightforward in nucleon physics, although it can become complex.
  • A participant introduces the concept of nuclear binding energy and its relevance to fusion and fission processes.
  • A further inquiry is made regarding the applicability of simple energy conservation in relativistic scenarios versus the need for 4-vector formalism.
  • Another participant explains that conservation laws are typically applied directly, often using center-of-mass coordinates, and discusses the implications of momentum conservation on the directions of the photon and deuteron.
  • It is noted that the energy of the interaction can lead to various outcomes, including the possibility of multiple photons being produced in high-energy scenarios.

Areas of Agreement / Disagreement

Participants generally agree on the conservation of energy and momentum in the reaction, but there is no consensus on the sufficiency of simple energy conservation in relativistic contexts versus the use of more complex formalism.

Contextual Notes

The discussion does not resolve the complexities introduced by relativistic effects or the specifics of the energy calculations in different reference frames.

mitch_1211
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Hi,

I'm considering the following process

n+p→d+\gamma where d is the deuteron and \gamma a photon.

I want to find out the energy of the photon. I know it will be much less than the rest mass of the deuteron (1875.666 MeV/c2). Can I simply use conservation of energy here?

i.e E\gamma = Ei - Ef?

Thanks :)
 
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Energy is certainly conserved - yep.
Momentum is also conserved and photons carry momentum.
 
So is it really as simple as E\gamma = (En+Ep) - Ed?
 
Pretty much. On the scale of nuceons physics gets real simple ... and then it gets weird.
Anyway, the deuteron mass-deficit is termed it's "nuclear binding energy". This energy is released in fusion and you have to supply this energy for fission.
 
thanks for clearing that up :)
 
just one more thing, if considering the particles to be relativistic, is it still sufficient to apply simple energy conservation?

Or should the 4-vector formalism be used?
 
It is usual to go right for the conservation laws - the math is normally done in center-of-mass coordinates. You use ##E_{tot}=\gamma mc^2## etc. It will be a linear transformation to the lab frame to get what your equipment is supposed to see.

In your example, if the proton and neutron are effectively at rest, then the photon and deuteron will have to go in opposite directions (to conserve momentum) ... so you do have a kinetic energy term to consider.

In general, the energy of the interaction can do all kinds of things ... for instance, there need not be only one photon. High energy photons can pair-produce ... all sorts of things. That's why when you look at the CERN stuff, the detectors are always shown with a shower of tracks inside them.
 

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