Can positive energy nucleons be bound together in nuclear forces?

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Discussion Overview

The discussion revolves around the binding of nucleons, specifically the formation of a deuteron from a proton and a neutron, and the role of energy states in this process. Participants explore the implications of kinetic and potential energy in nuclear forces, as well as the mechanisms involved in neutron capture and photon emission.

Discussion Character

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

Main Points Raised

  • One participant questions how a proton and neutron can become bound when the initial kinetic energy of the proton is positive, while the potential energy required for binding is negative.
  • Another participant mentions that a photon is emitted during the process of neutron capture, which may change the energy state of the nucleons involved.
  • A participant seeks clarification on whether the emission of a gamma ray results in the relative energy of the nucleons becoming negative, prompting further inquiry into the underlying mechanisms.
  • Concerns are raised about the standard quantum mechanics framework not adequately describing how particles with higher energy can become bound, leading to a request for mathematical explanations rather than qualitative descriptions.
  • One participant suggests that second quantization and quantum electrodynamics (QED) provide the necessary framework to understand these processes, although it is noted that this is often not covered in introductory courses.
  • Another participant references a specific textbook that discusses the capture of slow neutrons and related processes, indicating that detailed mathematical treatment can be found in more advanced literature.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the mechanisms of nucleon binding and the role of energy states. There is no consensus on the clarity of the explanations provided, and some participants seek more detailed mathematical frameworks.

Contextual Notes

Participants highlight limitations in standard quantum mechanics education regarding the binding of particles with positive initial energy. The discussion indicates a need for more advanced theoretical frameworks to fully explain the phenomena being questioned.

Who May Find This Useful

This discussion may be of interest to students and professionals in nuclear physics, quantum mechanics, and those exploring the interactions of fundamental particles.

JK423
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Say we have a proton and a neutron. How can we get them bound to form a deuteron? If the neutron is still in the lab's framework, we bombard it with protons with such a kinetic energy that they can form a deuteron with the neutrons.
But if we look at the potential of the nuclear force between the two nucleons, we will see that in order for them to get bound their relative energy must be negative!
(The "potential well" is in the negative energies.)
However, protons have an initial kinetic energy at a distance where the potential is zero. That means they have a positive energy.
Then, how can they get bound in the first place?

Thanks in advance.
John
 
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Usually, a photon is emitted, so the process (called neutron capture) is
n + p --> d + gamma.
 
You mean that with the emittion of a gamma ray their relative energy become negative?

Its very weird ... Any more detailed mechanism known?
 
That's also what happens when an electron is captured by a proton to form the hydrogen atom. What is weird about it?
 
What is weird is this. From non-relativistic QM i know that if the particle has higher energy than the potential then there is a probability to get scattered.
But to "accidentally" get bound?? This is not described from the standar QM I am taught at university so i ask you what procedure explains this.. I mean with math, not words..
 
You need to second quantize the EM field, leading to QED where photons can be emitted and absorbed. The weird thing is that this is not even mentioned in some first level QM courses. If you want math, buy a textbook. It all is shown in about ten pages.
 
Thanks a lot! Yeah its not mentioned, not even as a "question". I never wondered till now how the hell these particles get bound when the don't have the right energy..
Can you tell me with a little greater detail what to search for in a textbook?
Maybe you know a specific one that applies the theory in such a case (particles getting bound by emmiting photon) ?

Thanks in advance,
John
 
Anyone?
 
There is a nice discussion in Section 10.8, Capture of Slow Neutrons by Hydrogen, in Emilio Segre's text, Nuclei and Particles, 2nd Ed., W. A. Benjamin, 1977, pp.491-496. The radiative capture process is discussed.

n + p <=> d + \hbarω

Chapter 8 addresses gamma emission.
 
  • #10
Thanks a lot..
Maybe you have it in ebook form? Cause i dont..
 
  • #11
I am afraid you will find it only in older books. If you can get to an academic library, look through the stacks for nuclear physics books.
 
  • #12
Ok thanks, i'll look for it in my university's library
 

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