Can positive energy nucleons be bound together in nuclear forces?

In summary, the process of forming a deuteron by binding a proton and a neutron requires the relative energy between the particles to be negative. However, protons typically have a positive initial kinetic energy, so a photon must be emitted in order for the particles to become bound. This process is known as neutron capture and is similar to the capture of an electron by a proton to form a hydrogen atom. The mathematical explanation for this process involves second quantizing the EM field and is not often mentioned in introductory QM courses. More information can be found in textbooks such as Emilio Segre's "Nuclei and Particles" in the sections discussing neutron capture and gamma emission.
  • #1
JK423
Gold Member
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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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  • #2
Usually, a photon is emitted, so the process (called neutron capture) is
n + p --> d + gamma.
 
  • #3
You mean that with the emittion of a gamma ray their relative energy become negative?

Its very weird ... Any more detailed mechanism known?
 
  • #4
That's also what happens when an electron is captured by a proton to form the hydrogen atom. What is weird about it?
 
  • #5
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..
 
  • #6
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.
 
  • #7
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
 
  • #8
Anyone?
 
  • #9
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 + [itex]\hbar[/itex]ω

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
 

1. What is the process of getting two nucleons bound?

The process of getting two nucleons bound is called nuclear fusion, where two atomic nuclei combine to form a heavier nucleus. This process releases a large amount of energy.

2. What are the conditions required for two nucleons to be bound?

Two nucleons can be bound together if they have enough kinetic energy to overcome the repulsive force of their positively charged protons. This can be achieved through high temperatures and pressures, such as in the core of a star.

3. How does the strong nuclear force play a role in binding two nucleons?

The strong nuclear force is responsible for binding two nucleons together. It is a short-range force that overcomes the repulsive force between protons and holds the nucleus together. It is one of the four fundamental forces of nature.

4. What are the different types of nucleons that can be bound together?

Nucleons refer to both protons and neutrons, which are the building blocks of atomic nuclei. Therefore, any combination of protons and neutrons can be bound together to form a nucleus.

5. What are the potential applications of understanding the process of nucleon binding?

Understanding the process of nucleon binding is essential for nuclear energy production and nuclear weapons development. It also plays a crucial role in our understanding of the structure and composition of matter in the universe.

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