Can positive energy nucleons be bound together in nuclear forces?

[JK423]

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

 

[Meir Achuz]

Usually, a photon is emitted, so the process (called neutron capture) is
n + p --> d + gamma.

 

[JK423]

You mean that with the emittion of a gamma ray their relative energy become negative?

Its very weird ... Any more detailed mechanism known?

 

[Meir Achuz]

That's also what happens when an electron is captured by a proton to form the hydrogen atom. What is weird about it?

 

[JK423]

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..

 

[Meir Achuz]

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.

 

[JK423]

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

 

[JK423]

Anyone?

 

[Astronuc]

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.

 

[JK423]

Thanks a lot..
Maybe you have it in ebook form? Cause i dont..

 

[Meir Achuz]

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.

 

[JK423]

Ok thanks, i'll look for it in my university's library