# Getting two nucleons bound

1. Feb 11, 2010

### 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?

John

2. Feb 11, 2010

### clem

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

3. Feb 12, 2010

### JK423

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

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

4. Feb 12, 2010

### clem

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

5. Feb 12, 2010

### 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 im taught at university so i ask you what procedure explains this.. I mean with math, not words..

6. Feb 12, 2010

### clem

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. Feb 12, 2010

### 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 dont 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) ?

John

8. Feb 14, 2010

### JK423

Anyone?

9. Feb 14, 2010

### Astronuc

Staff Emeritus
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 + $\hbar$ω

10. Feb 14, 2010

### JK423

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

11. Feb 14, 2010

### clem

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. Feb 14, 2010

### JK423

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