Interaction between neutrons and nuclei during scattering

[Mayan Fung]

TL;DR Summary

How neutrons interact with nuclei during scattering?

When we learn about the scattering of a particle, the context is usually a charge shooting towards a Coulomb potential. With some assumptions, we can derive the scattering cross-section pretty reasonably. Therefore, the scattering cross-section of different elements in X-ray spectroscopy is proportional to the atomic(electron) number (because X-ray interacts with the electron cloud).

When it comes to neutron scattering, the situation becomes complicated. Intuitively, the scattering amplitude should also be, in some way, proportional to atomic number. However, there is no obvious pattern, as shown in the attached figure. Many books and notes on neutron scattering do not address the interactions between neutrons and nuclei in a complete theoretical framework. Many assume that the scattering section is known and focus on the interpretation of the data in a neutron scattering spectroscopy. Due to my limited knowledge about the fundamental forces, I suspect that strong force should be responsible for the interaction (I guess this is the "Potential scattering contribution" labeled in the attached figure). I wonder if there is a complex theoretical explanation of the scattering amplitude trend in the elements? How are the neutrons interacting with the nuclei? I am not looking for precise computation of each element. I am just curious about the factors and models describing a neutron scattering with a nucleus, instead of assuming the interaction as a black-box process. Thanks!

 

[WernerQH]

I suspect that strong force should be responsible for the interaction (I guess this is the "Potential scattering contribution" labeled in the attached figure).

You are right. An atomic nucleus is a complex system for which many different models have been developed. One is the liquid drop model that provides a rather coarse description (and may give rise to that smooth 'potential scattering' contribution). Another is the shell model, and depending on the exact numbers of protons and neutrons (odd or even) the spins of the nucleons can be stacked up quite differently from nucleus to nucleus. Then also the scattering amplitudes for the different nucleons would add up differently. And there may be resonance scattering when a neutron might form an intermediate state with the nucleus. Complicated indeed. :-)