Question

In this answer by Arturo don Juan, and also, in section 7.8

of Sakurai's Modern Quantum Mechanics, it is argued that resonances in the scattering cross-section at certain energies are due to the existence of quasi-bound states supported by the effective potential. The occurrence of such quasi-bound states is, in turn, caused by a repulsive tail of an otherwise attractive potential. This repulsive tail is either due to an angular momentum barrier ℏ2ℓ(ℓ+1)2mr2
for ℓ≠0
or could be entirely due to the shape of the potential itself. For example, it is caused by the Coulomb barrier seen by charged particles (e.g., protons) accelerating towards a nucleus.

If, on the other hand, a beam of slow neutrons is bombarded at a target nucleus, the neutrons do not experience a Coulomb barrier. Moreover, if we consider slow neutrons i.e. s
-wave scattering, there is also no angular momentum barrier. Therefore, the potential will have no repulsive tail. Therefore, there exist no quasi-bound states. Thus, one would expect to observe no s
-wave resonances. However, contrary to expectation, s−
wave resonances are indeed observed in s
-wave neutron scattering. What is going on here?

Answer 1

The occurrence of s-wave resonances in neutron scattering, despite the absence of a Coulomb barrier and angular momentum barrier, can be attributed to the presence of potential wells created by the strong force between neutrons and protons within the nucleus.

Step-by-step explanation:

In the context of slow neutron scattering, the absence of a Coulomb barrier and the consideration of s-wave scattering eliminate the traditional reasons for the existence of quasi-bound states and resonances. However, the strong nuclear force between neutrons and protons within the nucleus creates potential wells that can lead to the formation of quasi-bound states, even in the absence of Coulomb and angular momentum barriers.

Unlike charged particles that experience a Coulomb barrier, slow neutrons do not face this hindrance. Moreover, in s-wave scattering, there is no angular momentum barrier. In the absence of these classical barriers, the strong force takes center stage. The attractive nature of the strong force generates potential wells, overcoming the lack of traditional barriers and allowing for the existence of quasi-bound states and s-wave resonances in neutron scattering.

In summary, the unexpected observation of s-wave resonances in slow neutron scattering can be explained by the presence of potential wells created by the strong force within the nucleus. These potential wells, arising from the attractive nature of the strong force, facilitate the formation of quasi-bound states even in the absence of Coulomb and angular momentum barriers. This nuanced understanding highlights the complex interplay of forces in quantum mechanical systems.