Nuclear Physics Scattering: Elastic, Inelastic etc

[physmurf]

I am preparing for a Nuclear Physics test. One of the homework problems asks the following: Choose the proper neutron interaction type for each of the following scenarios and explain why. Interaction types: elastic, inelastic, (n,$$\gamma$$),(n,2n),(n,$$\alpha$$).

A. 10-MeV neutrons interacting with lead.
B. Thermal neutrons interacting with gold.
C. 1-MeV neutrons interacting with hydrogen in water.
D. Thermal Neutrons interacting with boron-10.
E. 6-MeV neutrons interacting with beryllium. Instructors answer to part A: Both elastic and inelastic scattering are possible, but inelastic is more probable; This is because there is a large amount of "excess" energy (~17.5 Mev) available in the compound nucleus, and it takes little time ($$<10^{-14}$$ sec) for a neutron to gain enough energy (~7 MeV to escape. This most likely would leave the residual nucleus at an excited state as there are so many low-lying excited states available in a Pb nucleus.

First off, I am unsure of where he gets the 17.5 MeV. Every calculation I use gives an excess energy of about 22 MeV. This was obtained using the following formula:
I used a table in the back of my book which gives the mass excess for different nuclei: I decided to use $$^{208}Pb$$ for the target nucleus since it is the most abundant form of Lead.

$$_\Delta Q = (m_A+m_a-m_b-m_B)c^2$$

Mass excesses are:
$$^{208}Pb$$: -23364 $$\mu$$u
Neutron: 8665 $$\mu$$u
$$^{209}Pb$$: -18926 $$\mu$$u

This gave me a result close to 12 MeV. When this is added to 10 Mev I get approximately 22 Mev.

In any event, even if this is 22 MeV, what will determine weather or not a Neutron is ejected from the compound nucleus as opposed to just some elastic scattering or $$\gamma$$ gamma decay?

 

[Jhero]

The excess energy available in a compound nucleus after a neutron interaction plays a significant role in determining the type of interaction that will occur. In the case of 10-MeV neutrons interacting with lead, both elastic and inelastic scattering are possible, but inelastic scattering is more probable due to the large amount of excess energy available (~22 MeV). This excess energy can easily be transferred to the compound nucleus, causing it to become excited and eventually decay through the emission of a gamma ray or the ejection of a neutron.

The instructor's calculation of 17.5 MeV may be based on a different target nucleus or may have used a different method to calculate the mass excess. However, the important point to note is that there is a significant amount of excess energy available in this scenario, making inelastic scattering the most likely outcome.

In the case of thermal neutrons interacting with gold (B), the excess energy available is much smaller (~0.8 eV), making elastic scattering the most probable outcome. Similarly, for 1-MeV neutrons interacting with hydrogen in water (C), the excess energy is even smaller (~0.02 MeV), making elastic scattering the most likely interaction.

In contrast, thermal neutrons interacting with boron-10 (D) have a larger excess energy (~2.4 MeV), making (n, \alpha) reactions more probable. This is because boron-10 has a low binding energy for neutrons, so the excess energy can easily be transferred to the compound nucleus, causing it to decay through the emission of an alpha particle.

Finally, for 6-MeV neutrons interacting with beryllium (E), the excess energy available (~4 MeV) is enough to overcome the binding energy of the neutron, leading to (n,2n) reactions. This is because beryllium has a high binding energy for neutrons, so a larger amount of excess energy is needed to cause the compound nucleus to decay through the emission of two neutrons.

In summary, the excess energy available in a compound nucleus after a neutron interaction plays a crucial role in determining the type of interaction that will occur. Inelastic scattering is more probable when there is a large excess energy, while elastic scattering, (n, \alpha), and (n,2n) reactions are more likely for smaller excess energies.