Nuclear Interactions: Inelastic and elastic scattering

[physmurf]

I originally posted this in the homework section until I realized the homework section only covers through undergraduate courses. The course I am currently in is a graduate level Medical Physics course. So if you don't mind, here is the thread I posted in the homework section.

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? This is perhaps my biggest "hang up" with this. What do any of you think?

Thanks.

 

[mfb]

Photons are generally unlikely if there is a process that happens via the strong interaction.

The 17.5 MeV might be an approximation from the average binding energy per nucleon, which is roughly 7.5 MeV for heavy nuclei (+10 for the incoming neutron). That doesn't take into account specific nuclides and even small variations in the binding energy per nucleon can lead to large differences in the overall binding energy, so this is a very poor approximation method.