# Nuclear Interactions: Inelastic and elastic scattering

1. Nov 12, 2007

### 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.