# Capture Cross Section for a Neutron

## Homework Statement

DT fusion produces 14.1 MeV neutrons. A diagnostic for a total fusion yield is the Cu-63(
n, 2n)Cu-62 reaction. A) what is the threshold for this reaction? Cu-63 also undergoes a radiative capture reaction yielding Cu-64. This reaction has a thermal cross section of 4.5b and the first resonance occurs for neautron energies of 402.66 eV. B) What is the capture cross section for a neutron having an energy of 75 eV? C) what is the excited state enrgy corresponding to the first resonance and in what nuclide is this excited state? The copper sample to be activated is often around concrete. ASSUME that concrete can be treated as an element with a mass number, A, of 24. D) How many collisions will be required on the average to slow a neutron down from 14.1 MeV to the (n, 2n) reaction theshold? How many to slow it down to thermal energy? E) If the copper sample is placed between the fusion neutron source and the conrete wall, what is the maximum energy that a neutron having an initial enrgy of 14.1 MeV can have if it scatters from the concrete back into the copper?

## Homework Equations

I'm just going to name off equations I have available to me, but I'm just entirely lost on part B. I am using Introduction to Nuclear Engineering - Lamarsh (3rd ed). And we have gotten up to Chapter 3.7)

Breit-Wigner Formula (pretty sure you don't use this... too many variables and I can't just create a system of equations or anything.)

Ʃ = δ*N (macroscopic cross section = microscopic * Number density)

I = N*v ('intensity' = number density * velocity)

λ = 1/Ʃ (mean-free path = 1/macroscopic)

δ_γ(E) = δ(E_0)/sqrt(E_0/E)

## The Attempt at a Solution

I tried to use the last equation for part B but maybe I didn't use the right values I used 4.5b for δ(E_0), .0253 eV for E_0, and 75 ev for E.

If you could point me in the right direction, it would be greatly appreciated.

## Answers and Replies

You will need some more equations to work out the number of scatters required
Try this book by the DOE http://energy.gov/sites/prod/files/2013/06/f2/h1019v1.pdf
It has a section on neutron moderation (page 23) and gives you the scattering equations you will need

Are you allowed to use cross section data to work this out or must it be done with equations
You can look up nuclear data and neutron cross sections here www.cross-section-plotter.com