Question

I have the answers, but I'm not sure how to provide the work to get these answers. Please help.

(a) Estimate the capture cross section of Boron-10 for 100-ev neutrons. (ANSWER: 60.7 barns)

(b) What is the capture probability per cm for a 100-ev neutron in pure Boron-10 (density=2.17 g/cm^3)? (ANSWER: 7.93 cm^-1)

(c) Estimate the probability that a 100-ev neutron will penetrate a 1-cm Boron-10 shield and produce a fission in a 1-mm Pu-239 foil (density=18.5 g/cm^3) behind it. Neglect energy loss of the neutron due to elastic scattering. (ANSWER: 1.9 X 10^-5)

initial cross-section for B-10: 3840 barns

initial cross-section for Pu-239: 747 barns

Answer 1

Solution :-

Neutron capture cross section is given by

A is capture cross section

is radius of captured neutron which depends on energy

The cross section area hence depends on energy of the neutrons

Assuming that the radius of the neutron is equal to it's De-Broglie wavelength

Using this value, cross section area can be calculated

Cross section area is usually represented in barns. (1bn=10^-24 cm^2)

Capture probability per centimeter would be

Where R is radius of the Boron nucleus

A=10 (Atomic mass number of Boron-10)

Cross section/cm (Converting barn to cm^2)