Calculating Nuclear Cross Section for Materials

[Apollo14LMP]

Homework Statement

What is the cross section if the density of atoms in a material is 10^26 metres-3, and 0.04% of a beam of neutrons is stopped in a 2 cm slab of the material ?

Homework Equations

Sigma = event rate per nuclei / incident flux

The Attempt at a Solution

I have no idea ..

 

[mfb]

If the density would be 1/meter^3 and 1% would be stopped in 1meter (imagine a cube of 1m side length with exactly one atom in it), can you calculate the cross-section?
Then you just have to scale this to get the original numbers.

 

[Apollo14LMP]

Cant really visualise this ... but I guess there would 10^26m-3 with 0.04 % stopped in it ? I need to calculate the barns. Still not sure about the 2 cm mentioned ...

I have gone away and come up with the following -

I have converted the 10^26 m-3 to centimetres = 1.0000^32cm3

I have then calculated using a formula found on the internet

https://facultystaff.richmond.edu/~ggilfoyl/research/CrossSectionIntro.pdf

1.0000^32cm3 x 2cm x 6.022^23 / 0.04 = 3.00 x 10^57

I cannot see where I am wrong but some advice would be a big help

I am assuming you must convert the m-3 to cm3, and calculated my answer as per the research article I found. Thank you

 

[Astronuc]

Homework Statement

What is the cross section if the density of atoms in a material is 10^26 metres-3, and 0.04% of a beam of neutrons is stopped in a 2 cm slab of the material ?

Homework Equations

Sigma = event rate per nuclei / incident flux

The Attempt at a Solution

I have no idea ..

Can one write the relationship between the macroscopic cross-section, ∑, and the microscopic cross-section, σ, which is what one wishes to find?

Then write the equation for attenuation of particles passing through a slab of material, i.e., write the equation for dI(x)/dx, where I(x) is the beam intensity as a function of distance from the surface into the material.

 

[mfb]

The formula uses the density in g/cm^3 and uses the Avogadro constant to convert this to atoms/cm^3. You know atoms/cm^3 so you can skip that step in the formula.

This is easier to see if you work with units everywhere (a good habit in general).

 

[Apollo14LMP]

Thank you for your help ..

0.04 % / 1.0000^32cm3 x 2cm = 8.00 x 10^-34

that is N events (0.04%) / beam particles per unit area (1.0000^32cm3 / target particles (2cm)

 

[mfb]

The units are missing, but apart from that it looks good.

 

[Apollo14LMP]

Thanks struggled to solve that you have both been very helpful .. I appreciate your time and trouble so much ..