Neutron microscopic cross section data

In summary, there is a 14% chance of an incident proton colliding with a silicon nucleus in a 1-cm-by-1-cm block.
  • #1
Hi guys,

I am trying to calculate the macroscopic cross section (scattering and absorption) for high energy neutrons between 1 MeV and 10^7 MeV in Silicon. I am using the macroscopic cross section to determine the mean free path. To calculate the macroscopic cross section, i need to know the microscopic cross section for the given material, as a function of neutron energy, as given in the following link:

http://www.tpub.com/content/doe/h1019v1/css/h1019v1_113.htm"

Is there an analytical expression to generate this curve for a given material, or can i get this curve from some type of database online? I need the curve for both scattering and absorption.

Thanks, any help is appreciated,

Pete.
 
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  • #3
Thanks for the reply Bob, this is exactly what i was looking for. The only issue is, i need the cross sections up to 1E13 eV. The maximum energy seems to be fixed at ~ 1E8 eV on the plot. I didn't see any options, but is there any way of increasing the limits? If not, do you have any idea how the cross section decays after 100 MeV ? Thanks very much.

Pete.
 
  • #4
PBurke1985 said:
Thanks for the reply Bob, this is exactly what i was looking for. The only issue is, i need the cross sections up to 1E13 eV. The maximum energy seems to be fixed at ~ 1E8 eV on the plot. I didn't see any options, but is there any way of increasing the limits? If not, do you have any idea how the cross section decays after 100 MeV ? Thanks very much.
Look at the cross section plots in:

http://pdg.lbl.gov/2002/contents_plots.html


First, look at np (same as pn). This is essentially barns per nucleon (proton). Now look at pp, which goes up to ~ 109 GeV (~1018 eV). At these energies, neutron and proton cross sections are about the same (minimum ~ 40 mb per nucleon at 100 GeV). For silicon, I would multiply per nucleon cross sections by ~282/3 = 9.3 (geometric cross section).

Bob S
 
  • #5
Thanks again for the info Bob. This is exactly what i need. My last question (honest), what does the 'initial state' np, pn and pp refer to? Sorry if this is a really basic question, but I'm very new to particle physics. I have only dealt with photon interactions with matter before and charged particle interactions are a lot more difficult to understand. Thanks.

Pete.
 
  • #6
PBurke1985 said:
My last question (honest), what does the 'initial state' np, pn and pp refer to? Sorry if this is a really basic question, but I'm very new to particle physics. I have only dealt with photon interactions with matter before and charged particle interactions are a lot more difficult to understand.
np refers to a neutron of energy E colliding with a proton (like in a liquid hydrogen target), while pn refers to a proton of energy e colliding with a neutron at rest (like a neutron in deuterium target). In the latter, the experimental measurement, the pd (proton on deuterium) cross section is measured, and then the contribution from pp (proton hitting a proton) has to be subtracted. The pp cross section is easily measured using a proton beam on a liquid hydrogen target.

A note on cross sections. Assume the radius of a proton is R = ~1.2 x 10-13 cm. The frontal geometric surface (target) area is thus πR2 = [STRIKE]31[/STRIKE] 45 x 10-27 cm2 = [STRIKE]31[/STRIKE] 45 millibarns.

Suppose you have a block of silicon with A=28 that is 1-cm-by-1-cm wide by z cm deep (volume z cm3). What is the probability of an incident proton (or neutron) colliding with a silicon nucleus in the block? The "volume" of the nucleus scales as A which is proportional to R3, but the frontal geometric "area" scales as R2, so the geometric frontal area scales as A2/3 = 9.3. So if the geometric area is [STRIKE]31[/STRIKE] 45 millibarns for 1 nucleon, then the geometric area of a silicon nucleus is ~9.3 x [STRIKE]31[/STRIKE] 45 millibarns = [STRIKE]290[/STRIKE] 400 millibarns per silicon nucleus. For the above silicon block, the density is 2.33 grams per cm3, so the mass of the block is 2.33 z grams. Because the gram molecular weight of silicon is 28 grams per 6 x 1023 atoms, the block contains 6 x 1023 x 2.33 z/28 silicon nuclei.

The probability of an incident proton colliding with one nucleus in the block is just the ratio of areas, which is (using [STRIKE]31[/STRIKE] 45 millibarns per nucleon or [STRIKE]290[/STRIKE] 400 millibarns per silicon nucleus)

probability ratio = 6 x 1023 x (2.33 z/28) x [STRIKE]290[/STRIKE] 400 millibarns/atom = [STRIKE]0.014[/STRIKE] 0.02 z per cm2.

So the "collision length" is about 1/[STRIKE]0.014[/STRIKE] 0.02 = [STRIKE]72[/STRIKE] 50 cm, or [STRIKE]31[/STRIKE] 115 grams per cm2. This is the thickness that reduces the incident proton flux by the factor 1/e.

The actual estimated collision length for silicon is ~ 70 grams per cm2 and interaction length ~108 grams per cm2, as shown in

http://pdg.lbl.gov/2009/reviews/rpp2009-rev-atomic-nuclear-prop.pdf

Bob S
 
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  • #7
Thanks Bob, those calculations make sense.

Cheers,

Pete.
 

1. What is neutron microscopic cross section data?

Neutron microscopic cross section data refers to the measurements of the probability of a neutron interacting with a nucleus as it passes through a material. This data is important in understanding the behavior of neutrons in various materials, such as nuclear reactors.

2. How is neutron microscopic cross section data collected?

Neutron microscopic cross section data is collected through experiments using neutron beams and various detectors. These experiments involve bombarding materials with neutrons and measuring the resulting interactions.

3. Why is neutron microscopic cross section data important?

Neutron microscopic cross section data is important for various applications, including nuclear energy, nuclear medicine, and materials science. It helps scientists understand the behavior of neutrons in different materials and can aid in the design and safety of nuclear reactors.

4. What are some common uses of neutron microscopic cross section data?

Some common uses of neutron microscopic cross section data include neutron shielding design, nuclear reactor design, and nuclear waste management. It is also used in medical imaging and cancer treatment with neutron beams.

5. How is neutron microscopic cross section data analyzed?

Neutron microscopic cross section data is analyzed using various mathematical models and computer simulations. These methods help to interpret and predict the behavior of neutrons in different materials and under different conditions.

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