Much contained in this FAQ is already in print here, but scattered. I was stunned to find this subject not in a FAQ here. I hope Carl Willis will add to this important effort, as his knowledge here far exceeds my own.

Moderation for detecting and counting neutrons:

Neutrons produced by the fusor are all considered "Fast neutrons". All neutron sources tend to produce fast neutrons. All of the best detectors for neutrons rely on "thermal neutrons" to be detected by some secondary process.

For detection of fusor produced and any man made source of neutrons, (fast), it is incumbent on the would-be neutron metrologist to slow these neutrons down to thermal velocities allowing detectors sensitive to these "slow neutrons" to count them.

The act of slowing down fast neutrons to create slow or "thermal" neutrons is called "moderation". The assembly needed to do this is called a "moderator".

Moderators can be made of a number of materials, but moderators made of hydrogen rich materials work best and take up the least amount of space. Moderation or "slowing" of neutrons occurs when neutrons effectively "hit" a proton within the hydrogen of the moderator causing the proton to recoil, much like a billiard ball. Of course, just like the billiard ball, the proton is sent recoiling off as some of the cue ball's, (neutron's), momentum is transferred or stolen from it. Thus, the proton flies off while the neutron is slowed down. Note, that both particles, like the billiard balls, are "scattered" off at angles not necessarily along the path of the original cue ball (neutron).

If the moderating material is thick enough, many such collisions of the scattered neutrons are possible and more slowing down is seen to occur as well as more wild scattering within the material.

There is a point where a beam of fast neutrons entering the moderator, "hydrogenous material", are slowed and scattered to such a high degree that it, the moderator, may appear as a neutron source of isotropically emitted "slow neutrons". These neutrons are said to be "thermalized".

Thermal neutrons are those neutrons that have a velocity equal to that of the atoms and molecules of their surrounding environment. They are in thermal equilibrium with all that is around them. (At the same effective temperature). Most all neutron counter detection schemes respond to thermal neutrons. Thus, the need for moderators and neutron moderation.

The detector is generally placed within the moderator such that any fast neutron beam that enters the moderator will thermalize to such a degree that the detector will be bathed in a sea of thermalized, easily counted, neutrons from all directions.

Moderation for neutron activation:

Neutron activation of common materials is a separate study, whereby, various materials are bombarded by neutrons in an attempt to "activate" or make them radioactive. This effort usually demands a source of thermal neutrons. Therefore, moderation is also valuable in this area of study as well.

The moderator - materials and sizing:

The preferred moderator materials most encountered in amateur use are, in order of use....

1. Low Density Polyethylene "LDPE"

2. High Density Polyethylene "HDPE"

3. Water

4. Paraffin wax

The polyethylenes can be obtained in large cities at a commercial or retail plastics dealer in both cylinder and thick sheet forms. Pre-cut pieces can be assembled or built up into a moderator.

Water is a great, zero cost, moderator, but requires a tank and must be maintained, (evaporation, airborne dirt and dust, etc) Tanks are subject to leakage and breakage.

Water allows for extreme fine-tuning of detection and activation by moving the detector or material to be activated around the tank for more or less moderation.

Paraffin is easily obtained at many grocery stores in block or plate form. However, paraffin is flammable and poses a fire hazard when assembled in large amounts, should a fire break out in the lab. Prior to modern plastics, Paraffin was the number one moderator used in instrumentation and in small laboratories.

The above list is not complete at all, but has served the amateur and even the professional communities well in the past and at present.

Thickness of the moderator:

The moderator should, ideally, be a sphere for detection and measuring purposes, but this is not always practical. In general, a detector or material to be activated will need about 2-3 inches of the above moderating material surrounding it on all sides.

More on moderating for activation:

Less thickness in a moderator will slow neutrons to "epi-thermal" velocities where a lot of activation materials have what are termed "capture resonances" to neutrons of energies just above thermal energies. These resonances can present monstrously huge cross sections for "neutron capture" within the material to be activated. This means that in some activation scenarios, a broad band of resonances and large capture cross sections might best be utilized for activation where the neutrons are at less than thermal energies.

If a moderator is made so large that the neutrons are slowed to velocities well below that of the surrounding molecules, they are termed "cold neutrons". For detection purposes, there is not much advantage for obtaining cold neutrons. However for activation studies cold neutrons, below thermal energy, increase the capture cross section and improve activation on a more or less linear scale based on the classic 1/V law. (neutron physics) There is a limit, however, as the neutron flux (neutrons per sq. cm.) is reduced in this effort due to increasing moderator volume and a trade off point is reached for any given incident flux of fast neutrons outside the moderator.

There is much more to this story to which it is hoped others will contribute in replies. However, this is the "quick rinse" promised on moderation and moderators.

Richard Hull

## FAQ - Moderators, Neutron moderation, what it does, how to do it, why do it?

- Richard Hull
- Site Admin
**Posts:**10656**Joined:**Fri Jun 15, 2001 1:44 pm**Real name:**Richard Hull

### FAQ - Moderators, Neutron moderation, what it does, how to do it, why do it?

Progress may have been a good thing once, but it just went on too long. - Yogi Berra

Fusion is the energy of the future....and it always will be

Retired now...Doing only what I want and not what I should...every day is a saturday.

Fusion is the energy of the future....and it always will be

Retired now...Doing only what I want and not what I should...every day is a saturday.

### Re: FAQ - Moderators, Neutron moderation, what it does, how to do it, why do it?

I'd just like to add a little bit to this:

The key concept to understanding neutron moderation is the 'neutron cross section' (denoted sigma).

Now, the first thing to understand is that atoms consist of protons and neutrons in the nucleus, and electrons orbiting around. Neutron interact via the strong force with protons and neutrons. When they interact, they can have several effects including scattering, absorption, fission, etc. More on these interactions latter.

Also, it is important to understand the concept of number density. you can think of number density as the number of objects per cubic cm; If you have 100 apples in a cubic meter box, then its number density will be 100 apples per cubic meter. in this case, the number of atomic nuclei per cubic cm is the number density we are concerned with.

Imagine a situation where you have a infinitesimally thin slab of material filled with atomic nuclei. (you can imagine some electrons orbiting these nuclei, but they don't matter with neutrons). This slab has an infinitesimal width 'dx' and an area 'S'. The nuclei in this slab will each have a cross sectional area of 'sigma' which is normal to the face of this volume.We often call this 'sigma' value the microscopic cross section Since the volume is infinitesimally thin, there is an infinitesimal number of molecules in this volume which we shall denote with 'dN'. If there is a number density of 'C' such nuclei within this slab volume, then it follows that the total number of atoms within this volume will be:

dN =Sdx

Furthermore, the total area filled by molecules will be given by:

(Area-Occluded) = sigma*dN

If we imagine a beam of neutrons with intensity 'I' incident upon the face of this infinitesimally thin volume, then we can see intuitively that a fraction of those neutrons will undergo some sort of reaction of type 'x' with the nuclei in that volume.

It follows that the probability that a neutron will interact within a nuclei within this volume will be given by the ratio of the occluded area to the total area or

P_x = ((sigma) dN) / S

Expanding our term dN out we arrive at

P_ = ((sigma)CSdX/S)

-> P_x = (sigma)Cdx

The product C*(sigma) we shall henceforth refer to as (Sigma) (note the capital) or the macroscopic cross section.

Thus, P_x = (Sigma)dx [eqn A]

Now, if we consider the initial beam of neutrons incident upon the face of the slab, it is intuitive that the product of initial beam intensity on the probability of interaction x will yield the decrease in beam intensity, which we shall denote '-dI'. note the use of the 'delta' interpretation for the differential quantity rather than the infinitesimal interpretation.

-dI = p_x * I

-> p_x = -dI/I [eqn B]

by substituting in [eqn A] into [eqn B] we arive at a first order linear differential equation commonly know as 'Beer's Law'.

-dI / I = (Sigma)*dx

if set the beam between some initial intensity 'I_0' and 'I' and the distance through which the beam travels between 0 and 'x', then as we all learned in kindergarten, this equation will have the solution

I=I_0*exp(-(Sigma)*x)

okay, great, but what does this have to do with moderation?

Well, to moderate neutrons, you need to slow them down, and you slow them down by bouncing them off, or 'scattering' them off atoms.

What is the probability that a neutron will scatter off an atom? well, that's given by its cross section. Where do you find cross sections? Well, you just look to your handy dandy National Nuclear Data Center's Evaluated Nuclear Data File (ENDF) available here: http://www.nndc.bnl.gov/sigma/

Now, recall that the probability of an interaction of type x occurring is given by

p_x = (Sigma)dx,

that means that in 1 cm, the probability of collusion is (Sigma). Thus, the common interpretation of (Sigma) is the probability of interaction per path length.

So,now unless you're very lucky or rich, you'll probably be using some sort of Boron-10 neutron detector. These work by the reaction:

B_10 +n -> alpha + Li

The charged alpha particle is picked up by the detector cathode, and it produces an electrical signal that reads as a 'count'

Now, if you look at the cross section for B_10

http://www.nndc.bnl.gov/sigma/getPlot.j ... 07&nsub=10

Notice that the cross section increases as your energy decreases.

Thus, to maximize your probability of detecting a neutron, you need to minimize your neutron energy.

How do you do this? Moderation!

The energy of a neutron after a collision is given by E'=(alpha)E

where (alpha) is your collision parameter.

I might show in a later derivation that

(alpha) = ((A-1)/(A+1))^2

where A is the atomic mass of your target nucleus

it's clear that this equation is at a maximum when A=1

And, what nucleus has A=1? Hydrogen!

Thus, to slow down neutrons the fastest, you must pass your neutron field through a hydrogen rich material to slow them down.

That's all I have to add for now, I might write a word file or something on this when I get some time to better show the equations and what not.

-TJP

The key concept to understanding neutron moderation is the 'neutron cross section' (denoted sigma).

Now, the first thing to understand is that atoms consist of protons and neutrons in the nucleus, and electrons orbiting around. Neutron interact via the strong force with protons and neutrons. When they interact, they can have several effects including scattering, absorption, fission, etc. More on these interactions latter.

Also, it is important to understand the concept of number density. you can think of number density as the number of objects per cubic cm; If you have 100 apples in a cubic meter box, then its number density will be 100 apples per cubic meter. in this case, the number of atomic nuclei per cubic cm is the number density we are concerned with.

Imagine a situation where you have a infinitesimally thin slab of material filled with atomic nuclei. (you can imagine some electrons orbiting these nuclei, but they don't matter with neutrons). This slab has an infinitesimal width 'dx' and an area 'S'. The nuclei in this slab will each have a cross sectional area of 'sigma' which is normal to the face of this volume.We often call this 'sigma' value the microscopic cross section Since the volume is infinitesimally thin, there is an infinitesimal number of molecules in this volume which we shall denote with 'dN'. If there is a number density of 'C' such nuclei within this slab volume, then it follows that the total number of atoms within this volume will be:

dN =Sdx

Furthermore, the total area filled by molecules will be given by:

(Area-Occluded) = sigma*dN

If we imagine a beam of neutrons with intensity 'I' incident upon the face of this infinitesimally thin volume, then we can see intuitively that a fraction of those neutrons will undergo some sort of reaction of type 'x' with the nuclei in that volume.

It follows that the probability that a neutron will interact within a nuclei within this volume will be given by the ratio of the occluded area to the total area or

P_x = ((sigma) dN) / S

Expanding our term dN out we arrive at

P_ = ((sigma)CSdX/S)

-> P_x = (sigma)Cdx

The product C*(sigma) we shall henceforth refer to as (Sigma) (note the capital) or the macroscopic cross section.

Thus, P_x = (Sigma)dx [eqn A]

Now, if we consider the initial beam of neutrons incident upon the face of the slab, it is intuitive that the product of initial beam intensity on the probability of interaction x will yield the decrease in beam intensity, which we shall denote '-dI'. note the use of the 'delta' interpretation for the differential quantity rather than the infinitesimal interpretation.

-dI = p_x * I

-> p_x = -dI/I [eqn B]

by substituting in [eqn A] into [eqn B] we arive at a first order linear differential equation commonly know as 'Beer's Law'.

-dI / I = (Sigma)*dx

if set the beam between some initial intensity 'I_0' and 'I' and the distance through which the beam travels between 0 and 'x', then as we all learned in kindergarten, this equation will have the solution

I=I_0*exp(-(Sigma)*x)

okay, great, but what does this have to do with moderation?

Well, to moderate neutrons, you need to slow them down, and you slow them down by bouncing them off, or 'scattering' them off atoms.

What is the probability that a neutron will scatter off an atom? well, that's given by its cross section. Where do you find cross sections? Well, you just look to your handy dandy National Nuclear Data Center's Evaluated Nuclear Data File (ENDF) available here: http://www.nndc.bnl.gov/sigma/

Now, recall that the probability of an interaction of type x occurring is given by

p_x = (Sigma)dx,

that means that in 1 cm, the probability of collusion is (Sigma). Thus, the common interpretation of (Sigma) is the probability of interaction per path length.

So,now unless you're very lucky or rich, you'll probably be using some sort of Boron-10 neutron detector. These work by the reaction:

B_10 +n -> alpha + Li

The charged alpha particle is picked up by the detector cathode, and it produces an electrical signal that reads as a 'count'

Now, if you look at the cross section for B_10

http://www.nndc.bnl.gov/sigma/getPlot.j ... 07&nsub=10

Notice that the cross section increases as your energy decreases.

Thus, to maximize your probability of detecting a neutron, you need to minimize your neutron energy.

How do you do this? Moderation!

The energy of a neutron after a collision is given by E'=(alpha)E

where (alpha) is your collision parameter.

I might show in a later derivation that

(alpha) = ((A-1)/(A+1))^2

where A is the atomic mass of your target nucleus

it's clear that this equation is at a maximum when A=1

And, what nucleus has A=1? Hydrogen!

Thus, to slow down neutrons the fastest, you must pass your neutron field through a hydrogen rich material to slow them down.

That's all I have to add for now, I might write a word file or something on this when I get some time to better show the equations and what not.

-TJP

- Carl Willis
**Posts:**2840**Joined:**Thu Jul 26, 2001 11:33 pm**Real name:**Carl Willis**Location:**Albuquerque, New Mexico, USA-
**Contact:**

### Re: FAQ - Moderators, Neutron moderation, what it does, how to do it, why do it?

Hi Richard,

Perhaps I should make a more unified effort at a FAQ on moderators. It may take me a while to do that. In the mean time, I'll point out that I have considered a lot of specific questions on the subject over the years, and my links to those discussions are bound to be informative to the types of questions that are "frequently asked".

My prior FAQ about neutron detector setup is related:

viewtopic.php?f=13&t=6053#p34497

Optimal paraffin moderator thicknesses for Ag and B-10:

viewtopic.php?f=13&t=6021#p39812

Moderator thicknesses for silver and indium activation:

viewtopic.php?f=13&t=6104#p40456

Various moderator materials and thicknesses compared:

viewtopic.php?f=13&t=5384#p33828

Jon Rosenstiel's cute moderator experiment is a must-read:

viewtopic.php?f=13&t=5269#p33713

I'll note again that the geometry of the detector and the geometry of the source both influence optimum configuration of the moderator. There is no single, general answer about optimum thickness. But if you have a common hydrogenous material being used to detect DD fusion with a slow-neutron-sensitive detector like B-10 or Ag-108 or In-115 or He-3, the optimal thickness is always going to be "about" 6 cm, and precision in this number is not critical to detector performance.

-Carl

Perhaps I should make a more unified effort at a FAQ on moderators. It may take me a while to do that. In the mean time, I'll point out that I have considered a lot of specific questions on the subject over the years, and my links to those discussions are bound to be informative to the types of questions that are "frequently asked".

My prior FAQ about neutron detector setup is related:

viewtopic.php?f=13&t=6053#p34497

Optimal paraffin moderator thicknesses for Ag and B-10:

viewtopic.php?f=13&t=6021#p39812

Moderator thicknesses for silver and indium activation:

viewtopic.php?f=13&t=6104#p40456

Various moderator materials and thicknesses compared:

viewtopic.php?f=13&t=5384#p33828

Jon Rosenstiel's cute moderator experiment is a must-read:

viewtopic.php?f=13&t=5269#p33713

I'll note again that the geometry of the detector and the geometry of the source both influence optimum configuration of the moderator. There is no single, general answer about optimum thickness. But if you have a common hydrogenous material being used to detect DD fusion with a slow-neutron-sensitive detector like B-10 or Ag-108 or In-115 or He-3, the optimal thickness is always going to be "about" 6 cm, and precision in this number is not critical to detector performance.

-Carl

- Richard Hull
- Site Admin
**Posts:**10656**Joined:**Fri Jun 15, 2001 1:44 pm**Real name:**Richard Hull

### Re: FAQ - Moderators, Neutron moderation, what it does, how to do it, why do it?

Thanks Terry for the precision mathematical treatment and thank you Carl for compiling all your former related material into this FAQ.

This FAQ should now serve as a base and jumping off point for those searching FAQ titles for the mysterious term....."moderation" or "moderator".

Carl's videos are tremendously instructive! My suggesstion is to down load each if you are smart. I have 'em on all 3 of my computers and a thumb drive as backup! Nothing on the internet is forever.

The amateur fusioneer is now armed with about all he or she will need to get a neutron detector going or to do activation with respect to the obligatory moderator and moderation.

Richard Hull

This FAQ should now serve as a base and jumping off point for those searching FAQ titles for the mysterious term....."moderation" or "moderator".

Carl's videos are tremendously instructive! My suggesstion is to down load each if you are smart. I have 'em on all 3 of my computers and a thumb drive as backup! Nothing on the internet is forever.

The amateur fusioneer is now armed with about all he or she will need to get a neutron detector going or to do activation with respect to the obligatory moderator and moderation.

Richard Hull

Progress may have been a good thing once, but it just went on too long. - Yogi Berra

Fusion is the energy of the future....and it always will be

Retired now...Doing only what I want and not what I should...every day is a saturday.

Fusion is the energy of the future....and it always will be

Retired now...Doing only what I want and not what I should...every day is a saturday.

- Adam Szendrey
**Posts:**1333**Joined:**Fri Mar 29, 2002 10:36 pm**Real name:**Adam Szendrey**Location:**Budapest, Hungary

### Re: FAQ - Moderators, Neutron moderation, what it does, how

Well, somehow it was kind of "lost" as I don't see it here (or it had errors in it, and I wasn't told), but way back in 2004 I did a moderator thickness calculation ( I actually named it FAQ - neutron moderators originally, I think it was renamed later by the admins). I see there is one above here already, but I thought I'd copy paste my own here as well. Feel free to point out any errors in the math, or physics of it, I didn't re-check it, and it was done a long time ago. It might be useful or something. If it's crap, then feel free to delete it.

******Start of orignal text******

Hi folks!

I figured i should chime in with some neutron moderator math i learned today.

I looked at the Fusion fuels FAQ to see, how energetic neutrons are produced in an average fusor , using D as fuel.

The number i found is 2.45 MeV. This seems to be quite close to what U-238 fission requires.

I googled around for data on calculating moderator thicknesses for a desired neutron energy.

I found a very good source of info (http://www.tpub.com/content/doe/h1019v1/index.htm ), and a word document on the theory side.

Here i will try to calculate the required thickness of a carbon (C-12) neutron moderator, to get 2 MeV neutrons. This can be VERY useful info for those who seek information on calculating neutron moderator thicknesses (a kind of FAQ maybe).

First of all every material has a constant, called the "average logarithmic energy decrement", or ξ (xi).

It is the average decrease per collision, in the logarithm of neutron energy.

For lighter nuclei this constant can be approximately calculated using the following formula:

ξ = 2/(A+(2/3))

Where A is the mass number. According to the article, this is accurate for mass numbers above 10, below that, it can produce an error greater than 3 %.

For C-12 this value is 0.158.

The number of collision (scattering events) required to decrease the energy of a neutron is given by:

N = ln(E1/E2)/ξ

Where N is the number of collisions, E1 is the initial energy of the neutron, and E2 is the resulting energy of that neutron, and ξ you

know.

For carbon, to slow 2.45 MeV neutrons to 2 MeV:

N=ln(2.45/2)/0.158 = 1.28 collisions.

Now that we have the required number of collisions, we need to know, what is the SCATTER mean free path of the neutron in C-12:

λs=1/(Nc*σs)

For this we need to know the atomic density of carbon (Nc), that is about 9e22 1/cm³, and the fast neutron scattering cross section (σs), which is 423 barns in our case.

Nc*σs is the so called macroscopic cross section of a material (Σs), from which σs is the microscopic cross section (all for scattering).

λs = 1/((4.23e-24)*(9e22)) = 2.62 cm

Now we can calculate the "slowing down length", which is the actual moderator thickness required:

Ls² = (N*λs²) / (3*(1-cosδ))

Only cosδ we don't know from this formula, that is the scattering angle.

cosδ = 2/(3A)

Where A is the mass number. For carbon cosδ = 0.0555 .

Ls² = (1.28*2.62²)/(3*(1-0.0555) = 3.1 cm²

That gives us 1.76 cm.

So the required moderator thickness made of C-12, to slow down 2.45 MeV neutrons to 2 MeV is 1.76 cm , according to the above.

Appendix:

For small nuclei (like hydrogen), cosδ is large, and three new factors arise:

Instead of simple mean free path, comes transport mean free path:

λtr = λs/(1-cosδ)

Microscopic cross section becomes, microscopic transport cross section:

σtr = σs/(1-cosδ)

And finally, in place of macroscopic cross section, macroscopic transport cross section:

Σtr=Σs/(1-cosδ)

The macroscopic slowing down power (MSDP):

The ability of a given material to slow down neutrons is called the macroscopic slowing down power, or MSDP.

It can be calculated from the formula below:

MSDP = ξ*Σs

It shows how rapidly a neutron is slowed down in a material.

The moderating ratio (MR):

The best measure of the effectiveness of a moderator, is called the moderating ratio (MR).

MR = MSDP/Σa

Where MSDP you know, and Σa is the macroscopic cross section for ABSORPTION (Nc*σa).

For eg. the MR of D2O is 4830 ,while the MR of H2O is 62.

If a material has a high cross section for absorbing neutrons it is a poor moderator.

**************************************************************************************************

This post took me quite some time to get together, so please point out all errors in it (it's rather late here now), as this is my first

attempt at calculating moderator thickness. Hope i'm not completely wrong here lol. So be kind!

Thank you!

Adam

******End of orignal text******

******Start of orignal text******

Hi folks!

I figured i should chime in with some neutron moderator math i learned today.

I looked at the Fusion fuels FAQ to see, how energetic neutrons are produced in an average fusor , using D as fuel.

The number i found is 2.45 MeV. This seems to be quite close to what U-238 fission requires.

I googled around for data on calculating moderator thicknesses for a desired neutron energy.

I found a very good source of info (http://www.tpub.com/content/doe/h1019v1/index.htm ), and a word document on the theory side.

Here i will try to calculate the required thickness of a carbon (C-12) neutron moderator, to get 2 MeV neutrons. This can be VERY useful info for those who seek information on calculating neutron moderator thicknesses (a kind of FAQ maybe).

First of all every material has a constant, called the "average logarithmic energy decrement", or ξ (xi).

It is the average decrease per collision, in the logarithm of neutron energy.

For lighter nuclei this constant can be approximately calculated using the following formula:

ξ = 2/(A+(2/3))

Where A is the mass number. According to the article, this is accurate for mass numbers above 10, below that, it can produce an error greater than 3 %.

For C-12 this value is 0.158.

The number of collision (scattering events) required to decrease the energy of a neutron is given by:

N = ln(E1/E2)/ξ

Where N is the number of collisions, E1 is the initial energy of the neutron, and E2 is the resulting energy of that neutron, and ξ you

know.

For carbon, to slow 2.45 MeV neutrons to 2 MeV:

N=ln(2.45/2)/0.158 = 1.28 collisions.

Now that we have the required number of collisions, we need to know, what is the SCATTER mean free path of the neutron in C-12:

λs=1/(Nc*σs)

For this we need to know the atomic density of carbon (Nc), that is about 9e22 1/cm³, and the fast neutron scattering cross section (σs), which is 423 barns in our case.

Nc*σs is the so called macroscopic cross section of a material (Σs), from which σs is the microscopic cross section (all for scattering).

λs = 1/((4.23e-24)*(9e22)) = 2.62 cm

Now we can calculate the "slowing down length", which is the actual moderator thickness required:

Ls² = (N*λs²) / (3*(1-cosδ))

Only cosδ we don't know from this formula, that is the scattering angle.

cosδ = 2/(3A)

Where A is the mass number. For carbon cosδ = 0.0555 .

Ls² = (1.28*2.62²)/(3*(1-0.0555) = 3.1 cm²

That gives us 1.76 cm.

So the required moderator thickness made of C-12, to slow down 2.45 MeV neutrons to 2 MeV is 1.76 cm , according to the above.

Appendix:

For small nuclei (like hydrogen), cosδ is large, and three new factors arise:

Instead of simple mean free path, comes transport mean free path:

λtr = λs/(1-cosδ)

Microscopic cross section becomes, microscopic transport cross section:

σtr = σs/(1-cosδ)

And finally, in place of macroscopic cross section, macroscopic transport cross section:

Σtr=Σs/(1-cosδ)

The macroscopic slowing down power (MSDP):

The ability of a given material to slow down neutrons is called the macroscopic slowing down power, or MSDP.

It can be calculated from the formula below:

MSDP = ξ*Σs

It shows how rapidly a neutron is slowed down in a material.

The moderating ratio (MR):

The best measure of the effectiveness of a moderator, is called the moderating ratio (MR).

MR = MSDP/Σa

Where MSDP you know, and Σa is the macroscopic cross section for ABSORPTION (Nc*σa).

For eg. the MR of D2O is 4830 ,while the MR of H2O is 62.

If a material has a high cross section for absorbing neutrons it is a poor moderator.

**************************************************************************************************

This post took me quite some time to get together, so please point out all errors in it (it's rather late here now), as this is my first

attempt at calculating moderator thickness. Hope i'm not completely wrong here lol. So be kind!

Thank you!

Adam

******End of orignal text******