# Presentation: 422149

## neutrons essentially interact only with the atomic nucleus

cross-sections can vary dramatically and erratically based on complex interactions between all the nucleons in the nucleus and the incident neutron

huge effort and money has been spent to measure these cross-sections for many materials and a wide range of neutron energies

**cross-sections can vary dramatically and erratically based on complex interactions between all the nucleons in the nucleus and the incident neutron**
**huge effort and money has been spent to measure these cross-sections for many materials and a wide range of neutron energies**

**Neutron Interactions**

## needed for shielding calculations and for many basic and applied type s of research:

neutron scattering, crystal studies, DNA

neutron activation analysis

neutron radiography, paintings

weapons research, neutron bombs

nuclear structure

neutron depth profiling

neutron dosimetry

**neutron scattering, crystal studies, DNA**
**neutron activation analysis**
**neutron radiography, paintings**
**weapons research, neutron bombs**
**nuclear structure**
**neutron depth profiling**
**neutron dosimetry**

**Neutron Interactions**

##  nuclear reactor most prolific source

energy spectrum from the fission of 235U extends from several keV to more than 10 MeV

most probable energy ~ 0.7 MeV

average energy ~ 2 MeV

there are no naturally occurring radioisotopes which emit neutrons 

**energy spectrum from the fission of ****235****U extends from several keV to more than 10 MeV**
**most probable energy ~ 0.7 MeV**
**average energy ~ 2 MeV**
**there are no naturally occurring radioisotopes which emit neutrons **

**Sources of Neutrons **

## Slide 4

##  1. one can manufacture a radioactive neutron source by combining an alpha emitting radionuclide such as 210Po, 226Ra or 239Pu with a light metal such as Be or B

the reactions that follow are:
		9Be(, n)12C
		10B(, n)13N
		11B(, n)14N

there is a continuous energy spectrum

**the reactions that follow are:**
**	****	****9****Be(********, n)****12****C**
**	****	****10****B(********, n)****13****N**
**	****	****11****B(********, n)****14****N**
**there is a continuous energy spectrum**

**Sources of Neutrons**

## Slide 6

## Sources of Neutrons (α,n)

**Sources of Neutrons (****α****,n)**

## 3.  Photoneutron sources using (,n) reactions

by choosing radioisotopes with a single -ray then monoenergetic neutrons can be produced

the sources are produced in a reactor using conventional (n,) reactions except for 226Ra

 's then interact as follows:
		9Be(,n)8Be
		2He(,n)1H

**by choosing radioisotopes with a single ********-ray then monoenergetic neutrons can be produced**
**the sources are produced in a reactor using conventional (n,********) reactions except for ****226****Ra**
****** ****'s then interact as follows:**
**	****	****9****Be(********,n)****8****Be**
**	****	****2****He(********,n)****1****H**

**Sources of Neutrons**

## Sources of Neutrons 

## 4.  Accelerator Neutrons

particle accelerators are used to generate neutrons by means of nuclear reactions such as:  D-T, D-N, P-N

3H(d,n)4He - Q-value = 17.6 MeV 14.1MeV neutrons

2H(d,n)3He - Q-value = 3.27 MeV

7Li(p,n)7Be - Q-value = 1.65 MeV 

positive Q-values means the nuclear reaction can be induced with only several hundred keV ions

**particle accelerators are used to generate neutrons by means of nuclear reactions such as:  D-T, D-N, P-N**
**	**
**3****H(d,n)****4****He - Q-value = 17.6 MeV ********14.1MeV neutrons**
**2****H(d,n)****3****He - Q-value = 3.27 MeV**
**7****Li(p,n)****7****Be - Q-value = 1.65 MeV **
**positive Q-values means the nuclear reaction can be induced with only several hundred keV ions**

**Sources of Neutrons**

## 5. Spontaneous Fission Sources

some heavy nuclei fission spontaneously emitting neutrons

some sources include:  254Cf, 252Cf, 244Cm, 242Cm, 238Pu and 232U

in most cases the half-life for spontaneous fission is greater than alpha decay

254Cf decays almost completely by spontaneous fission with a 60 day half-life

**some heavy nuclei fission spontaneously emitting neutrons**
**some sources include:  ****254****Cf, ****252****Cf, ****244****Cm, ****242****Cm, ****238****Pu and ****232****U**
**in most cases the half-life for spontaneous fission is greater than alpha decay**
**254****Cf decays almost completely by spontaneous fission with a 60 day half-life**

**Sources of Neutrons**

## 252Cf undergoes spontaneous nuclear fission at an average rate of 10 fissions for every 313 alpha transformations

half-life of 252Cf due to alpha emission is 2.73 years
    with spontaneous nuclear fission its effective half-life is 2.65 years

neutron emission rate is 2.31  106 neutrons per second per microgram of 252Cf

emitted neutrons have a wide range of energies with the most probable at ~ 1 MeV and the average value ~ 2.3 MeV

**half-life of ****252****Cf due to alpha emission is 2.73 years**
**    ****with spontaneous nuclear fission its effective half-life is 2.65 years**
**neutron emission rate is 2.31 ******** 10****6**** neutrons per second per microgram of ****252****Cf**
**emitted neutrons have a wide range of energies with the most probable at ~ 1 MeV and the average value ~ 2.3 MeV**

**Sources of Neutrons**

## neutrons are classified according to their energy

thermal neutrons have an energy of about ~ 0.025 eV

epithermal neutrons, resonance neutrons, slow neutrons have energies between 0.01 MeV and 0.1 MeV

fast neutrons - 0.1 MeV and 20 MeV

relativistic neutrons

**thermal neutrons have an energy of about ~ 0.025 eV**
**epithermal neutrons, resonance neutrons, slow neutrons have energies between 0.01 MeV and 0.1 MeV**
**fast neutrons - 0.1 MeV and 20 MeV**
**relativistic neutrons**

**Classification of Neutrons**

## at thermal energies neutrons are indistinguishable from gas molecules at the same temperature and follow the Maxwell-Boltzman distribution:

**where:**
***	******	******ƒ *****(E) = fraction of neutrons of energy**
** ****	****	****	****e/unit energy interval **
**	****	****k = Boltzman constant  ******** 10****-23**** J/oK**
**	****	****T = absolute temperature oK**

**Classification of Neutrons**

## most probable energy is:
Emp = kT

average energy at any given temperature is:

**E****mp**** = kT**
**average energy at any given temperature is:**

**for neutrons at 293 oK most probable energy is 0.025 eV**

**Classification of Neutrons**

## velocity:

**neutron half-life is 10 minutes**
**cold neutrons are much slower**

**Classification of Neutrons**

## neutrons are uncharged and can travel appreciable distances in matter without interacting

neutrons interact mostly by inelastic scattering, elastic scattering and absorption

**neutrons interact mostly by inelastic scattering, elastic scattering and absorption**

**Interaction of Neutrons**

##  1. Inelastic scattering (n,n)

a part of the kinetic energy that is transferred to the target nucleus upon collision

the nucleus becomes excited and a gamma photon/photons are emitted:   
  			12C(n,n)12C

this interaction is best described by the compound nucleus model  

**a part of the kinetic energy that is transferred to the target nucleus upon collision**
**the nucleus becomes excited and a gamma photon/photons are emitted:   **
**  ****	****	****	****12****C(n,n********)****12****C**
**this interaction is best described by the compound nucleus model  **

**Interaction of Neutrons**

## a threshold exists for such interactions

infinity for hydrogen (inelastic scattering can not occur) - 6 MeV for oxygen and less than 1 MeV for uranium

cross-section for inelastic scattering is small, usually less than 1 barn for low energy fast neutrons but increases with increasing energy

**infinity for hydrogen (inelastic scattering can not occur) - 6 MeV for oxygen and less than 1 MeV for uranium**
**cross-section for inelastic scattering is small, usually less than 1 barn for low energy fast neutrons but increases with increasing energy**

**1 barn = 10****-24**** cm****2**** **

**Interaction of Neutrons**

##  2.  Elastic scattering (n,n’)

most likely interaction between fast neutrons and low atomic number z

most important process for slowing down neutrons

interaction is a ‘billiard ball’ collision     

scattering reactions are responsible for neutron – slowing in reactors 

**most likely interaction between fast neutrons and low atomic number z**
**most important process for slowing down neutrons**
**interaction is a ‘billiard ball’ collision     **
**scattering reactions are responsible for *****neutron – slowing *****in reactors**** **

**Interaction of Neutrons**

## in general neutrons emitted in fission have an average energy of 2 MeV

these fast neutrons lose K.E. as a result of scattering collisions with nuclei which act as moderators (eg - water, graphite)

n contrast cross-sections for inelastic scattering are small for low energy fast neutrons but increase with increasing energy

consider a neutron with energy Eo, mass M and velocity V hitting a nucleus m:

**these fast neutrons lose K.E. as a result of scattering collisions with nuclei which act as moderators (eg - water, graphite)**
**n contrast cross-sections for inelastic scattering are small for low energy fast neutrons but increase with increasing energy**
**consider a neutron with energy Eo, mass M and velocity V hitting a nucleus m****:**

**Interaction of Neutrons**

## Interaction of Neutrons

**Interaction of Neutrons**

## total kinetic energy and momentum are conserved and we have:

**solving for v****1  ****and substituting into:**

**Interaction of Neutrons**

## Interaction of Neutrons

**the energy transferred to target nucleus is:**

## Interaction of Neutrons

**when:  M = m;    E = E****max****  **
**for neutrons in a head on collision with hydrogen all the kinetic energy can be transferred in one collision since the mass of neutrons and protons are almost equal**

## important aspect in shielding for fast neutrons, (paraffin wax, H2O) and also for abundance of H in tissue; n-p scattering is the dominant mechanism when neutrons deliver a dose to tissue

**Interaction of Neutrons**

## Maximum Fraction of Energy Lost, Qmax/E by Neutron in Single Elastic Collision with Various Nuclei

| Nucleus | Qmax/E |
| --- | --- |
| 1H | 1.000 |
| 2H | 0.889 |
| 4He | 0.640 |
| 9Be | 0.360 |
| 12C | 0.284 |
| 16O | 0.221 |
| 56Fe | 0.069 |
| 118Sn | 0.033 |
| 238U | 0.017 |

## 3. Absorption / Radiative Capture (n,) 

capture cross-sections for low energy neutrons generally decreases as the reciprocal of the velocity as the neutron energy increases

phenomenon called 1/v law

valid up to 1000 eV

if the capture cross-section σ0 is known for a given neutron velocity v0 or energy E0, then the cross-section at some other velocity v or energy E can be estimated: 

**capture cross-sections for low energy neutrons generally decreases as the reciprocal of the velocity as the neutron energy increases**
**phenomenon called 1/v law**
**valid up to 1000 eV**
**if the capture cross-section σ****0**** is known for a given neutron velocity v****0**** or energy E****0****, then the cross-section at some other velocity v or energy E can be estimated: **

**Interaction of Neutrons**

## problem
    the cross-section of for the 10B(n, )7Li reaction is 753 barns for thermal (0.025 eV) neutrons.  What is the cross-section at 50 eV?

**    ****the cross-section of for the ****10****B(n, ********)****7****Li reaction is 753 barns for thermal (0.025 eV) neutrons.  What is the cross-section at 50 eV?**

**Interaction of Neutrons**

## Slide 30

## Interaction of Neutrons

**Interaction of Neutrons**

**Total Cross Section of ****238****U**

## as with 's neutrons are also removed exponentially when absorbers are placed in front of them:
I= I0e-Nt
where:
	σ = microscopic cross-section
	N = no. of absorber atoms in atoms/cm3
	t = thickness
neutron cross-section is strongly energy dependent

**I= I****0****e****-********Nt**
**where:**
**	****σ = microscopic cross-section**
**	****N = no. of absorber atoms in atoms/cm****3**
**	****t = thickness**
**neutron cross-section is strongly energy dependent**

**Interaction of Neutrons**

## problem: 
a 1 cm thick lead absorber attenuated an initial 10 MeV neutron beam to 84.5% of its value

what is total cross-section given that the atomic weight of Pb = 207.21 and its density is 11.3 gm/cm3?

**a 1 cm thick lead absorber attenuated an initial 10 MeV neutron beam to 84.5% of its value**
**what is total cross-section given that the atomic weight of Pb = 207.21 and its density is 11.3 gm/cm****3****?**

**Interaction of Neutrons**

## Interaction of Neutrons

**    ****=  5.1 barns (microscopic cross-section)**
** ******** ****macroscopic cross-section:**
**	******** ****= ****σ****N**
**	******** ****= 5.1 ******** 10****-24**** cm****2****  ******** 3.29  ******** 10****22**** cm****-3**
**	******** ****= 0.168 cm****-1**

**Interaction of Neutrons**

## production of a radioactive isotope by the absorption of a neutron, eg:

(n, ) (n,p) (n,) (n,n’)

if NT target atoms with a cross-section σcM2 are being neutron irradiated with a fluence of n cm-2 sec-1 then the production rate of daughter atoms is:

**(n, ********) (n,p) (n,********) (n,n’)**
**if N****T**** target atoms with a cross-section σcM****2**** are being neutron irradiated with a fluence of n cm****-2**** sec****-1**** then the production rate of daughter atoms is:**

**Neutron Activation**

## the number of daughter atoms is N having a decay constant 

the rate of loss of daughter atoms is N

the rate of change is 

**the rate of loss of daughter atoms is ********N**
**the rate of change is **

**in the number of daughter atoms presented at any time while the target is bombarded is:**

**Neutron Activation**

## assume the neutron fluence rate is constant and the original number of atoms is not being excessively depleted so NT is constant:

				let N = a + beλt   
				be-λt = NT -a -b e-λt

both exponential terms cancel out   

**	****	****	****	****let N = a + be****λt****   ******
**	****	****	****	****b********e****-λt**** = ********N****T**** -a******** -b******** e****-λt**
**both exponential terms cancel out   ******

**Neutron Activation**

## therefore the original solution is:

**the constant b depends on the initial conditions**
**at N = 0, t = 0 we get**

**the  final expression is:**

**Neutron Activation**

## where:
	N - represents activity of daughter as a
		  function of t
 σNt - is called saturation activity 
           representing maximum activity at
           time t    ∞

when neutrons are not monoenergetic as in a reactor, an average cross-section is used for σ

**	********N - represents activity of daughter as a**
**	****	****  ****function of t**
-  σ**N****t**** - is called saturation activity **
**           ****representing maximum activity at**
**           ****time t   ******** ∞**
**when neutrons are not monoenergetic as in a reactor, an average cross-section is used for σ**

**Neutron Activation**

## the previous equation is the activity just at the end of production

if one is interested in the activity sometime later the following terms must be added:

**if one is interested in the activity sometime later the following terms must be added:**

**where:**
**	****t****i**** = irradiation time**
**	****t****d**** = decay time**
**	****t****e**** = counting time**

**Neutron Activation**

## Slide 41

## a certain radioisotope is produced by neutron activation of a sample that contains 5  1022 target atoms with an activation cross section of 2 barns

the neutron rate, 1011 cm-2 s-1, is constant

the half-life of the isotope is 8.5 hours.

a. calculate the saturation activity in Bq

**the neutron rate, 10****11**** cm****-2**** s****-1****, is constant**
**the half-life of the isotope is 8.5 hours.**
**a. calculate the saturation activity in Bq**

**problem: **

**Neutron Activation**

##  the induced activity A as a function of time t after starting the exposure is given by: 

A= NT (1- e-t)
where:
	  = neutron fluence rate or flux density
	 σ  = cross section
	NT = no. of target atoms in sample

activity, starting with A=0 when t=0, builds up as t increases   

**A= ********N****T**** (1- e****-********t****)**
**where:**
**	**** ******** ****= neutron fluence rate or flux density**
**	**** ****σ  = cross section**
**	****N****T ****= no. of target atoms in sample**
**activity, starting with A=0 when t=0, builds up as t increases   **

**Neutron Activation**

## when t becomes very large  exponential term in above formula becomes negligibly small; and the activity approaches its maximum, or saturation value

**Neutron Activation**

## b. calculate the activity reached after exposure for 24 h

c. what fraction of the saturation activity is reached at this time?

solution:  
b. use with:     

**c. what fraction of the saturation activity is reached at this time?**
_**solution**_**:****  **
**b. use with:****     **

**Neutron Activation**

## decay constant is:

**therefore:**

**fraction of the saturation activity is:**

**Neutron Activation**

## problem:

Three grams of 32S are irradiated with fast neutrons
having a fluence rate of 155 cm-2sec1 - cross-section is 
0.200 barns and the half-life of 32P is 14.3 days

 a. what is the maximum 32P activity that can be induced?

solution:  
a.  

**Three grams of ****32****S are irradiated with fast neutrons**
**having a fluence rate of 155 cm****-2****sec****1**** - cross-section is **
**0.200 barns and the half-life of ****32****P is 14.3 days**
** ****a. what is the maximum ****32****P activity that can be induced?**
**solution:  **
**a.**** **** **

**Neutron Activation**

## b. how many days are needed for the level of the activity to reach 3/4 maximum?

solution:
b. time t needed to reach 3/4 of the value can be calculated:

_**solution**_**:**
**b. time t needed to reach 3/4 of the value can be calculated:**

**since there are 3.7 ******** 10****10**** disintegrations/ second/Curie   ******

**Neutron Activation**

## 4. charged particle reactions (n,p) (n,α)
	 	- important in neutron dosimetry
5. neutron-producing reactions (n,2n)
		- associated with high energy neutrons
		-  14 MeV neutron accelerators
6. fission
		- the binding energy per nucleon for 	heavy elements (A > 230) decreases as 	the atomic mass increases

**	**** ****	****- important in neutron dosimetry**
**5. neutron-producing reactions (n,2n)**
**	****	****- associated with high energy neutrons**
**	****	****-  14 MeV neutron accelerators**
**6. fission**
**	****	****- the binding energy per nucleon for ****	****heavy elements (A > 230) decreases as ****	****the atomic mass increases**

**Neutron Activation**

## when a thermal neutron is absorbed in 235U (580 barns), 239Pu (747 barns) or 233U (525 barns) vibrations in these nuclei cause them to split (fission) under mutual electrostatic repulsion of its parts

in general:

**in general:**

**Fission **

## Slide 51

## Distribution of Energy Among Products Released by Fission of 235u

| kinetic energy of charged fission fragments | 162 MeV |
| --- | --- |
| fission neutrons |     6 |
| fission gamma rays |     6 |
| subsequent beta decay |     5 |
| subsequent gamma decay  |     5 |
| neutrinos |    11 |
| total | 195 MeV |

**Distribution of Energy Among Products Released by Fission of ****235****u**

## the fission process is bimodal in distribution

all fission fragments are radioactive and there are several steps before stable daughters are produced

decay of the collective fission-product activity following fission of a number of atoms is:

A  10-16 t-1.2 curies/fission

where t is in days

**all fission fragments are radioactive and there are several steps before stable daughters are produced**
**decay of the collective fission-product activity following fission of a number of atoms is:**
**A ******** 10****-16**** t****-1.2**** curies/fission**
**where t is in days**

**Distribution of Energy Among Products Released by Fission of ****235****U**

## Slide 54

## 1H(nth,)2H 
which releases a 2.22 MeV -ray that irradiates the surrounding tissue

it is one of the two important interactions by which thermal neutrons deposit energy in tissue

often seen as a background gamma-ray in power and research reactors

**which releases a 2.22 MeV ********-ray that irradiates the surrounding tissue**
**it is one of the two important interactions by which thermal neutrons deposit energy in tissue**
**often seen as a background gamma-ray in power and research reactors**

**Neutron Reactions Important to Health Physicists**

## 3He(nth,p)3H
which is the basis for the use of 3He as a gas in several types of neutron proportional counters

6Li(nth,t)4He or 6Li(nth,α)3H
which releases a tritium nucleus (triton) and a helium nucleus (alpha particle)

it is used in many neutron detection instruments, including thermoluminescent dosimeters (TLDs)

**which is the basis for the use of ****3****He as a gas in several types of neutron proportional counters**
**6****Li(n****th****,t)****4****He or ****6****Li(n****th****,α)****3****H**
**which releases a tritium nucleus (triton) and a helium nucleus (alpha particle)**
**it is used in many neutron detection instruments, including thermoluminescent dosimeters (TLDs)**

**Neutron Reactions Important to Health Physicists**

## 10B(nth,α)7Li
which is used in neutron shielding and as the basis for neutron detectors utilizing BF3 gas or boron-lined counter tubes

14N(nth,p)14C
which releases 626 keV and contributes approximately 1% of the total dose equivalent in soft tissue for neutron energies less than 10 MeV

the absorbed dose is delivered locally at the interaction site, since the ranges of the proton and 14C recoil nucleus are short

**which is used in neutron shielding and as the basis for neutron detectors utilizing BF****3**** gas or boron-lined counter tubes**
**14****N(n****th****,p)****14****C**
**which releases 626 keV and contributes approximately 1% of the total dose equivalent in soft tissue for neutron energies less than 10 MeV**
**the absorbed dose is delivered locally at the interaction site, since the ranges of the proton and ****14****C recoil nucleus are short**

**Neutron Reactions Important to Health Physicists**

## 23Na(nth,γ)24Na
which activates human blood sodium
the decay of 24Na (half-life = 7  15 h; two γ's of 100% intensity:  1.37 and 2.75 MeV) can be used to quick-sort personnel after a suspected criticality

32S(nf,p)32p
which requires a neutron with a kinetic energy of at least 2.7 MeV in order to react (an energy threshold)

this reaction is used in many threshold criticality dosimeters

**which activates human blood sodium**
**the decay of ****24****Na (half-life = 7 ******** 15 h; two γ's of 100% intensity:  1.37 and 2.75 MeV) can be used to quick-sort personnel after a suspected criticality**
_**32**__**S(n**__**f**__**,p)**__**32**__**p**_
**which requires a neutron with a kinetic energy of at least 2.7 MeV in order to react (an energy threshold)**
**this reaction is used in many threshold criticality dosimeters**

**Neutron Reactions Important to Health Physicists**

## 113Cd(nth,γ)114Cd
which is used in neutron shielding and reactor control rods

115In(nth,γ)116mIn
which is the basis for the popular indium foils used in many criticality dosimeters

197Au(nth,γ)198Au
used for criticality monitoring (gold foils)

**which is used in neutron shielding and reactor control rods**
**115****In(n****th****,γ)****116m****In**
**which is the basis for the popular indium foils used in many criticality dosimeters**
**197****Au(n****th****,γ)****198****Au**
**used for criticality monitoring (gold foils)**

**Neutron Reactions Important to Health Physicists**

## 235U(nth,f)
which releases approximately 200 MeV of energy during the fission (f) process

fission in 235U can also be caused by fast neutrons

**which releases approximately 200 MeV of energy during the fission (f) process**
**fission in ****235****U can also be caused by fast neutrons**

**Neutron Reactions Important to Health Physicists**