Lecture 2 Macroscopic Interactions

22.106 Neutron Interactions and Applications Spring 2010

Objectives

• Macroscopic Interactions

• A tom Density

• M ean Free Path

• Moderation in Bulk Matter

• N eutron Shielding

• E ffective Dose Equivalent

Macroscopic interactions

• S uppose a target of thickness X is placed in a monodirectional beam of intensity I 0 and that a neutron detector is placed at some distance behind the target. It is also assumed that the target and the detector are small so that the detector only detects the neutrons that do not interact.

• Let I(x) be the intensity of the non interacted neutrons after penetrating the distance x into the target.

• In traversing an additional distance dx , the intensity of the beam will be decreased by the number of neutron that have interacted in dx . This decrease in intensity will be given by:

- d I(x) = N  t I(x)dx

where N is the atom density in the target (at/cc)

• Integrating the previous equation from 0 to

x , we get

I(x) = I 0 exp(-N  t x)

• We define the macroscopic x.s. has

 = N 

units of  are cm -1

• T h u s

-dI(x) =  t I(x)dx or -dI(x)/I(x) =  t dx

• -dI(x)/I(x) in the previous equation is equal to the fraction of the neutrons that have penetrated the distance x into the target without interacting, which subsequently interact in the distance dx

– Equivalent to the probability that a neutron which survives up to x and interacts in the next dx

– T h u s  t dx is the probabilit y tha t a neutro n interact s in

dx

– It foll ows that  t is the probability per unit path length that a neutron will undergo an interaction

• I(x)/I 0 = exp(-  t x ) is equal to the probability that a neutron can move through this distance without interacting.

• Let the quantity p(x)dx be the probability that a neutron will have its first interaction in dx in the neighborhood of x .

p(x)dx = exp(-  t x) .  t dx

First interaction probability distribution function

• Examples

– C alculate first interaction probability between

x = a and x = b

– C alculate probability of not interacting in slab

• Macroscopic interactions are the simplest way to evaluate gamma ray attenuation

– Low energy gamma’s are more likely to be absorbed

– N eutrons on the other hand are more likely to scatter, which interferes with the measurements.

• If the target is a compound, the total macroscopic x.s. is the sum of the individual elements macroscopic x.s.

 t =  1 +  2 + …

Atom Density

• T he atom density of each element i is given by:

N i =  N a n i / M m

where  = density of compound (g/cc)

M m = molecular mass (g/mol)

N a = Avogadro number

n i = number of atoms of element i

in one molecule

•  =  N a (n 1  1 + n 2  2 + …) / M m

• Example of Natural Uranium

Mean Free Path

• T he distance that a neutron moves between interactions is called a fre e path , and the average distance is known as the mea n free path .

• Integral of xp(x)dx between 0 and infinity

Significance

• If the mean free path of neutrons emitted by a sample in a passive assay instrument is long compared to the dimensions of the sample, it is likely that most neutrons will escape the sample and enter the detection region.

• If we know the number of collisions to thermalize, we can estimate the needed moderator thickness (must also consider the scattering angle)

• If the thickness of a shield is many times the mean free path of a neutron trying to penetrate the shield, then the shield fulfills its purpose (complicated by the energy dependance of the x.s.)

Objectives

• N eutron Moderation

• S hielding

• D o s e

Moderation in Bulk Matter

• M oderation is often times needed for

– N eutron detection

– T hermal reactors

– N eutron diffraction

– Small angle neutron scattering (SANS)

• P u r p o s e :

– I ncrease the probability of interaction in “1/v” r egion

– O r, produce neutrons with low energy for condensed matter studies

Slowing Down

• N eutrons are slowed down by collisions in the manner of a random walk

• S ince fast neutrons have much more energy than the molecules they are colliding with, the neutrons will lose energy

• Extent of slowing down depends on

– T emperature of medium

– S ize, shape and nature of moderation medium

Mine Detection

• N eutron sources and neutron moderation are used to detect land mines

• C f252 source

– S pontaneous fission with spectrum in slides of Lecture 1

• Explosives

– O rganic compounds with lots of Carbon and Hydrogen

Mine Detection

7

1

4

6

2

5

3

8

E x p e r i m e n t a l a r r a n g e m e n t . D e t e c t o r c o n s i s t i n g o f s i x 1 4 - i n c h , 4 - a t m o s p h e r e 3 H e t u b e s ( 1 ) h e l d b e t w e e n t w o A l p l a t e s ( 7 ) . T i m e - t a g g e d n e u t r o n s o u r c e ( 2 ) i s l o c a t e d d i r e c t l y b e l o w d e t e c t o r . S i m u l a t e d m i n e ( 3 ) i s b u r i e d i n s a n d ( 5 ) ; s a n d i s h e l d i n 4 - f o o t s t o c k t a n k ( 6 ) s u p p o r t e d o n a w o o d e n p a l l e t ( 8 ) . C d s h e e t

( 4 ) f o r m s t h e r m a l n e u t r o n s h i e l d . F o r w e t - s a n d t e s t s , a s t a i n l e s s s t e e l p a n i s b u r i e d i n s a n d a n d f i l l e d w i t h d r y s a n d . W a t e r i s a d d e d t o g i v e t h e d e s i r e d w a t e r c o n t e n t .

Image by MIT OpenCourseWare.

Mine Detection

• F ast neutrons enter soil

• I f there is no explosive they scatter in sand, soil,

…

– N ot really good moderators

• I f a plastic explosive is found

– N eutrons scatter off hydrogen and carbon

– L ower energy neutrons are reflected and detected on the surface

• P otential issues

– W et soil, requires very fine calibration

Moderating Power

• C ompares ability of materials to moderate neutrons

• T wo important factors to consider

– P robability of scattering interaction

– A verage change in kinetic energy of the neutron after scattering

• D efine as

 s  : average logarithmic energy decrement

 s : scattering macroscopic x.s.

Average Log Energy Decrement

•  = ln (E 0 /E 1 )

• A ssuming isotropic elastic scattering only, we can find the following expression

E l a s t i c S c a t t e r i n g

N e u t r o n

N e u t r o n

T a r g e t N u c l e u s

T a r g e t N u c l e u s

Image s by MIT OpenCourseWare.

Number of collisions

• If we lose  at every collision, we can approximate the average number of collisions it takes to go from E 0 to E n

which yields

Image by MIT OpenCourseWare.

Image by MIT OpenCourseWare.

Derivation: See PDF on Neutron Moderation on stellar

Moderating Ratio

• A material with a large moderating power might still not be practical if it has a large absorption x.s.

• M oderating ratio helps in selecting a good moderator:  s /  a

Image by MIT OpenCourseWare.

Shielding Objectives

• Limit radiation exposure of staff, patients, visitors and the public to acceptable levels

• O ptimize protection of patients, staff and the public

• P rotect electronics (i.e. computer chips, transistors, …) in satellites or other instruments

• R educe background counts in detectors

Considerations

• Source characterization

– P article type

– E n e r g y

– R ate of emission

– D irection of the source

– U tilization factor

• Geometry of the room

– Shielding is a 3-D problem

• L ocation

– 1 0 th floor vs b a sement

• R equirements

– S ize, cost, weight, …

Images removed due to copyright restrictions.

• M ust consider

– Primary beam

– Scattered beams

– Leakage from source

Image by MIT OpenCourseWare.

Gamma Shielding

• Low energy gamma

– Lead

• H igh energy gamma

– C oncrete (high density)

• C ost plays a major role in the decision

– Lead is much more expensive than concrete!

• V ery little scattering present

Neutron shielding

• M uch more scattering than neutrons

• A ttenuation depends very strongly on neutron energy

• S hielding designs require multiple layers

P r e m o d e r a t o r

M o d e r a t o r

G a m m a S h i e l d

– P remoderator

– M oderator

– G amma shield

Image by MIT OpenCourseWare.

Typical Materials – Premoderator

• S catter the high energy neutrons to facilitate efficient of other two layers

– I r o n

• L ow activation, high Z number

• C orrodes

– T ungsten

• D ense, high Z number

• E xpensive

– Lead

• L ow activation, high Z number

• T o x i c

Images removed due to copyright restrictions.

Typical Materials – Moderator

• Absorbs and slows neutrons down

• C oncrete

– C heap

– Loses water (i.e. hydrogen) at high temperatures, H creates 2.2 MeV gamma

• Borated concrete

– Increase absorption

– Boron depletes over time

• W ater

– G ood absorption

– N o structural integrity, H creates 2.2 MeV gamma

• Polyethylene

– L ightweight, good absor ption

– H creates 2.2 MeV gamma, C creates 4.4 MeV gamma

Image removed due to copyright restrictions.

Typical Materials – Gamma Shield

• Lead

– E xcellent gamma absorption

– T o x i c

• D epleted uranium

– V ery high Z number

– expensive

10 5

10 4

10 3

10 2

10 1

10 0

10 -1

10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1

10 0

10 1

Ener gy (MeV)

• T hermal neutrons can be easily shielded by Boron or Cadmium as they have large neutron cross sections in the thermal region

– C d has the disadvantage of emitting high energy gamma’s after neutron capture whic h requires additional gamma shielding

• High speed neutrons are more difficult to shield against, because absorption x.s. are smaller in that range.

– T hus it is first necessary to moderate the neutrons

Image by MIT OpenCourseWare.

Geometry - M aze

Radiation along the Maze

Calculate dose rate at reflection point by ISL, then reduce this by 0.1% to give the dose rate at 1 metre from reflection point.

Isocentre

Image by MIT OpenCourseWare.

Activation

• N eutrons tend to activate shield material which can create disposition problems and can also contribute to dose to environment

– Must carefully select materials with low activation and short-lived decay

• E ffective radiation shields consist of combinations of materials

– Low A materials to moderate

– T hermal neutron absorbers

– H igh Z materials to absorb gamma’s

• Examples

– P olyethylene – lead

– C oncrete – I ron

– Lithium hydride

• C hoice of material depends on sample to shield, cost, space, weight restrictions, …

Pb- 208

10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 10 -3 10 -4 10 -5 10 -6 10 -9 10 -8 10 -7 10 -6 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 10 1 Ener gy (MeV)		H-1
Image by MIT OpenCourseWare. Image by MIT OpenCourseWare.	1 0 5 1 0 4 1 0 3 1 0 2 1 0 1 1 0 0 1 0 - 1 1 0 - 2 1 0 - 3 1 0 - 4 1 0 - 5 1 0 - 6 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 1 0 E n e r g y ( M e V )

Effective Dose Equivalent

• T he energy absorbed from any type of radiation per unit mass of the absorber is defined as the absorbed dose

– H istorical unit is the rad = 100 ergs/gram (1 erg = 10 -7 J)

– S I unit is the Gray (Gy) = 1J/gram (1 Gy = 100 rad)

• S ince neutron and gamma’s are relatively penetrating radiations, the dose equivalent is easier to estimate from fluence

– D ose equivalent (H) = Dose (D) x Quality (Q)

• Quality factor is a function of the type of radiation

• If D is in rad, H is in rem

• If D is in Gy, H is in Sievert (Sv)

• F luence is given by Φ

– I ntegral of the flux over time of exposure

• In air, since there is almost no attenuation, we can estimate fluence to be

Φ = N / 4 π d 2

where d is the distance from the source and N the total integrated number of neutrons

• Conversion from fluence-to-dose must take into account

– S econdary particle production

– K inetic energy of these particles

– Q uality factor of particle type

• Fast electrons Q = 1

• G amma’s Q = 1

• A lpha Q = 20

• N eutrons Q = 5-20 (depends on energy level)

• C onversion will also depend on specific target

– T issues and organs

– O rientation

– S elf-shielding

– Attenuation

• E ffective dose equivalent is correlated to the flux

H E = h E Φ

w here h E is the fluence-to-dose factor and is evaluated for different models using photon-neutron-electron transport calculations

Conversion factor

1.0 E-09

Neutrons

1.0 E-10

AP P A LA T

ROT

1.0 E-1 1

1.0 E-12

1E-7 1E-6

1E-5 1E-4 1E-3 0.01

Ener gy (MeV)

0.1 1.0 10

Neutrons Photons

1 . 0 E - 1 0

G a m m a R a y s

1 . 0 E - 1 1

1 . 0 E - 1 2

1 . 0 E - 1 3

1 . 0 E - 1 4

A P P A L A T R O T

I S O

1 . 0 E - 1 5

1 . 0 E - 1 6

0 . 0 1

0 . 1

E n e r g y ( M e V )

1 . 0

1 0

Image s by MIT OpenCourseWare.

• Estimation of the effects of a given exposure to ionizing radiation is by its nature an inexact science.

• B iological effects are not absolute physical quantities that can be measured with high precision.

• E ffective dose calculations provide guidance in approximating the potential effects of a given exposure to radiation.

M IT OpenCourseWare http://ocw.mit.edu

22.106 Neutron Interactions and Applications

Spring 2010

For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .