Bai giang ve tuong tac

Interaction of particles and radiation with matter • Ionization Losses Due to Collisions of Charged Particles - Stopping power • Bohr's Formula for Specific Ionization.. Relativistic E

Hµnéi , 20-2.2006

NguyÔn TriÖu Tó

8261730 0904505414

2

cell Atom Atomic nucleus

Radius of Earth Radius of observable universe

15000.000.000.light -years

Processing

Energy and Intensity

Environment

Industrial application Medical diagnosis

Energy

GeV

keV MeV

Intensity(s -1 ) Concentration Bq/g

Dose(nGy/h) )

10 -2 1 10 2 10 4 10 6 10 8 10 10 10 12 10 14

Medical treatment

Accelerator, Cosmic rays

Radioisotopes

interaction of particles and radiation with matter

The measurement of nuclear radiation is based on its

interaction with the detector

1* The function of nuclear radiation detectors

2* The absorption phenomena in

the measurement of the radiation

3* With respect to radiation protection.

 We shall deal with the most important mechanisms of the interaction between nuclear radiation and matter in their basic features.

In order to understand:

To organize the discussions that follow, it is convenient to arrange the four major categories of

radiations into the following matrix:

Heavy charged particles

(characteristic distance 10 -5 m)

Fast electrons

(characteristic distance 10 -3 m)

Neutrons (characteristic length 10 -

M¶nh giÊy

L¸ nh«m

TÊm ch×

Interaction of particles and radiation with matter

• Ionization Losses Due to Collisions of Charged Particles -

Stopping power

• Bohr's Formula for Specific Ionization Relativistic Effects

and the Density Effect

• Dependence of ionization Losses on the Medium

• ionization Losses on the Medium

Radiation Losses for Electrons.

Cherenkov Radiation

n and  -radiation Interaction with matterradiation Interaction with matter

h

k e

11

the photoelectric effect cross section

1/ With decreasing E  (increasing ratio of the electron binding to the increasing ratio of the electron binding to the photon energy I K /E  ), the cross section increases first as 1/E, and later (increasing ratio of the electron binding to the as E  approaches I k ) more rapidly as 1/ E7/2

2/ The probability of photoeffect depends very strongly on the charge

Z of the atom in which the effect is observed:  phot  Z 5

phot  Z5/E7/2

for E > IK

* Photoeffect is especially signifficant for heavy materials where

the probability is considerable even for high energies of -quanta.quanta.

* In light materials, this effect becomes significant only for relatively low energies of -quanta.quanta.



 h

incoming 

-ray

scattered  -ray

( recoil electron).



 h

recoil electron.

Compton scattering

.A photon interacts with an electron, giving a partial energy, and scatters for different direction.

.Energies of the scattered photon and the secondary electron are calculated by:

Scattered photon:

hν’= h / { 1 + α ( 1 -cos) }  = h / m 0 c 2

E=hν

//'

with the scattering angle  in such a way that:

for

2

,2/

,00

2 However, for scattering at a given angle , the

quantity  is independent of 

 is determined only by  and is independent of 

h h

h

e

4 The kinetic energy of the recoil electron:

) cos 1

( 1

) cos 1

( 2

2 '

c m

h h

h h

E

e

e e

2

2

2 1

2

c m h

c m

h h

2

2 2

m E

e e e

e e

m c

E P

2 2

 The threshold energy :

MeV c

Pair production

A Photon produces an electron (e - ) and a positron (e + ) near the nucleus, and total kinetic energy of both

electrons is :

Ee - + Ee +

= h ν -2 m 0 c 2

Pair production

Positron combines with an electron nearby, after losing kinetic energy, then the electron and positron pair annihilates and emits two photons ( annihilation

This process is called positron annihilation.

17

Độ quan trọng t ơng đối của ba hiệu ứng phụ thuộc vào năng l ợng

và điện tích Z của chất hấp thụ

Z

1/ Hiệu ứng quang điện trong chì 2/ Hiệu ứng Compton trong chì.3/.Hiệu ứng tạo cặp trong chì.4/ Hệ số suy giảm toàn phần đối với chì 5/ Hệ số suy giảm toàn phần đối với thiếc 6/Hệ số suy giảm toàn phần đối với đồng 7/.đối với nhôm

The total cross section

 = phot + Com + pair

  phot  Z 5 / E7/2 ( E ) is the cross section for the photoeffect.

  Com  Z/ E is the compton effect cross section

  pair  Z 2 ln 2E is the cross section for pair formation.

17

Energy distribution of secondary electrons

Energy distribution of secondary electrons

C) Pair production

E+E = h -2 m 0 c 2,  m0c 2 = 511 keV

D) Positron Annihilation

FEA = h

SPE = h-511 keV DPE = h-1022 keV

Energy distribution of

SPE DPE

Ionization is the main cause of energy loss as a heavy charged particle passes through matter In this mechanism, the kinetic energy of the particle is spent in exciting and ionizing the atoms of the substance through which it passes In order to determine the factors on which ionization losses depend and to find the ionization range of the particle over which it loses all its energy, let us first consider the basic pattern of interaction of the charged particle with one electron and then sum the effect for all electrons with which the particle interacts.

Bohr's Formula for Specific Ionization Relativistic Effects and

the Density Effect

Stopping power

1/ The effect for one electron

e z n TVn

dT

e

e e

e z

n dx

4 )

(

Calculation of min & max

It is well known that the maximum energy that a heavy particle moving with a velocity v<< c can impart to a

2 2

min 2

4 2

v m ze

v

m v

m

e z T

e class

e e





However, it can be shown

that the integration limits are

not 0 and  but have some

finite values min and max

Consequently

 

 max

4 2

e z n d

dx

dT dx

dT

e e

The total specific loss is obtained by integrating over all the possible values of the impact parameter 

(from 0 to )

Difficulties are encountered for  = 0, since  is

in the denominator of the expression (5), and for = since the integral is divergent.

The condition for max is obtained from classical considerations by taking into

account the fact that electrons are bound in the atom For large values of the impact parameter , the transmitted energy T becomes comparable with the binding energy

of electrons in the atom Electrons can no longer be treated as free, and for quite

large  the transmitted energy may not be sufficient to excite the atom.Consequently,

max must be associated with the average ionization potential of the atom Finally, to calculate ln(max/min), we must take into account the relativistic effects.

Tmax = 2mev 2 /(1 -  2 ) Exact calculations lead to the following formula for specific ionization losses :

m

e z

n dx

e

e ion

2 ln 4

The condition for max 

e z

n dx

e

e ion

2 ln 4

where I is the average ionization potential of the absorber

atoms, and U are terms taking into account the density effect and the fact that K and L- electrons are bound

The main result following from formula 

 v n

z dx

Formula (9) shows that with increasing particle energy, the specific ionization losses first decrease very rapidly (ininverse proportion to energy), but the decrease becomes slower as the particle velocity approaches the velocity of light At a certain value of energy, the specific energy loss on ionization attains its lowest value This

means that the denominator in formula (9) contains a nearly

constant quantity v 2  c 2 However, an examination of terms in the brackets shows that starting from a certain quite high particle

energy, the magnitude of dT/dx again starts increasing slowly

(logarithmically) and reaches a certain plateau.The suppression of the logarithmic growth of dT/dx is associated with the polarization

of atoms near the particle trajectory, which leads to a decrease in the electromagnetic field acting on remote electrons This effect is proportional to the density of the substance (more exactly, to the density of electrons) and is therefore called the density effect.

2 2

2

2 2

4 )

(

1 1 8 / 1 1

1 1

2 2

ln 1

2 ln

2

I

T v m v

m

n

e dx

e e e

ton e

where Te is the relativistic kinetic energy of an electron, ne is the electron density in the medium, is the correction for the density effect.

Ionization and Excitation of α&β-rays)

Hạt tích điện mất năng l ợng trong vật chất

thông qua các quá trình iôn hoá và kích thích , tạo thành

nhiều êlectrôn và iôn (trong chất khí ) hoặc lỗ trống

( trong chất rắn) Năng l ợng trung bình tạo cặp êlectrôn

iôn trong chất khí bằng 305 eV, trong bán dẫn ~3eV

Êlectron δ có động năng đủ để iôn hoá các

nguyên tử khác Iôn âm sẽ đ ợc tạo thành nếu

êlectrôn bị một nguyên tử trung hoà chiếm bắt

Mức năng l ợng của êlectrôn để giải thích

Iôn hoá kích thích

β-ray

Electron

Sự phóng đại hình bên trái

Tính chất hấp thụ và quãng chạy của hạt 

Absorption characteristics and range of α-rays

Quỹ đạo của hạt  là một đ ờng thẳng vì hạt  nặng hơn êlectrôn ~7000 lần Số cặp iôn dọc theo quỹ đạo tăng lên khi tốc độ của hạt α giảm ,nh đ ờng cong Bragg chỉ ra Quãng chạyR của hạt α trong không khí có thể đ ợc tính một cách gần đúng bằng biểu thức: R = 0,318E3/2

Ví dụ : E=5.3 MeV  R=3.85cm Trong Si, R=25~50 μm m với E=5~8 MeV

quãng chạy R

Quỹ đạo của hạt  trong không khí

Quỹ đạo của hạt  trong không khí

Quãng chạy ngoại suy chiều dày hấp thụ

Stopping power for α-rays (calculated)

Kh¶ n¨ng h·m :- dE/dX (increasing ratio of the electron binding to the Stopping power )

Energy loss per unit path length in material

Ranges of charged particles in Silicon

Qu·ng ch¹y R : R=aE b ( Range )

Path length where charged particle loses the full energy and stops

Các tia β giảm theo hàm mũ khi chiều dày chất hấp thụ tăng.

Hệ số hấp thụ (μm ) và quãng chạy cực đaị R( mg/cm 2 ) đ ợc tính một cách gần đúng bằng các ph ơng trình sau:

A/A0= exp(-μm d ) μm =0,017E-1,43

R=542E-133 ( E > 0,8 MeV)

R = 407E1,38 (0,15 MeV <E < 0,8 MeV)

Quá trình mất năng l ợng của các tia là q/t

va chạm với các êlectrôn quỹ đạo cùng khối

l ợngvà tán xạ(Bremsstrahlung) ở gần hạt

nhân Do đó h ớng của tia β thay đổi sau mỗi

lần t ơng tác và quỹ đạo của các tia  trở

thành l ợn sóng một cách phức tạp

Quãng chạy R

Quỹ đạo của hạt β

Dependence of ionization Losses on the

Medium

Let us suppose that two particles with the same charge (say, a proton and

a deuteron) move in the same medium (ne = const).

*In this case, the value of dT/dx will be the same for both particles in the regions of equal

p

dx

dT dx

T T

p T

T

d

dx

dT dx

Similarly, we can calculate the value of dT/dx for particles

with other values of z (z  1).

In this case, we must remember that a particle with z  1 has z 2 times higher value of dT/dx than a particle with z = 1 moving at the same velocity.

o

p T

dT dx

It is well known that the electron number density ne in a medium

is equal to nnucZ, where Z is the charge of the nuclei constituting

the medium and nnuc is their number density.

However, nnuc const for all media, and therefore we must introduce for recalculations the factor Z2/Z1, where Z1 and Z2 are

the nuclear charges for the first and the second medium

respectively

The ionization losses for a particle moving in lead will be 14 times higher than the ionization losses for the same particle if it were to move in carbon

Thus, dT/dx varies strongly as

we go over from one medium

to another.

Hence we sometimes use the term specific ionization losses dT/d, which is calculated not per unit length x (in cm), but per unit "density" , expressing the thickness in g/cm 2

Obviously,  = x, where  is the

density of the medium This gives

dx dx

dT d

dT

  Z  dT/dx  Z,  (dT/dx) (1/)  const.

Thus, the quantity dT/d is practically constant for all media and is therefore moreconvenient that dT/dx for quick rough calculations

(dT/d)airMeV/(g.cm -2 )

(dT/d)Pb MeV/(g.cm -2 )

Table 1

The rapid deceleration of a charged

particle in the electric field of the

atomic nucleus and atomic electrons

results in radiation losses)

(bremsstrahlung)

The loss of energy (dT/dx)rad by radiation is

proportional to the square of acceleration

Bremsstrahlung

 dT / dx rad  zconst  1 / m2

A well-known example of radiation losses

continuous X-ray spectrum which is created when electrons are stopped by the

anticathode in the X-ray tube.

X-Ray tube

The energy dependence of

this spectrum is given by the

law

N(v)  1/v

The intensity of radiation

has a maximum in the direction

perpendicular to the

direction

of motion of electrons

16 2 e2

e rad

r

Z nT dx

where n is the number density

of atoms, Z is the nuclear charge, re = e2/mec2

and Te<<mec2 (nonrelativistic case);

(3)

2 2

c m

T n

r

Z nT dx

dT

e

e

e e

2 2

Z n

r

Z nT dx

e rad

 where Te >> 137mec2Z-1/3 (complete screening)

(4)

(5)

Z dx

Comparing formula (6) with formula for ionization

losses of electrons written in the simplified form

nZ dx

Z T dx

dT dx

dT

e ion

dx dT dx

dT

e ion

e rad

This means that the radiation losses in water (Z=8)

become comparable with ionization losses at T e 

100MeV

Such a situation arises in lead at T e 10MeV

The energy at which radiation losses become comparable with ionization losses is called the critical energy

The radiation length for water (and air), aluminium and lead is approximately equal to 36, 24 and 6g/cm2

respectively)

The distance x o at which the mean electron

energy is reduced to 1/e of its value on account

of radiation losses is called the radiation length.

In 1934 P.A Cherenkov,

a post graduate student of Acad S I Vavilov investigated the luminescence of uranyl salts under the action of -rays from radium and discovered a new type of luminescence which could

not be explained by the ordinary fluorescence mechanism

The polarization of the luminescence changes sharply when a magneticfield is applied This means that the luminescence is caused by charged particles rather than by -quanta In Cherenkov's experiment, these particles could

be electrons produced by the interation of

-quanta with the medium due to the photoelectric effect or the Compton effect

The intensity of the radiation is independent of the charge

Z of the medium; hence it cannot be of radiative origin

3/ The radiation is at a certain angle to the direction of motion of charged particles

*The Cherenkov radiation was explained in 1937 by Frank and Tamm on the basic of classical electrodynamics.They observed that the statement of classical electrodynamics concerning the impossibility of energy loss by radiation for

a charged particle moving uniformly and rectilinearly in vacuum is no longer valid if we go over from vacuum to a

medium with a refractive index n>1.

* The conclusion drawn by Frank and Tamm can be illustrated with the help of the following arguments based on the laws of conservation of energy and

momentum

* Suppose that a charged particle uniformly moving in

a straight line can lose energy and momentum through radiation In this case, the following equality must be

satisfied:

rad part dp

dE dp