phys 342 - lecture 15 notes - f12

8/11/2019 PHYS 342 - Lecture 15 Notes - F12

1/13

Lecture 15

Antimatter in the Milky Way

!! +"+ +#ee


2/13

Lecture 15

Applications in Modern Medicine

Positron Emission Tomography (PET) Scan

A medical diagnostic to study the path and location of a

position-emitting radioactive chemical that has been

injected into the human body.!! +"+

+#ee


3/13

Lecture 15

As particles, not only can photons transfer their energy to

other normalparticles, they can also transfer their

momentum during interactions, e.g., collisions.

Compton effect: in a collision a photon loses its energy to

an electron. The effect manifests itself observationally in

the increase of the wavelength of the radiation after the

collision.

Inverse Compton effect: in a collision a photon gains

energy from an electron, i.e., the wavelength of the

radiation decreases after the collision.

The Compton Effect


4/13

Lecture 15

Photon-Electron Collision

incident photon

h!0, h!0/c "

$

scattered photon

h!, h!/c

recoiling electron

Ee, pe

Assuming that the incident photons all have the same frequency

(monochromatic) and the target electrons are initially at rest in

the laboratory frame, the final products include scattered photons

and recoiling electrons, as shown.


5/13

Lecture 15

Momentum Conservation

" $p0

p

pe

Momentum conservation:

eppp!!"

+=0

!cos2 02

0

22ppppp

e "+=

c

hp

c

hp

!!== ,00

Since


6/13

Lecture 15

Energy Conservation

!

!""""

cos))((2)()(

cos2

022

022

022

02

hvhvhvhvcpc

h

c

h

c

h

c

hp

e

e

#+=

$

%

&'

(

)$

%

&'

(

)#$

%

&'

(

)+$

%

&'

(

)=

we have

Energy conservation:

200

200 )( cmhvhvEEhvcmhv ee +!="+=+


7/13

Lecture 15

Putting All Together

420

02

0022

0

4200

20

20

2

)(2))((2)()(

)(2)(

cm

hvhvcmhvhvhvhv

cmhvhvcmhvhvEe

+

!+!+=

+!+!=

420

022

042

022 cos))((2)()(

cm

hvhvhvhvcmcpe

+

!+=+ "

We have already had


8/13

Lecture 15

We Have

)cos1)()((2)(2 0020 !"

="

hvhvhvhvcm

42

0

222cmcpE ee +=

)cos1(000

0!"="=

"

cm

h

v

c

v

cc

vv

vv

)cos1(0

0 !"" #=#cm

h


9/13

Lecture 15

Compton Wavelength

Acm

hc 024.0

0

=!")cos1(0 !""" #=# c

The wavelength of photons that are scattered by 90 degrees

is increased by one Compton wavelength.

The wavelength of photons that are scattered by 180 degrees

(i.e., head-on collisions) is increased by twice the Compton

wavelength

The Compton effect does not depend on the wavelength of

the incident light, so it is more observable when the light

of shorter wavelength (e.g., X-ray or gamma ray) is used.


10/13

Lecture 15

Experimental Setup

"

$

X- or %-ray

source

target X- or %-ray counter

electron counter


11/13

Lecture 15

Experimental Data


12/13

Lecture 15

Explanation

Detection of the Compton effect in the scattered photons

and verification of the angular dependence of the

wavelength of the scattered photons

Detection of photons of original wavelength, which are

the result of incident photons being scattered elastically

by tightly bound electrons.

Detection of recoiling electrons and verification of theangular dependence of the kinetic energy of the electrons

and the correlation between the scattering angles of

electrons and photons


13/13

Lecture 15

Useful Facts

( )

!""

!"

"#

"!

222

2

20

cos)1(

cos2

,2

cot1

1tan

$+=

=%&'

()*

+

=

hvE

cm

hvwhere

K

Properties of recoiling electrons:

In certain energy ranges, in particular for medium-hard X-rays,

the Compton effect is the principle cause of scattering and

attenuation of radiation in matter.

In Compton scattering, the incident and the scattered radiation

are incoherent relative to each other.

phys 342 - lecture 15 notes - f12

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