Compton Scattering

Reporter: Hui He

Outline

• Theory• Experimental setup• Experimental results• (1) Calibration• (2) Angular Distribution of the 137Cs Source• (3) Total Cross Section• (4) the Energy of the Scattered Photon• (5) the Differential Scattering Cross Section• Conclusion

Theory

• Conservation of momentum and energy:•

22 1

1 1 1(1 cos )

eE E m c

• The quantum mechanical calculation for Compton scattering yields the Klein-Nishina formula:

• The total cross section is:

2 2 220

2

1 (1 cos )(1 cos )

2 (1 (1 cos )) 1 (1 cos )

rd

d

20 2 2

1 2(1 ) 1 1 1 32 ln(1 2 ) ln(1 2 )

1 2 2 (1 2 )

dd r

d

Experimental setup

Experimental Results

• 1. Calibration• basic fitting of Energy vs Channel

• 2. Angular Distribution of the 137Cs Source

• the distribution of the photons emitted by the source satisfy Gaussian distribution, which is highly concentrated

• the highest grossing rate lies in closer to -10 rather than 00

• 3. the Total Cross Section for Compton Scattering

• Calculation:

0

0

( )

ln ( ) ln

nxdIndx I x I e

II x I nx

( ) 0.092 5.4Ln I x

23 323 30 6.02 10 / 1.18 / 54

3.84 10 /100 /

N Z mol g cmn cm

A g mol

0.092n

25 22.40 10 cm

20 2 2

25 2

2 sin

1 2(1 ) 1 1 1 32 ln(1 2 ) ln(1 2 )

1 2 2 (1 2 )

2.57 10

comp

dd

dd

dd

r

cm

213

0 22.82 10

4 e

er cm

m c

2

6621.30

511v

e

E Kev

m c Kev

6.61%comp

comp

• 4. the Energy of the Scattered Photon

• Experimentally, we have:

3 311.73 10 (1 cos ) 1.54 10

vE

2

1 1 1(1 cos )

v evE m cE

3 22

11.73 10 578e

e

m c KeVm c

311.54 10 649v

v

E KevE

• In theory

662vE Kev

2 511em c KeV

exp 662 649( ) 100% 1.96%

662vthe v

vvthe

E EE

E

2 2exp2

2

( ) ( ) 578 511( ) 100% 13.11%

( ) 511e the e

ee the

m c m cm c

m c

• 5. the Differential Scattering Cross Section• To get the right value of differential scattering cross

section, two corrections should be made here.• (1) the energy dependence of the efficiency of the NaI should

be considered. The linear attenuation coefficient of NaI can be expressed empirically, between 100 and 700 KeV, as

• The probability that a scattered photon of energy E will be recorded by the NaI is given by:

2.85 0.45 1( ) 5.18 0.539E E E cm

( ) 1 te

• (2) multiple Compton Scattering

• V is the volume of the scattering, • R=2.83cm, • • is the linear attenuation coefficient at the

scattered photon energy, :

2 2 2sin cos ( )y R r r

s

vE 0.365 1( ) 0.205E E cm

2

2 0 0

1( )

y ys sRHe dV re drd

V R H

• With the two corrections:( )

( )( ) ( )corr

CC

( )corr

dAC

d

( )

2 sin ( )

corr comp

comp

corr

dA C d d

d

AC d

25

272.4 102 sin ( ) 108.34 2.22 10

108.34 108.34comp

corrC d A

( )corr

dAC

d

• In theory:

2 2 220

2

1 (1 cos )(1 cos )

2 (1 (1 cos )) 1 (1 cos )

rd

d

Conclusion

• we have verified the energy dependence of gamma radiation upon scattering angle

• Also, we calculated the total cross section as well as the differential scattering cross section for Compton Scattering

• The differential scattering cross section we obtained from the experimental data is similar to the theoretical one calculated from the Klein-Nishina formula but there is still many differences because of the influence of noises and operation error

• Thank you !