Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1)...
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![Page 1: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/1.jpg)
Compton Scattering
Reporter: Hui He
![Page 2: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/2.jpg)
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
![Page 3: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/3.jpg)
Theory
• Conservation of momentum and energy:•
22 1
1 1 1(1 cos )
eE E m c
![Page 4: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/4.jpg)
• 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
![Page 5: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/5.jpg)
Experimental setup
![Page 6: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/6.jpg)
Experimental Results
• 1. Calibration• basic fitting of Energy vs Channel
![Page 7: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/7.jpg)
• 2. Angular Distribution of the 137Cs Source
![Page 8: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/8.jpg)
• 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
![Page 9: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/9.jpg)
• 3. the Total Cross Section for Compton Scattering
![Page 10: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/10.jpg)
• 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
![Page 11: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/11.jpg)
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
![Page 12: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/12.jpg)
• 4. the Energy of the Scattered Photon
![Page 13: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/13.jpg)
• 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
![Page 14: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/14.jpg)
• 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
![Page 15: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/15.jpg)
• 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
![Page 16: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/16.jpg)
• (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
![Page 17: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/17.jpg)
• 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
![Page 18: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/18.jpg)
• In theory:
2 2 220
2
1 (1 cos )(1 cos )
2 (1 (1 cos )) 1 (1 cos )
rd
d
![Page 19: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/19.jpg)
![Page 20: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/20.jpg)
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
![Page 21: Compton Scattering Reporter: Hui He. Outline Theory Experimental setup Experimental results (1) Calibration (2) Angular Distribution of the 137 Cs Source.](https://reader037.fdocuments.us/reader037/viewer/2022110323/56649d7d5503460f94a602ac/html5/thumbnails/21.jpg)
• Thank you !