Protokoll_Compton

8/6/2019 Protokoll_Compton

1/25

JLU Gieen SS 2011

Fortgeschrittenenpraktikum Part II

R e p o r t : C o m p t o n s c a t t e r i n g

Daniel Schury

[email protected]

Benjamin Vollmann

[email protected]

22nd of March, 2011

Supervisor

Yutie Liang


2/25


3/25

SS 2011 Compton scattering 22/03/2011

1 A s s i g n m e n t o f t a s k s

Compton scattering describes the process, in which a photon hits a quasi-free electron and

scatters. In this experiment we use a plasctic szintillator as a scattering target and a NaI sz-

intillator as a detector. The photon sources are radioactive caesium and sodium. The goal

of the experiment is to measure the Compton Wavelength of backscattered photons, the con-

nection of scattered photon energy and the scattering angle and as a result to determine the

electron mass as well as to compare between the calculated cross section and the measured

cross section at different angles.

Figure 1.1: Experimental setup

3


4/25


2 F u n d a m e n t a l s

2 . 1 S o r t s o f n u c l e a r r a d i a t i o n

Nuclear radiation mainly consists of three different types of radiation: -, - and -rays.

-rays are nothing more than a two times positive charged helium nucleus. Their energy dis-

tribution is a line spectrum and their penetration is quite short. -rays are electrons/positrons

with a continuous energy distribution and a much deeper penetration than -rays. Last but not

least -rays consist of photons with an energy of 250 keV up to 10 MeV and more. Because

we only use -rays in this experiment, we will only talk about them in detail.

2 . 2

- r a y s

-rays are electromagnetic waves with a photon energy between 250 keV and more than 10

MeV. They originate from the interaction of the nucleus with electromagnetic fields. Almost

all radioactive elements decay under -ray-emission. The nucleus often stays after the decay

of- or -radiation in an excited state. From there he calms down to its initial state or to a

state of a lower energy level while emitting the spare energy as a photon.

AZXAZ X +

For this reason the energy distribution of -rays is discrete, because the distribution of the

different energy states is not continuous but discrete, too.

2 . 2 . 1 T e r m s c h e m e o f

1 3 7

C s a n d

2 2

N a

Our -ray sources are 137Cs and 22Na, at which 22Na is just used to gauge the szintillation

detector. Both Term schemes are showed in figure 2.1.137Cs decays with a probability of 95% through a -decay into a stimulated state of 137Ba,

from which it relaxes to a stable state of 137Ba by emitting -rays of 662 keV. With a small

probability of 5 % 137Cs decays direcly into the stable state of 137Ba.22Na decays through a +-decay into a stimulated state of 22Ne, from which it relaxes to a

stable state of 22Ne by emitting -rays of 1,275 MeV. Beside the 1,275 MeV peak you will

also find a peak at 511 keV, wich is a result of the +-decay: The produced positron anhillates

with the electron by emitting two gamma-rays of their rest masses.

4


5/25


(a) Caesium (b) Sodium

Figure 2.1: Term scheme of 137Cs and 22Na

2 . 3 I n t e r a c t i o n s b e t w e e e n

- r a y s a n d m a t t e r

In general we have three possible interactions between -rays and matter: The photoelectric

effect, compton scattering and pair production. Figure 2.2 shows at which energy scale which

phenomena is dominant.

Figure 2.2: Total cross section = ++

5


6/25


2 . 3 . 1 T h e P h o t o e l e c t r i c e e c t

The photoelectric effect dominates when low-energy photons, with an energy from a few

electronvolts up to low numbers of keV, interact with matter. In the photoelectric effect thewhole energy of the photons is absorbed by the matter. As a consequence of the absorbtion

electrons get kicked off the electron shell. The kinetic energy of the electrons is given by the

energy of the incoming photon subtracted by the energy that is needed to set the electron free:

Ekin = hW

2 . 3 . 2 P a i r p r o d u c t i o n

Pair production can take place in case of high energies. If you have an amount of energy that

is at least equivalent to the double of the rest mass of an electron (511 keV) it is possible to

produce an electron positron pair. The production must take place in the close enviroment of

a nucleus, otherwise it is not possible to fulfill the conservation of momentum and energy.

2 . 3 . 3 C o m p t o n s c a t t e r i n g

Compton scattering is the dominating phenomena in the mid-energy sector. It describes the

scattering of a photon at a nearly disengaged electron. In this case nearly disengaged means,

that the bond energy of the electron is small in comparison to the energy of the incoming

photon. The phenomena can be solved through a conventional ansatz describing a collision

between two bodies. The incoming photon has the energy E = h and the momentum p =

hc , the static electron the energy Ee = mec2 = 511keV and the momentum pe = 0. Afterthe collision the at an angle of vartheta scattered photon has the energy E = h

and the

momentum p=h

c. The electron gains kinetic energy by the collision whereby it achieves the

energy Ee =

m2e c4 + p2e c

2 as well as the momentum pe. The principle of linear momentum

Figure 2.3: Compton scattering

provides

p = p

+pe or rather pp

= pe (2.1)

6


7/25


If you square this equation you get:

p2e = p2+ p

22pp

cos (2.2)

From the conservation of energy you get:

E+Ee = E

+E

e or rather h+ mec2 = h +

p2e c

2 + m2ec4 (2.3)

Or:

p2e =

h

c

2+

h

c

22

h

c

h

c+

2mec2

c2(hh) (2.4)

You can now equalize 2.4 and 2.2 and after some additional transformations you get the energy

of the scattered photon:

h =h

1 + hmec

2 (1 cos)(2.5)

For the inverse energy shift you find

1

E=

1

h

1

h=

1

mec2(1 cos) (2.6)

or rather for the modificated wavelength of the scattered photon with = c

= + hm0c(1 cos) (2.7)

or

= C(1 cos) (2.8)

Where C =h

m0cis the Compton wavelength.

K l e i n - N i s h i n a f o r m u l a

The Klein-Nishina formula gives the probability in which direction the photon gets scattered.

It is more precisely the differential cross section of one photon, that gets completly elasticscattered at a free, single electron:

d

d= Zr0

1

1 +(1 cos)

21 + cos2

2

1 +

2(1 cos2)

(1 + cos2)[1 +(1 cos)]

Here is = hmec

2 and r0 the classical electron radius 2,818 1015m. You can see the distribu-

tion in figure 2.4. It is obvious that forward scattering is preferred at high energies as we have

in our experiment.

7


8/25


Figure 2.4: Klein-Nishina formula

2 . 3 . 4 T h e c h a r a c t e r i s t i c

- r a y s p e c t r u m

Figure 2.5 shows a typical -spectrum, which results of the three interactions that have been

discussed previous.

The photopeak is the result of the photoelectric effect that was described in 2.3.1: It occurs

when the scattered photon activates an electron in the szintillator which relaxes later by emit-

ting another photon. It is mportant that the whole amount of energy of the incoming photon is

transferred. It is the phenomena were looking for in our evaluation.

The Compton edge is the result of equation 2.5: If the photon is scattered at an angle of 180

it transferres the maximum energy amount unto the electron:

Ee,kin = EE = EE

1 +E

mec2 (1 cos)

(2.9)

with = 180:

Ee,kinmax =2E2

mec2 + 2E(2.10)

In the spectrum you see a continuum from 0 unto the Compton edge. In our experiment the

scattering takes place in the plastic szinitillator.

The escape peak is connected to the discussed pair production: If the generated electron

positron pair annihilates, two photons with the energy of 511 keV will occur.

2 . 4 F u n c t i o n a l i t y o f a s z i n t i l l a t i o n d e t e c t o r

In the experiment a szintillation detector is used for the detection of the photons. The radiation

strikes the szintillator crystal, in our case NaI, which is doped with Thallium. In account of

8


9/25


Figure 2.5: A typical -spectrum with photopeak, Compton edge and Escape peak

this electrons are lifted from the valence band into the conduction band, where they can freely

move until they hit a defect. Now they fall down to the energy level of the defect, which is

located in the valence-conduction band gap, and emitt photons of the energy between the va-

lence band and the energy level of the defect. Therefore the photons have a wavelength withinthe visible window and can be detected with a common photomultiplier. The photomultiplier

Figure 2.6: Sketch of the szintillation detector with photomultiplier

transforms the optical signal into an electrical signal: The incoming photons hit the photo-

cathode of the photomultiplier and strike out electrons through the photoelectric effect. Now

the electrons are accelerated by voltage to the first dynode, where every electron strikes out

9


10/25


several other electrons. These electrons are again accelerated to the next dynode, where again

every electron strikes out several secondary electrons. This incident is repeated a few times

until the original signal is amplified by the factor of 105

108

.

Figure 2.7: Band structure

10


11/25


3 E x p e r i m e n t a l s e t u p a n d a c c o m p l i s h m e n t

3 . 1 E x p e r i m e n t a l s e t u p

The Compton scattering gets analyzed with the help of a NaI szintillator and a plastic szin-

tillator. As -sources 137Cs and 22Na were used, in which 22Na was just needed to gauge

the NaI szintillator. The emitted photons strike the plastic szintillator, which has the function

of an active scattering medium. The scattered photons are detected with the NaI szintillator.

Figure 3.1: Scheme of the scattering process

This experimental setup enables us to measure the energy of the photons after the collision in

dependence of the scattering angle, as well as the calculation of the energy of the electrons

on which the photons were scattered, because the electrons depose their energy in the plas-

tic szintillator. We only measure the events when both detectors produce a signal in a short

time window with the help of an coincidence circuit, on which we focus in the next section.Thereby we admit to measure random events that would degrade our result. Because of the

fact that the plastic detector is much faster than the NaI detector, we have to delay the signal of

the plastic detector. This is realised through long cabels. The delay times are shown in figure

3.2.

11


12/25


3 . 2 S i g n a l p r o c e s s i n g

A already said we used a coincidence circuit to dispose just the events that were detected in

both detectors at almost the same time. The circuit shown in figure 3.2 consists of different

electric components that make sure that the evaluation software records just true signals and

no other random events. In the following e take a closer look upon some electric components:

Figure 3.2: Coincidence circuit

3 . 2 . 1 C o n s t a n t F r a c t i o n D i s c r i m i n a t o r ( C F D )

With the help of a constant fraction discriminator a digital signal is created out of an analog

signal. In general this is realized by displaying a digital signal if the analog signal oversteps

a given barrier. It can be realised on different ways (see figure 3.3): The CFD is a relatively

complex method, but it transformes the signal very exact. The less complex leading edge

discriminator only displays a signal if the analog signal oversteps a given barrier. It is prob-

lematic that in case of signals with different amplitudes the outgoing signals are created at

different times. To prevent this problem called walk, the CFD delays the incoming signal

by a adjustable time and mute and invert it at the same. The sum of these two signals have a

zero crossing, which marks the barrier.

12


13/25


Figure 3.3: Left: Leading Edge; Right: Constant Fraction

3 . 2 . 2 A N D / O R l o g i c

The AND logic lets the signal only pass if it gets a signal from both of the two inputs. The

module can also be changed to an OR logic, then it lets the signal pass if there is at least a

signal at one input.

3 . 2 . 3 T i m e t o D i g i t a l C o n v e r t e r ( T D C )

This module transforms a period of time into a binary number. It gets started by a signal and

stops by another signal. The TDC is quite important for this experiment, because it measures

the delay between the plastic szintillator and the NaI szintillator.

3 . 2 . 4 C h a r g e t o d i g i t a l c o n v e r t e r ( Q D C )

A charge to digital converter measures the charge at the income by integrating the voltage over

a given time. Subsequent the charge is displayed in a binary signal and can be processed by a

PC.

3 . 2 . 5 G a t e g e n e r a t o r

The gate generator creates an outgoing signal of a constant duration for every incoming signal,

independent of the length of the signal. The length of the outgoing signal can be chosen by

the experimentator.

3 . 3 A c c o m p l i s h m e n t

In the beginning we checked the coincidence circuit for about an hour before we calibrated the

NaI detector by relating the energy of characteristic points of the emitted -rays of the 137Cs

and 22Na sources to the channel numbers where they appeared. This is possible, because the

13


14/25


relation between channel number and energy is linear.

After this we measured the photopeak of the scattered photons in the NaI detector at several

angles from 40

up to 180

. Out of this peaks we were able to calculate the wavelength orrather the energy of the scattered photons.

14


15/25


4 E v a l u a t i o n

4 . 1 E n e r g y g a u g i n g

Channel Energy [keV]

Cs 412,6 662

Na 352,6 511

Pedestal 108,6 0

Table 4.1: Data for the linear gauging fit

The purpose of this part of the evaluation is

to create a correlation between the measured

channel numbers and the photon energy. We

use the photopeaks of 137Cs and 22Na with

known energies and the pedestal, the peak

the QDC creates when there is no incomingsignal, so that we have three points which

we can use for a linear fit. This measure-

ment was created without the coincidence

coupling to speed the counting up but with-

out affecting the result. With the data points

aside we were able to create a linear fit to

convert the measured channel into an energy.

Events

0

10

20

30

40

50

60

70

0

10

20

30

40

50

60

70

Channel100 200 300 400 500 600

100 200 300 400 500 600

Function: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc)/w)^2)Chi^2/doF= 3,4304343330725e+01R^2= 0,89996A = 9,563e+03 +/- 1,649e+03w = 101,625 +/- 8,203xc= 412,583 +/- 7,309y0= -17,227 +/- 7,402

(a) Caesium gauging fit

Events

0

20

40

60

80

0

20

40

60

80

Channel0 500 1.000

0 500 1.000

Fnct.: y0+A*exp(-(x-xc)^2/(2*w^2))

Chi^2/doF = 1,6481882105444e+00

R^2= 0,8311152229674

A = 1,401e+01 +/- 6,143e-01

w = -3,758e+00 +/- 0,193e+00

xc= 108,854e+00 +/- 0,1887e+00

y0= 2,517e-01 +/- 1,122e-01

Fnct.: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc)/w)^2)

Chi^2/doF = 19,471

R^2= 0,105

A =161,869 +/- 87,057

w = 30,611 +/- 12,955

xc= 352,629 +/- 2,024

y0= 16,676 +/- 0,960

(b) Sodium gauging fit

Figure 4.1: Fits of the gauging measurements for caesium and sodium

15


16/25


Energy[keV]

-100

0

100

200

300

400

500

600

700

-100

0

100

200

300

400

500

600

700

Channel100 150 200 250 300 350 400 450

Energy [keV]-20,68 87,07 194,8 302,6 410,3 518,1 625,8 733,6

Function: A*x+BChi^2/doF = 2,1603165834254e+02R^2 = 0,9991025678652B = -236,180 +/- 20,624A = 2,155 +/- 0,065

Figure 4.2: Linear gauging fit

As you can see, the formula we get is y = (2,155 0,065) x (236,18 20,624), where [4.1]y corresponds to the energy in keV and x corresponds to the channel number.

4 . 2 B a c k s c a t t e r i n g

Eve

nts

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Channel150 200 250 300 350 400 450 500

Energy [keV]87,07 194,8 302,6 410,3 518,1 625,8 733,6 841,3

Function: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc) /w)^2)

Chi^2/doF = 2,0578263771721e+01

R^2 = 0,9045280280017

A = 1717,028 +/- 68,561

w = 34,554 +/- 1,230

xc = 198,113+/- 0,505

y0 = 1,961 +/- 0,582

Figure 4.3: Backscattering fit

In this part we want to determine the value

of the Compton wavelength of an elec-

tron. Therefor we measure the energy of the

backscattered photons, which have by for-

mula 2.5 at an angle of 180 a wavelength

of

Compton =1

2

(hc

E

hc

E

)

E is caesiums known photopeak energy of

662 keV and E was determined by the fit

aside. We find E at channel 198,113

0,505 or an energy of (190,753 1,088) keV.

With this we find the Compton wavelength

Compton as Compton = (2,323 0,019) 1012m. The literature value is 2,426

16


17/25


1012m. So our measured value varies with an error of 5% around the literature value, which

is quite a good result, even not as good as expected.

4 . 3 C o m p t o n s c a t t e r i n g a s a f u n c t i o n o f t h e s c a t t e r i n g a n g l e

For the following parts we need the energy of the scattered photons for the angles 40, 60,

80, 100, 120, 140, 160 and 180. We get them by fitting with a Gaussian distribution.

Events

0

5

10

15

20

25

30

35

40

0

5

10

15

20

25

30

35

40

Channel200 300 400 500

Energy [keV]194,8 410,3 625,8 841,3

Function: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc)/w)^2)Chi^2/doF = 1,3229456620261e+01R^2 = 0,8421200932028A = 2275,429 +/- 129,295

w = 77,994 +/- 3,347xc = 313,007 +/- 1,095y0 = 3,217 +/- 0,601

(a) 40

Events

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Channel200 300 400 500

Energy [keV]194,8 410,3 625,8 841,3

Function: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc)/w)^2)

Chi^2/doF = 1,8236940780592e+01

R^2 = 0,8942367586406

A = 2628,873 +/- 113,887

w = 60,356 +/- 2,073

xc = 295,188 +/- 0,717y0 = 7,195 +/- 0,634

(b) 60

Events

0

10

20

30

40

50

0

10

20

30

40

50

Channel150 200 250 300 350 400 450 500

Energy [keV]87,07 194,8 302,6 410,3 518,1 625,8 733,6 841,3


Chi^2/doF = 2,11347629028e+01

R^2 = 0,8756205973248

A = -2095,734 +/- 126,879

w = -48,828 +/- 2,198

xc = 263,714 +/- 0,709

y0 = 4,569 +/- 0,929

(c) 80

Events

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Channel150 200 250 300 350 400 450 500

Energy [keV]87,07 194,8 302,6 410,3 518,1 625,8 733,6 841,3


Chi^2/doF = 2,3830338747302e+01

R^2 = 0,8469385666978

A = 1785,921 +/- 169,254

w = 42,940 +/- 2,763

xc = 236,153 +/- 0,758

y0 = 3,256 +/- 1,515

(d) 100

Figure 4.4: Energy distribution at 40 to 100

From the fits we get the following data 4.2, which we need for further analysis. The energy is

17


18/25


Events

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Channel150 200 250 300 350 400 450 500

Energy [keV]87,07 194,8 302,6 410,3 518,1 625,8 733,6 841,3

Fnct.: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc)/w)^2)Chi^2/doF = 3,0876648105300e+01

R^2 = 0,8505878466118

A = 1685,462 +/- 229,107

w = 33,550 +/- 2,844

xc = 216,331 +/- 0,646

y0 = 3,874 +/- 2,743

(a) 120

Events

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Channel150 200 250 300 350 400 450 500

Energy [keV]87,07 194,8 302,6 410,3 518,1 625,8 733,6 841,3

Fnct.: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc)/w)^2)Chi^2/doF = 2,8873304522893e+01

R^2 = 0,8614973555779

A = 1337,503 +/- 130,925

w = 28,274 +/- 1,997

xc = 207,009 +/- 0,569

y0 = 10,015 +/- 1,675

(b) 140

Events

0

10

20

30

40

50

60

70

0

10

20

30

40

50

60

70

Channel150 200 250 300 350 400 450 500

Energy [keV]87,07 194,8 302,6 410,3 518,1 625,8 733,6 841,3

Fnct.: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc)/w)^2)

Chi^2/doF = 3,6728741089272e+01

R^2 = 0,8656525675626

A = 1409,298 +/- 163,951

w = 25,522 +/- 2,001

xc = 202,480 +/- 0,540

y0 = 8,938 +/- 2,472

(c) 160

Events

0

10

20

30

40

50

60

0

10

20

30

40

50

60

Channel150 200 250 300 350 400 450 500

Energy [keV]87,07 194,8 302,6 410,3 518,1 625,8 733,6 841,3


Chi^2/doF = 2,0578263771721e+01

R^2 = 0,9045280280017

A = 1717,028 +/- 68,561

w = 34,554 +/- 1,230

xc = 198,113+/- 0,505

y0 = 1,961 +/- 0,582

(d) 180

Figure 4.5: Energy distribution at 120 to 180

given by the channel number xc, which can be converted into an energy with formula 4.1. 1E

is given by 1E = 1E 1E.

18


19/25


angle 40 60 80 100 120 140 160 180

energy [keV] 438,35 399,95 332,12 272,73 230,01 209,92 200,16 190,75

1

E[ 1

keV] 0,771 0,990 1,500 2,156 2,837 3,25 3,485 3,732

Table 4.2: Data for the different angles

4 . 3 . 1 C o n n e c t i o n b e t w e e n t h e s c a t t e r e d p h o t o n e n e r g y a n d t h e s c a t t e r i n g a n g l e

We can now plot the scattered photon energy against the scattering angle and compare it with

formula 2.5.

Energy[keV]

150

200

250

300

350

400

450

500

550

150

200

250

300

350

400

450

500

550

Angle []20 40 60 80 100 120 140 160 180 200

20 40 60 80 100 120 140 160 180 200

Function: 662/(1+a*(1-cos(2*PI*x/360)))

Chi^2/doF = 7,6991025063412e+02

R^2 = 0,9155748338549

a = 1,2993618236982e+00 +/- 8,7768235068872e-02

Figure 4.6: Plot of the scattered photon energy against the scattering angle

As we can see, the measured data fits quite well with the theory. The fit parameter a has avalue of 1,29930,0878, whereas the theoretical value would be 1,2955.

4 . 3 . 2 P l o t o f

1E

a g a i n s t 1 cos

In this part we want to analyse the connection between 1E

and 1 cos, which should in

accordance with formula 2.6 be linear.

19


20/25


1/E[eV-1]

0,5

1

1,5

2

2,5

3

3,5

4

0,5

1

1,5

2

2,5

3

3,5

4

1-cos0 0,5 1 1,5 2 2,5

0 0,5 1 1,5 2 2,5

Function: A*x+B

Chi^2/doF = 1,1073645724695e-02R^2 = 0,9928961828059

A = 1,718 +/- 0,059

B = 0,206 +/- 0,083

Figure 4.7: Plot of 1E

against 1 cos

As we can see, the correlation between the measured data and the fitted line is very good.

We can now calculate the electron mass using the draft of the fitted plot. Referring to formula

2.6 1E

is proportional to 1cosm0c

2 . If we take the inverse of the draft, we get the electron mass:

me =1

1,7180,059 0,5820,021 =(58221) keV.

The theoretical value of the energy mass is 511 keV, so we miss the literature value with an

error of about 12%.

20


21/25


4 . 3 . 3 C r o s s s e c t i o n

angle [] 40 60 80 100 120 140 160 180

const 26,495 41,948 38,815 36,497 43,958 47,759 52,996 47,609

77,984 60,356 48,828 42,940 33,550 28,274 25,522 34,554

N 524388 470996 505666 521161 492443 477645 477602 377688

constN

[103] 3,941 5,375 3,748 3,007 2,995 2,827 2,832 3,807

Table 4.3: Data for measuring the cross section

Heigth*Width/Counts

2,5

3

3,5

4

4,5

5

5,5

2,5

3

3,5

4

4,5

5

5,5

Angle []20 40 60 80 100 120 140 160 180 200

20 40 60 80 100 120 140 160 180 200

Figure 4.8: Comparison between measured

and calculated cross section

In the end we want to see if the calcu-

lated cross section fits the theoretical values.

The theoretical cross section, as given in for-

mula 2.9, should be proportional to constN

,

whereas is given by the fits, const is the

heigth of the Gaussian distribution, which

can be calculated as the difference between

the value of the Gaussian distribution at xcand the offset y0 and N is the number of

total events that occured. Now we can plot

the data against the angle. If we compare it

with the theoretical Klein-Nishina-formula,

we see that all except the points for 60 and

180 fit quite well. For better results the

measurment time had has to been increased,

so that more statistical data could have been

raised.

21


22/25


4 . 4 E n e r g y g a u g i n g a f t e r t h e m e a s u r e m e n t

After we took all our measurements, we gathered a second gauging measurement with cae-

sium to see, if the correlation between the channel number and the energy was still unchanged.

Changes can happen because of changes for example in the room temperature, which is not

very unlikely, if you work for a few hours in a closed room. In the beginning of our mea-

Events

0

20

40

60

80

100

0

20

40

60

80

100

Channel200 400 600

100 200 300 400 500 600

Function: y0+A*sqrt(2/PI)/w*exp(-2*((x-xc)/w)^2)Chi^2/doF = 55,8598R^2 = 0,8089

A = -3765,792 +/- 284,594w = -68,209 +/- 3,684xc = 407,224 +/- 1,055y0 = 13,506 +/- 1,523

Figure 4.9: Second gauging fit

surement the caesium peak was at channel 412 7,309, after the measurement at channel

407 1,055. So we see that the calibration we made in the beginning is still valid for the

afterwards taken measurements.

22


23/25

B i b l i o g r a p h y

[1] D. Meschede: Gerthsen Physik, 23., berarbeitete Auflauge erschienen im Springer-

Verlag

[2] Ingolf V. Hertel, Claus-Peter Schulz: Atome, Molekle und optische Physik 1 - Atom-

physik und Grundlagen der Spektroskopie erschienen im Springer-Verlag

[3] Bogdan Povh, Klaus Rith, Christoph Scholz, Frank Zetsche: Teilchen und Kerne -

Eine Einfhrung in die physikalischen Konzepte, 8. Auflage erschienen im Springer-

Verlag

[4] Demtrder: Experimentalphysik 4, 3. Auflage, erschienen im Springer-Verlag

[5] H. Haken, H. C. Wolf: Atom- und Quantenphysik, 7. Auflage, erschienen im Springer-

Verlag

23


24/25

L i s t o f T a b l e s

4.1 Data for the linear gauging fit . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4.2 Data for the different angles . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4.3 Data for measuring the cross section . . . . . . . . . . . . . . . . . . . . . . 21

24


25/25

L i s t o f F i g u r e s

1.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2.1 Term scheme of137Cs and 22Na . . . . . . . . . . . . . . . . . . . . . . . . 5

2.2 Total cross section = ++ . . . . . . . . . . . . . . . . . . . . . . . . 52.3 Compton scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.4 Klein-Nishina formula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.5 A typical -spectrum with photopeak, Compton edge and Escape peak . . . . 9

2.6 Sketch of the szintillation detector with photomultiplier . . . . . . . . . . . . 9

2.7 Band structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

3.1 Scheme of the scattering process . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Coincidence circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

3.3 Leading Edge vs. Constant Fraction Discriminator . . . . . . . . . . . . . . 13

4.1 Fits of the gauging measurements for caesium and sodium . . . . . . . . . . 15

4.2 Linear gauging fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.3 Backscattering fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.4 Energy distribution at 40 to 100 . . . . . . . . . . . . . . . . . . . . . . . 17

4.5 Energy distribution at 120 to 180 . . . . . . . . . . . . . . . . . . . . . . . 18

4.6 Plot of the scattered photon energy against the scattering angle . . . . . . . . 19

4.7 Plot of 1E

against 1cos . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.8 Comparison between measured and calculated cross section . . . . . . . . . . 21

4.9 Second gauging fit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

25

Date post:	07-Apr-2018
Category:	Documents
Upload:	daniel
View:	217 times
Download:	0 times

Protokoll_Compton

Documents