Sadiq Thesis

Introduction

Positron

Positron is the antimatter of electron. Positrons have same mass as electron ( [math]511~\frac{keV}{c^2}[/math]), carries positive charge, and it is noted as "[math]e^+[/math]".

Positrons predicted by Paul Dirac in 1928, <ref name="Dirac1928"> The Quantum Theory of the Electron, P. A. M. Dirac, Proc. R. Soc. Lond. A February 1, 1928 117 778 610-624;</ref>, and experimentally observed by Dmitri Skobeltsyn in 1929 and by Carl D. Anderson in 1932 <ref name="e+_discover"> General Chemistry, Taylor and Francis. p. 660. </ref>. Anderson also coined the term positron and he won the Nobel Prize for Physics in 1936.

<ref name="name"> BOOK_Gernal, Auther, Month_Year,issue,page </ref>

Apparatus

HRRL Positron Beamline

HRRL beamline layout is given in the figure below, and the item descriptions are given in the table below.

HRRL beamline layout.

Item	Description
T1	Positron target
T2	Annihilation target
EnS	Energy Slit
FC1, FC2	Faraday Cups
Q1,...Q10	Quadrupoles
D1, D2	Dipoles
NaI	NaI Detecotrs
OTR	Optical Transition Radiaiton screen
YAG	Yttrium Aluminium Garnet screen

Som parameters of HRRL is given by:

Parameter	Unit	Value
maximum energy	MeV	16
peak current	mA	100
repetition rate	Hz	300
absolute energy spread	MeV	2-4
macro pulse length	ns	>50

Data Analysis

Signal extraction

For 3 MeV and on detector show all the steps

1. Raw counts target in and out (calibrated energy)
2. Normalized counts
3. background subtracted
4. Integral (zoomed in and with error)

Example of error propagation for the above

Raw counts target in and out

The ingeral shown in read is from the background is subtracted spectrum.

run in

run out

NaI Left: image with cut

NaI Right: image with cut

3735

3736

Reprate = 300 Hz

Run time = 1002 s

Pulses = 301462

Events = 9045 (Hz)

e+ rate NaI Left = 256 +- 16 (Hz).

Normalized counts

The ingeral shown in read is from the background is subtracted spectrum.

3735 and 3736

Reprate = 300 Hz

Run time = 1002 s

Pulses = 301462

Events = 9045

Total number of electrons in this run = 3.91669e+016 +- 2.25412e+015

Total charge of electrons in this run = 0.00627523 +- 0.000361151 C

e- rate = 3.90887e+013 +- 2.24963e+012 (Hz)

e- current:I_e- =6.26271e-006+-3.6043e-007 (A).

e+ rate = 0.254997 +- 0.0159527 (Hz).

Ne+/Ne-=6.52353e-015+-5.54538e-016.

Ne+/I_e-=0.255 Hz e+ / 6.2627 [math]\mu[/math]A e-

hand calculation of error

[math]R = \frac{N_{e^+}}{N_{e^-}} = \frac{ 0.25 \pm 0.015 Hz}{ (3.90887 \pm 0.224963) \times 10^{13} Hz} = 0.06395 \times 10^{-13} = 6.4 \times 10^{-15}[/math]

[math]R = 18.3 \times 10^{-16}[/math]

[math]\Delta R = \sqrt{\frac { \Delta N_p^{2} }{ N_e^{2} } + (- \frac{ N_p }{ N_e^{2} })^2 \Delta N_e^{2} } = \frac{\sqrt{ \Delta N_p^{2} + \frac{ N_p^{2} }{ N_e^{2} } \Delta N_e^{2} }}{ N_e}[/math]

[math]\Delta R = \frac{\sqrt{ 0.016^{2} + (\frac{ 0.25 }{ 3.909\times 10^{13} } 0.225 \times 10^{13})^{2} }}{ 3.909\times 10^{13}} = \frac{\sqrt{ 0.000256 + 0.000207 }}{ 3.909\times 10^{13}} = \frac{\sqrt{ 0.000463 }}{ 3.909\times 10^{13}} = \frac{0.0215}{ 3.909\times 10^{13}} = 0.0055 \times 10^{-13} = 5.5 \times 10^{-16}[/math]

References

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