Electron-positron
Annihilation
Experimentation and theoretical
application in Positron Physics
Veronica Anderson, David Tsao, Mark A. Rodgers
COSMOS, UC Santa Cruz
Overview
• The purpose of our project and experiment is
to measure (accurately) the mass of a
positron through the gamma-ray detection of
the annihilation between the positron and an
electron
Antimatter
• In 1932 British physicist Paul Dirac derived the
equation E2=m2c4+p2c2
• This equation tells us that for every type of particle
of ordinary matter (e.g. protons and electrons) a
particle of opposite charge and certain quantum
properties exists, called antimatter
• Antimatter particles are rarely found in nature, and
are therefore difficult to detect
• Antimatter is usually created in the modern
universe during nuclear decays
Positrons
• Positrons are the
antimatter equivalents
of electrons
• Positrons have a mass
equal to that of an
electron, but have an
opposite charge and
certain quantum
properties different
from those of the
electron
Artist’s conception of the Lawrence Livermore National Laboratories’
electron linac1, used for positron detection
Electron-positron Annihilation
•
•
•
•
•
When matter and anti-matter collide,
they destroy each other in a flash of
high-energy radiation
The gamma rays emitted in the
annihilation are easily detectable
In an electron-positron annihilation
the g-rays are emitted linearly
Sometimes the electron and positron
form a brief bond through the
electromagnetic force, creating
Positronium
When electron-positron pairs first
form Positronium, the direction of the
energy emitted from their
annihilation will not be linear
Positron detection
• The most practical method for
detecting positrons is measuring
the gamma emission of their
annihilation with electrons
• Many larger experiments utilize
particle accelerators, but we
used simpler apparatus
Photograph of the first
detection of the antielectron (positron), in
1932 at CERN
A large facility used for positron detection
(http://wwwpat.llnl.gov/H_Div/Positrons/PositronFacility.html)
http://athenapositrons.web.cern.ch/ATHE
NApositrons/wwwathena/an
derson.html
Objective
• Our primary objective was to detect the gamma-ray (g-ray)
emission of the annihilation during the collision of the
positron and electron
• From the g-ray emission we hoped to determine the mass
(m) of the positron itself
• Since Einstein’s equation E=mc2g tells us that mass and
energy are interchangeable, the energy of the emission
should directly correlate with the mass of the positron
• We also hoped to apply what we have learned about particle
physics and anti-matter to early universe astrophysics,
particularly the baryon asymmetry problem
Apparatus
• We used a 22Na positron source
for our experiment. 22Na emits
most positrons (b-rays), in
addition to a small number of
gammas.
• We used a stationary aluminum
plate of about .5 cm thickness to
prevent positrons from directly
striking our detector
• Our detector was a Sodium
Iodide Scintillator
• The entire experiment was
encased in lead bricks with
dimensions of about 5x10.5x20
cm
Sodium Iodide Detector2 (http://detectors.saintgobain.com/Media/Documents/S0000000000000000003/oper
20manl 200304.pdf)
We fed our data into a Canberra
Multi-channel Analyzer, and then
transferred the data onto a
computer for analysis
Our Apparatus
Scintillator
Lead
Shielding
Canberra
Below Screen
-24 V Power
Source
Digital
Oscilloscope
High
Voltage
Canberra 35-Series Multi-channel Analyzer
Our Positron Data on the Analyzer
Calibration
• To calibrate our Sodium Iodide
Scintillator, we used two g
sources of known energy levels:
137Cs and 133Ba
• The Cs isotope emitted a smooth
radiation curve with a peak
intensity of 662 KeV
• We also took a measurement
with no source to determine what
our background distribution
would be, and we found that our
Scintillator was picking up very
little noise
Our apparatus in calibration
Noise Reduction
Background Noise
1000
900
800
Number of Counts
700
600
500
400
300
200
100
0
0
500
1000
Energy (kev)
1500
Data Collection
• We collected our data using a
Canberra 35-Series Multichannel Analyzer
• We compared the data we
received with the noise and with
a calibration sources--the Barium
isotope did not emit the spectrum
we had expected to see
• The image at right is displaying
the data that we received for the
gamma emission of the cesium
source, with which we compared
our eventual positron (22Na)
annihilation energy
Our Canberra Multi-channel Analyzer
displaying Cesium data
Positron Data
5
4
x 10
Annihilation Energy of Positrons From a Sodium-22 Source
3.5
Number of Counts
3
• This is a graph of the
number of counts at
each energy level of the
photons emitted from the
Sodium-22 source
• The intensity peaks at
about 537 KeV
2.5
2
1.5
1
0.5
0
0
200
400
600
800
1000
Gamma Ray Energy (kev)
1200
1400
1600
Analysis
• We used several techniques for analysis of our data
• Using a computer program we wrote, we attempted to analyze the
energy of the detected gamma-rays
• Although the program failed to produce results, we were able to make
the calculations by hand
• We found that the intensity of the energy of detected gamma-rays
peaked at 537 KeV
• Theoretical values have the positron with a mass-energy of about 511
KeV
• Several discrepancies may account for the difference in energy detected
and the mass of the positron, especially the KE of the positron (and
possibly the electron as well)
Calculations
E=mc2
E=537.0 keV (8.603x10-14J), c2=8.988x1016
m=(E/c2)
Mass (m) in kg=(8.603x10-14)/(8.988x10 -16)
m=9.561x10-31kg
Theoretical mass= 9.1095x10-31 kg
Conclusions
• Using the value we measured for the energy of the gamma-ray emitted
from the annihilation, we were able to calculate the mass of the positron
in kg
• We calculated that the mass of the positron is 9.5499x10-31 kg, which is
spectacularly close to the accepted mass of the electron: 9.1095x10-31
kg
• Although we were slightly off from the mass we had hoped to find, our
error was very slight--we didn’t take KE or thermal energy into account
in our calculations
Acknowledgments
We have not, fortunately, conducted this project alone. Among
those to whom we owe the greatest thanks are Paul Graham
and Dave Dorfan, our spectacular physics professors.
Other thanks:
Department of Physics, University of California, Santa Cruz
Department of Physics, University of California, Berkeley
Santa Cruz Institute for Particle Physics
Fred Kuttner
John and Jason
Steve Kliewer
Stuart Briber
Nuri and Jessica (and the rest of the COSMOS staff)