Transcript Problem 1 : Energy of backscattered photon Compton Scattering

Designing a Compton Polarimeter
Lee Hyun Seok, Matthew Harrigan Advisor: Richard Jones
Physics Department, University of Connecticut, Storrs
The Q-weak Experiment
The Q-weak experiment is a precision Test of the Standard Model and Determination of the
Weak Charges of quarks through Parity-Violating Electron Scattering.
The spin of electrons in the electron beam is altered 30 times per second. The beam acts with
the weak interaction differently when it is left-handed and when it is right-handed.
Due to the parity violation of the weak
interaction, it acts differently on left-handed
and right-handed electrons. Therefore,
measuring the difference of the energy of
scattered particles between two type of electron
spins, we will be able to measure the weak
charge of proton precisely. Any significant
deviation of the weak charge from the Standard
Model prediction would be a signal of new
physics, whereas agreement would place new
and significant constraints on possible Standard
Model extensions.
Problem 1 : Energy of backscattered photon
Structure of the Compton Polarimeter
To use a Compton polarimeter, the possible range of the backscattered photons’ energy should be calculated.
Applying the laws of conservation of energy and momentum, we get three equations that can find the energy of the
backscattered photon, the momentum of the scattered electron, and the scattering angles.
Below is a simple model of a complete Compton polarimeter. First, the electron beam curves and goes
below its initial height. The laser light collides with the beam and, due to the Compton effect, some of the
photons are scattered. The photons are then sent to the detectors and their properties are measured. With the
energy data, we can calculate the polarization of the electron beam.
Assuming that the 1GeV electron beam
interacts with a 500nm green laser, we
solved these equations. Below is the
actual graph and logarithmic graph of
the backscattered photon’s energy as the
scattering angle of the photon changes.
Compton Scattering
For the experiment,
the polarization of the electron beam should be measured
,
precisely. To measure it, we will use a Compton polarimeter. Compton scattering is used by
the polarimeter to determine polarization. If the electron has its spin angular momentum in the
same direction as its momentum, ,it will have a greater Compton scattering probability.
The Compton effect is the interaction between electrons and photons when they collide
with each other. This phenomenon shows the particle-like behavior of light. In the interaction,
the photon and electron exchange energy and momentum. During the interaction, the total
energy and momentum are conserved, which is a fundamental law of physics.
With the graph, we can easily realize that the backscattered photons could get lots of energy from electrons,
compared to the other photons. The maximum energy gained from electrons is ~37 MeV; only about 3.7% of the
initial energy of the electrons.
Problem 2 : Positioning the mirrors
Above is the equation for
Compton scattering when
an gamma ray collides
with a stationary electron.
A Feynman diagram for
Compton scattering
For the Compton polarimeter to work, the thick laser light should be guided and focused
correctly to collide with thin electron beam.
Below is a simple model for the mirror arrangement.
Detectors
2) Calorimeter – to measure the Energy of photons
The detector works by sensing the energy deposited by photons
when they are absorbed. The total amount of energy deposited is
directly proportional to the photon energy. This picture of an X-ray
calorimeter shows a simple model of modern photon-calorimeters.
3) Magnetic field – to measure the Momentum of charged particles
According to Electromagnetism, a charged particle moving in
mv
radius r 
qB a magnetic field feels the ‘Lorentz force’ that makes it to move in a circle.
If one knows the charge of the particle, he or she can get the momentum
of the particle by measuring the radius of the circle.
This graph shows the
number of ‘Compton events’. A
Compton event is when either a
scattered photon or electron is
detected. As the electron beam’s
polarization changes 30 times
per second, the number of
Compton events also changes 30
times per second, due to the
effects of spin on Compton
scattering.
Time
Conclusion
1) Cherenkov detector – to measure the velocity of charged particles
Cherenkov radiation results when a charged particle, most commonly an
electron, exceeds the speed at which light is propagating in a dielectric
(electrically insulating) medium through which it passes. In a similar way to the
‘sonic boom,’ a charged particle can generate a photonic shockwave as it travels
through an insulator. By measuring the angle of radiation, we can get the velocity
of the charged particle.
Detectors
In conclusion, Q-weak experiment’s goal is to find out the accurate value of a proton’s weak charge
and possibly discover new physics. This experiment depends heavily on the polarization of an electron
beam because the weak charge can be separated from the electric charge due to parity violation (only lefthanded electrons can be affected by the weak neutral nuclear interaction).
The electron beam is curved twice by magnetic fields, and goes parallel to its initial
direction, but below its initial height. After it collides with the laser source, it is curved again,
and returned to the initial height. This is done to prevent damage the detectors for photons and
electrons that would be inevitable if they had to be placed in the electron beam.
The thick laser light is reflected by four identical mirrors, with a focus length equal to
the distance from the colliding point to itself, at the corners. The laser then goes to the ‘dump.’
During this one cycle, the light collides with the electron beam twice. In the case that the
angle between electron beam and laser light is very small(0~1 degree), we can ignore the
effect of angle and use our calculation for Problem 1.
However, to achieve this effect, the size of mirror should be small in order not to be
damaged by the 1GeV electron beam. Then, some parts of light would be reflected at the edge
of the mirrors, and we will have to predict the effect of this,
In this whole cycle, only a few of photons can collide with electron beam because the
beam is very thin. If a photon collides with an electron and backscattered, the detectors will
catch the photon and electron to measure the energy, velocity, momentum, etc..
The Q-weak experiment needs a polarimeter that can measure the beam’s polarization exactly
without interrupting the beam itself. That is a Compton polarimeter, which applies the property of Compton
scattering to measure the polarization.
In this project, we solved two problems relating to the design of the polarimeter: 1. The range of the
energy that scattered photons can have and 2. Positioning the mirrors that guide the laser light to collide
with electron beam.
The first problem was solved using the laws of conservation of momentum and energy. It was
obvious that the energy of scattered photons increases greatly as the scattered angle goes close to Pi;
however, the maximum energy of the completely backscattered photons was only 3.7% of the initial energy
of an electron.
To solve the second problem, we designed a mirror system that aims the approximately parallel laser
light beam at the electron beam. Also, convex mirrors were used to focus the relatively ‘fat’ laser beam to
about 50 microns (the width of the electron beam). With the beams positioned and focused correctly,
Compton scattering can take place, and the weak charge can be measured from data collected about the
backscattered photons and electrons.