Download Particle Detectors and Quantum Physics (2)

Particle Detectors and
Quantum Physics (2)
Stefan Westerhoff
Columbia University
NYSPT Summer Institute 2002
More Quantum Physics
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We know now how to detect light (or photons)
One possibility to detect charged particles is to have
them produce light
Charged particles produce light when exiting atoms or
molecules (for example fluorescence light)
So we need to learn more about atoms and how they
can be excited…
Positron or Electron ?
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Discovery of the positron
(Andersen, 1931)
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Magnetic field B is
perpendicular to the paper
plane, particles pass
through a lead plane
Positive charge going up, or
negative charge going
down ?
Particle loses energy in
the lead (absorber) !
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Lab Classes related to this lecture:
n Scintillators (this afternoon)
Towards a Model for the
Hydrogen Atom
(the rest is details… )
There’s a reason physicists are so
successful with what they do, and that is
they study the hydrogen atom and the
helium ion and then they stop.
Richard Feynman
Early Model of the Atom (Wrong)
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Discovery of the electron
in 1897 in cathode rays
Electrons are part of the
atom
First model: atom is a
homogeneous sphere
with electrons in it (plumpudding model)
Rutherford’s Experiment
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Beam of α-particles
(He nuclei with charge
+2e) is directed at a
thin gold foil
Expectation: only small
deflection (electrons
are lighter than α
particles, and the
positive charge in the
atom is spread out and
can’t do anything
either)
Results
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Most α particles pass through the foil as if it was empty
space
Some of the α particles are deflected at very large
angles, some even backward !
Rutherford: α particles must be repelled by a massive
positive charge concentrated in a tiny space
New Model (Still Wrong)
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Atomic model: electrons orbit a
tiny positive nucleus of radius
10−15 m
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The electron moves in orbits
around the nucleus like the
Earth around the sun
Movement is necessary so the
electron does not fall into the
nucleus (Coulomb !)
Why is it Wrong ?
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From Maxwell’s electrodynamics: electrons moving in a
circular orbit radiate electromagnetic waves – they
gradually lose energy.
In Rutherford’s model, the electron would lose energy
and get closer and closer to the nucleus until it falls into
the nucleus.
This would take about 10−11 s . The fact that you are still
sitting here shows that either Rutherford or Maxwell are
wrong.
Don’t argue with Maxwell.
The Bohr Model
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Bohr believed in Rutherford’s model and
tried to fix it
From Planck and Einstein he knew that
energy is quantized – so maybe the same
is true in atoms, and they can not lose
energy continuously, but only in quantum
jumps
Hydrogen is the simplest atom: just a
proton and one electron…
Energy Levels
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Electrons move about the
nucleus, but only certain
orbits are allowed
An electron in one of these
orbits has a definite energy
and moves on the orbit
without energy loss
− 13.6 eV
E=
2
n
with n = 1,2,3,...
Energy Levels
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Notice the minus sign ! This is a convention, but a good
one: it means that if the electron and the nucleus are very
far apart, the energy is zero (they are “free particles”)
The orbit closest to the nucleus, n = 1, has the lowest
energy E = -13.6 eV
The next highest state is n = 2, with a higher (!) energy of
E = -3.4 eV
The state with the lowest energy is the ground state, the
states with higher energy are excited states
Photon Emission
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Electrons can jump from one
level to another
If they jump into a state of lower
energy, a photon is emitted, with
a frequency corresponding to the
energy difference
h ⋅ f = Eu − El
Photon Absorption
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The opposite is also true – you can push an electron
into a state of higher energy if you send a photon in that
has exactly the right energy
The electron is typically in the ground state
If it is in an excited state, it will emit photons until it is
back in the ground state
Systems in physics always try to get into the state of
lowest energy (examples ?)
Transitions
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The different
transitions from one
level to another have
different names
Photons of the Balmer
series have
wavelengths in the
visible
Ionization
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If you provide 13.6 eV,
you remove the electron
from the atom and set it
free
This is called ionization,
and the energy required
to remove the electron
from the ground state is
called binding energy
Line Spectra
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Bohr’s model explains a phenomenon
that could not be explained otherwise –
an excited gas does not emit a
continuous spectrum, but a line
spectrum
Gas at low pressure in a tube with high
voltage
Excited gas emits light … but only
certain wavelengths !!
Line Spectra
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Examples: emission spectrum of hydrogen and helium
hydrogen
helium
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Emission spectra look different for different gases and can
be used to identify them – like fingerprints !
The emission spectra indicate what the energy levels are !
Balmer Series
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The Balmer series marks
the transitions from n=2
to n=3,4,5,6,…
These transitions are in
the optical range
Absorption Spectra
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Of course gases can absorb at the same wavelengths at
which they emit
If light that contains all wavelengths passes through a
gas, we get a spectrum where certain lines are missing !
Photons of these wavelengths have been used to move
electrons from one level to another and are therefore no
longer there !
These absorption spectra can help to identify gases – for
example in the sun !
Absorption Spectrum of the Sun
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In the light that reaches us from the sun, certain
wavelengths are missing - these photons have been
absorbed in the sun’s atmosphere
hydrogen
helium
sun
Why are the Energy Levels
Quantized ?
(if you really need to know…)
Why Quantized ?
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De Broglie’s bold hypothesis (1927):
if light is a wave and a particle…why
isn’t every particle also a wave ?
“This is outrageous… if this was
correct, then electrons should show
interference and diffraction just like
light !”
“Well, did we ever check ??”
Double Slit for Electrons
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Beam of electrons is send
through a two-slit
interference experiment just
like Young’s experiment
with light wave
Electrons should go either
through the first or the
second slit…
…shouldn’t they ??
Interference
7, 100,
3000, 20000,
70000 electrons
Diffraction
Trapped Waves
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Consider a wave confined to a
limited region of space, for
example a wave trapped
between two walls
Compare this to a string of
some length, which is fixed at
both ends
Discrete Frequencies
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Only certain standing waves are
allowed, since the string can only be
in a state where the two ends are
fixed
If an electron in an atom is “trapped,”
and electrons are waves, than only
certain modes of oscillation are
allowed, and each corresponds to a
different energy
Electrons in Atoms
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The electron in the
atom is trapped in
the Coulomb
potential
An electron is a
wave confined to a
limited region of
space
Consequently, the
electron’s energy is
quantized
e ⋅ (−e)
e2
U = F ⋅r =
=−
r
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Detectors for Charged Particles
Scintillation Detectors
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Certain materials emit a small flash of light (a scintillation)
when they are struck by a particle
Effect is used since 1903, and early experiments used the
human eye to detect the light flash (Geiger) – tedious !
Only with the invention of the photomultiplier tube did the
scintillation detector become popular again
Scintillator/photomultiplier devices have become one of
the most widely used detectors in particle physics
Emission of Photons
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A charged particle traveling
through scintillator leaves
excited molecules behind, and
the energy is released in part
as light
Wavelength depends on
material
If light is released immediately,
this is fluorescence
If re-emission is delayed, this is
called phosphorescence
Scintillation Detectors
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Different types of scintillator
n organic, liquid, plastic
n inorganic crystal (sodium
iodide)
Wavelength can be shifted by
other molecules incorporated
in the scintillator (UV to blue)
Scintillation Detectors
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Scintillators come in
different shapes,
depending on application
Different applications
require different scintillator
materials
Scintillation wavelength
and photomultiplier
sensitivity must match
A Particle Detector
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Scintillating material optically
coupled to a photomultiplier
(either directly or with a light
guide)
A particle passes through the
scintillator and causes a light
flash
Photons reach the
photomultiplier and are
converted into a current
Mounting a Scintillation Detector
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We need to wrap the scintillator
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(aluminum foil) so the light
gets reflected back into the
scintillator until it hits the
photomultiplier
n with black tape so no
ambient light gets in
Reflection and Refraction
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When light hits the boundary between two materials with
different index of refraction n, there is a refracted and a
reflected ray
n is a material constant
The ray in the denser material is bent towards the
normal
nvacuum = 1
Light in the medium travels with
speed c/n (so light is slower in
nair = 1.00029
water than in air)
nwater = 1.33
Angle of Refraction
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The reflected ray has an angle to
the normal equal to the angle of
incidence
The refracted ray has an angle to
the normal given by
n1
sin θ 2 = sin θ1
n2
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Refraction bends the light ray
toward the normal
Total Internal Reflection
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n1
There is no solution for the refraction law sin θ 2 =
sin θ1
n2
if the right-hand side is larger than 1
This happens if n1 > n2 and the incident angle is larger
than the critical angle
Total Internal Reflection
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Above the critical angle, there is no refracted ray and all
the light is reflected (total internal reflection)
When mounting the scintillator, we want the light to stay
in the scintillator until it hits the photomultiplier, so we
want a layer of air between aluminum and scintillator
Index of refraction of plastic scintillator is typically 1.58,
so critical angle is about 40 degrees
Optical Coupling
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The photomultiplier has to
be coupled to the
scintillator, and in this
case, we don’t want total
internal reflection
Use optical grease with
index of refraction of
scintillator
Literature
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W.R. Leo, Techniques for Nuclear and Particle Physics
Experiments, Springer (1987)
D.C. Giancoli, Physics, Vol. 2, 5th Edition, Prentice Hall
(1998)
D. Halliday, R. Resnick, J. Walker, Fundamentals of
Physics, Vol. 2, 6th Edition, J. Wiley (2001)