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    • Abstract: relativistic. M. nucl = infinite. no recoil. first order perturbation. theory (Z1α. em <<1) 21 ... Now often used in large water-filled. neutrino detectors and for other particle. physics ...

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Lectures 12-14
Particle interactions with matter
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 1
12.0 Overview
12.1 Introduction 13.1 Photons in matter
Photoelectric effect
12.2 Charged particles in
Raleigh scattering
matter
Compton scattering
Classification of interactions Pair production
Non-radiating interactions
γ-Nucleus interactions
(ionisation)
Radiating interactions 13.2 Detectors
Ionisation and the Bethe-Bloch For photons only
formula Photomultiplier and APD
For charged particles and γ’s
Radiating interactions
Photography
Cherenkov-radiation
Scintillators
Transition-radiation
Gas-counters
Bremsstrahlung Semi-conductors (GeLi, Si)
Synchrotronradiation em-calorimeters (see particle
The em-shower physics course)
13.3 Radiation units
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 2
12.1 Introduction
(why do we need to know this)
Measure properties of nuclei through decay product particles
Measure energy, momentum, mass & charge of particles with
M ∈ [0 (γ) ; few 100 GeV (fission fragment)]
Ekin ∈ [keV (Radioactiviy) ; few GeV (accelerator experiments)]
Q/e ∈ [0 (γ,n); O(100) (fission fragments)]
Need to translate microscopic particle properties into
quantitatively measurable macroscopic signals
Do this by interactions between particles and matter
Which interactions would be useful?
Weak? Too weak at low (nuclear) interaction energies
Strong? Some times useful but often noisy (strong fluctuations, few
scattering events per distance)
EM? Underlies most nuclear and particle physics detectors
Energies released ≤ Ekin(particle) often too small for direct
detection need amplification of signals
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 3
12.1 Introduction
Particle Ranges
a) If smooth energy loss via many steps a)
(i.e. ionisation from light ions)
sharply defined range, useful for
rough energy measurement
b) If few or single event stop particle
(i.e. photo-effect)
exponential decay of particle beam b)
intensity, decay constant can have
useful energy dependence
Sometimes several types of
processes happen (i.e. high energy
electrons)
mixed curves, extrapolated maximum c)
range
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 4
12.1 Introduction
Particles we are interested in
photons
exponential range (at low E often get absorbed in single events)
detect secondary electrons and ions liberated in absorption process.
charged particles
sharper range (continuously loose energy via ionisation)
leave tracks of ionisation in matter measure momentum in B
sometimes radiate photons can be used to identify particle type
neutrons
electrically neutral no first-order em-interaction devils to detect
react only via strong force (at nuclear energies!)
long exponential range (lots of nuclear scattering events followed by
absorption or decay)
need specific nuclear reactions to convert them into photons and/or
charged particles when captured by a target nucleus
if stopped, measure decay products, electron + proton + anti neutrino
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 5
12.2 Charged particles in matter
(classification of interactions)
If particle or medium emit photons, coherent
with incoming particle radiation process
Bremsstrahlung, Synchrotron-radiation: emitted
from particle
Cherenkov-radiation, Transition-radiation: emittted
from medium
If not non-radiating process
Ionisation, scattering of nuclei or atoms
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 6
12.2 Charged particles in matter
(non radiating interactions, what to collide with)
What could a charged particle collide with
Atomic electrons (“free”)
large energy loss ΔE≈q2/2me (small me, q=momentum transfer)
small scattering angle
Atomic nuclei
small energy loss (ΔE=q2/2mnucleus)
large scattering angle
Unresolved atoms (predominant at low energies)
medium energy loss (ΔEme(free))
medium scattering angle
atoms get excited and will later emit photons (scintillation)
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 7
12.2 Charged particles in matter
(Ionisation and the Bethe-Bloch Formula)
Deal with collisions with electrons first since
these give biggest energy loss.
Task: compute rate of energy loss per
pathlength, dE/dx due to scattering of a
charged particle from electrons in matter.
Remember a similar but inverse problem?
Scatter electrons of nuclei = Mott scattering
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 8
12.2 Charged particles in matter
(Ionisation and the Bethe-Bloch Formula, Rutherford vs. Mott)
Rutherford Scattering Mott Scattering
α (q=Z’e) ↔ nucleus (q=Ze) e- (q=1e) ↔ nucleus (q=Ze)
spin-0 ↔ spin-0 spin-½ ↔ spin-0
point ↔ point no unpolarised electrons
form-factors (average over all incoming
non-relativistic spin orientations)
Mnucl = infinite no point ↔ point no form-
recoil factors
first order perturbation relativistic
theory (ZZ’ αemme would need recoil corrections to apply results to
dE/dx of electrons passing through matter
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 10
12.2 Charged particles in matter
(Ionisation and the Bethe-Bloch Formula, transforming Mott)
Change variables from Ω to q2 (q = momentum transfer to
electron) to get to frame independent form
q 2 = P 2 + P ′2 + 2PP ′ cos θ
in elastic scattering of heavy nucleys: P = P ′ = p ⇒
θ P’
q 2 = 2p 2 (1 − cos θ ) = 4 p 2 sin2 q
2 θ
dq 2 P
= 2 p 2 sin θ

dθ 1
if no φ dependence: d Ω = 2π sin θ d θ ⇔
=
d Ω 2π sin θ
d σ d θ d σ d θ dq d σ
2
1 dσ p2 dσ
= = = 2p sin θ
2
=
d Ω d Ω d θ d Ω d θ dq 2 2π sin θ dq 2 π dq 2
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 11
12.2 Charged particles in matter
(Ionisation and the Bethe-Bloch Formula, transforming Mott)
dσ z α ( c )
2 2 2
−4 θ ⎡ V2 2θ⎤
= sin ⋅ ⎢1 − 2 sin ⎥
dΩ 4p V
2 2
2 ⎣ c 2⎦
2 θ q2
since: sin =
2 4p 2
dσ z α ( c )
2 2 2
4p 2 ⎡ V 2 q 2 ⎤
= ⋅ 1−
dΩ V2 q 4 ⎢ c 2 4p 2 ⎥
⎣ ⎦
dσ π dσ
since: = 2
dq 2 p dΩ
d σ 4π z α ( c )
2 2 2
⎡ V 2 q2 ⎤
= ⎢1 − 2
dq 2
V 2q 4 ⎣ c 4p 2 ⎥

21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 12
12.2 Charged particles in matter
(Ionisation and the Bethe-Bloch Formula, changing frames for Mott)
Change frame to:
electron stationary, nucleus moving with V
towards electron
p in formula is still momentum of electron moving
with relativeV p =meγV
q2 is frame independent
non-relativistic this is obvious (do it at home)
relativistic need to define q as 4-momentum transfer
Energy transfer to the electron is then defined via:
ΔE=ν=|q2|/2me dν/dq2=1/2me
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 13
12.2 Charged particles in matter
(Ionisation and the Bethe-Bloch Formula, Mott Bethe Bloch)
1 d σ 4π z α ( c )
2 2 2
dσ dν d σ ⎡ V 2 q2 ⎤
= = = ⎢1 − 2 2⎥
dq 2 dq 2 d ν 2me d ν V 2q 4 ⎣ c 4p ⎦
p =meγV
|q2|=ν/2me
2π z 2α 2 ( c ) 1 ⎡
2
dσ ν ⎛ V 2 ⎞⎤
dν = ⎢1 − ⎜1 − ⎟⎥ d ν
dν meV 2 ν 2 ⎣ 2me c 2 ⎝ c 2 ⎠ ⎦
Above is crossection for heavy particle of charge z to loose energy
between ν and ν+dν in collision with electron it approaches with velocity V
We want
kinetic energy lost = -dT
per path length dx ν max

in material of atomic number density n
with Z’ electrons per atom
−dT = nZ dx

v
∫ ν


min
number of colissions with
electrons in length dx average energy
lost per collision
21 Jan 2005, Lecture 12 Nuclear Physics Lectures, Dr. Armin Reichold 14
12.2 Charged particles in matter
(Ionisation and the Bethe-Bloch Formula, simple integral)
dT ⎡ 2π Z 2α 2 ( c )2 ⎤ ⎡ ⎛ ν max ⎞ ⎛ V 2 ⎞ ⎛ ν max − ν min ⎞ ⎤
− = nZ ′ ⎢ ⎥ ⎢ln ⎜ ⎟ − ⎜1 − ⎟⎜ ⎟⎥
dx ⎣ meV 2 ⎦⎣⎢ ⎝ ν min ⎠ ⎝ c 2 ⎠ ⎝ 2me c 2 ⎠ ⎥ ⎦
νmax via kinematics of “free”
Note: c=1 from here downwards!
electron since Ebind


Use: 0.3188