Kern- und Teilchenphysik I Lecture 12: Interaction of Particle with Matter

Kern- und Teilchenphysik I

Lecture 12: Interaction of Particle with Matter

Prof. Nico Serra

Mr. Davide Lancierini Dr. Patrick Owen

(adapted from the Handout of Prof. Mark Thomson)

http://www.physik.uzh.ch/de/lehre/PHY211/HS2017.html

Introduction

“New directions in science are launched by new tools much more often than by new concepts. The effect of a concept-driven revolution is to explain old things in new ways. The effect of a tool-driven revolution is to discover new things that have to be explained”

Freeman Dyson

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Particle Detection

- All particles apart for the proton, the electron and neutrinos decay (the neutron is stable inside nuclei)

- When we talk about “stable” particles in experiments we normally referring to particles that live long enough to interact with the detector and give some energy deposit.

- In case the interaction probability with the detector is small (e.g. neutrino for collider experiments) we talk about missing energy

- The particle we are most concern from detector point of view are

e^±, , µ^±, ⇡^±, K^±, K⁰, p^±, n c⌧ > 0.5mm

- Some particles are measured directly by the interaction with the detector, other particle (typically neutrals) by transferring energy to other (charged) particles.

Particle Detection

- Particle detection is (mainly) the art of measuring these 8 particles

5

Charge particle Interactions

Charged particle traversing a material have three effects:

- The particle loses energy by interacting the electrons and exciting or ionising the atoms

- The particle can be deflected by the nucleus (in general much heavier) multiple scattering, a bremsstrahlung photon can be emitted in this process

- If the particle velocity is larger than the speed of light in the medium Cherenkov light is emitted

Energy loss

- Let’s first consider the M>>me , energy loss for electrons is more complicated

- The trajectory of the particle is approximately unchanged after scattering with electrons

- The energy loss is given by

dE / Z²

ln a ^{2 2}

• Z: atomic number

• , : relativistic factors

7

Bohr derivation

A particle with charge Ze and velocity v moves through a medium with electron density n.

p_? = Z

F_?dt = Z

F_? dx v

F_? = eE_? ! p_? = e Z

E_? dx

v = 2ze² bv

Where Gauss theorem implies

Z

E_?(2⇡b)dx = 4⇡(ze)

The energy transferred to a single electron is given by E = p²_?

2m = 2z²e⁴ (b²v²)m_e

Energy loss

For n electrons distributed on a barrel n = N_e (2πb) db dx


dE

dx = 4⇡N_ez²e⁴ m_ev²

Z b_max b_min

db

b = 4⇡N_ez²r_e²m_ec²

2 ln b_max b_min

r_em_ec² = e²

Stopping power:

dE = p_?

2m_e 2⇡N_eb · db · dx = 4⇡N_ez²e⁴ m_ev²

db

b dx

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Energy loss

We have now to determine the bmin and bmax factor:

- bmin is for heads-on collisions, the energy loss we have E(b_min) = (2z²e⁴)

m_ev²b²_min

for bmin the lost energy is maximal

Energy loss by a massive projectile M>>me

- Electrons are bound in atoms with an average orbital frequency of <ve>, the

interaction has to happen in a minimum time T comparable to the electron orbital frequency

- bmax also corresponds to the distance at which the kinetic energy transferred corresponds to Emin = I (mean ionisation potential)

Bethe-Bloch equation

The Bethe-Bloch formula is valid for projectile with mass M>>me, e.g. p, K, pi, mu, …

: density of absorber Z, A: atomic number and weight of the absorbed I: mean ionisation potential

Absorver dependent quantities

Incident-particle-dependent quantities

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Bethe-Bloch equation

Bethe-Bloch equation

13

Bethe-Bloch equation

Dependence on Z and A

Z

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Examples

• A MIP looses 1-2 ^{M eV cm}_g ²

• Therefore it looses 1-2 MeV/cm in a material density of 1g/cm³

Examples

• E ' 1.8 ^{M eV cm}_g ² ⇥ 100cm ⇥ 7.87_cm^g 3 ' 1.1GeV

• A MIP looses 1-2 ^{M eV cm}_g ²

• Therefore it looses 1-2 MeV/cm in a material density of 1g/cm³

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Energy Loss by a particle

- For > 3 the energy loss is constant

- Below =3 the energy loss increases as

- Most of the energy is lost by the particle at low

- Therefore most of the energy is lost in the final part of the trajectory, this is known as Bragg peak it is important for hadron therapy of cancer

12

!

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Energy loss by a particle

- The average energy loss of a particle in a material is described by the Bethe-Bloch formula

- When a single particle pass through a material the energy loss is a stochastic process

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Energy loss by a particle

- Probability of interaction at distance x

• Interactions are exponentially distributed (rare events) with continuous variable which is the small probability of interaction per unit length

• Therefore the number of interaction is described by a Poisson distribution with P (n) = ^µ_n!ⁿ e ^µ, where µ is the average number of interaction in D

• Since the average length before interaction is , we will have µ = ^D

However we want the distribution of the energy lost, not the distribution of the number of interactions

P (x) = 1

exp ⇣ x⌘

= A N_A⇢

Energy loss by a particle

• The probability to lose E energy in any interaction is f(E) = ¹ _dE^d

• The probability to have only one interaction in D and to lose the energy E will be p₁(E) = P (1) ⇥ f(E), where P (1) is the Poisson probability to have only one interaction in the material

• We can also lose the total energy E = (E⁰) + (E E⁰) by having two interactions, we will have p₂(E) = P (2) ⇥ R

f(E E⁰)f(E⁰)dE⁰

• ... and so on Finally we obtain:

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Energy loss by a particle

We take Laplace transformation of p(E) and then we take the anti-Laplace- transformation

This integral can be solved and you get the Landau distribution, i.e. the energy loss distribution by a single particle

Energy loss and identification

Energy loss depends on the particle velocity and is ≈ independent of the particle’s mass M.

The energy loss as a function of particle

Momentum P= Mcβγ IS however depending on the particle’s mass

By measuring the particle momentum (deflection in the magnetic field) and

measurement of the energy loss on can measure the particle mass and identify the particle!

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Bremsstrahlung

• For muons in copper E_c ' 400GeV

• For electrons in copper E_c ' 20M eV

23 23

Total energy loss for electrons

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Photon Interaction

Interaction of photons with matter

- Photoelectric effect:

- Photon absorbed by electrons of the atoms

- Dominates at low energies

- Compton scattering

- Elastic scattering between photon and electrons

- Important at intermediate energies

- Pair production:

Photons interact in three possible ways

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Photoelectric effect

Compton scattering

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Compton scattering

Pair Production

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Summary on Gammas and Electrons

Summary on Gammas and Electrons

33

Photon interaction with matter

E.M. Calorimetry

- At high energies electrons lose energies via bremsstrahlung

- The emitted photon has large energy and produces electron-positron pairs

- This creates what is called an electromagnetic shower

Characteristic distance after which the electron loses 1/e of the energy via

bremsstrahlung

9/7 of X0 is also the mean three path for pair production by high energy photon

35

Hadron Showers

- When hadrons interact with matter, in addition to electromagnetic interactions (if they are charged), they have nuclear interaction

- This creates hadronic showers

Calorimetry

- Calorimeters measure the energy of particle by absorption

- It is a destructive measurement, i.e. the particle energy is deposited in the calorimeter

- There are two types of calorimeters:

- Electromagnetic calorimeters

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Calorimetry

- Homogeneous:

- total absorption calorimeters, better energy resolution

- Sampling:

- Sandwich of active and passive material, more compact

- Electron and photon showers mostly contained in the em calorimeter

- For hadrons/jets the showers is partially in the em calorimeter and partially in the hadron calorimeter

- Shower profile used for particle identification

Cherenkov Radiation

- When a particle passes through a medium exceeding the speed of light in the medium c/n (n is the refractive index) Cherenkov radiation is emitted

- Analogous to the sonic boom of an airplane exceeding the sound speed

- The angle of light emission depends on beta,

- There is a velocity threshold for emitting Cherenkov light

- Energy loss by Cherenkov radiation very small w.r.t. ionization (< 1%)

- Number of emitted photon per wavelength

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Cherenkov Radiation

Cherenkov Detectors

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Cherenkov Detectors

n_H2O = 1.3 ! ^th = 1/1.3 = 0.77

th

= p

1 _th²

= 1.56

E_th = m _th ! for the electron E_th ' 0.8M eV , for the proton E_th ' 1.5GeV

Cherenkov Detectors

⇡, K, p

n

n

> n

For a certain energy range of ⇡, K, p you can choose the material such that:

• pions give Cherenkov light in C₁ and C₂

• kaons give Cherenkov light only in C₂

• protons do not give Cherenkov light

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Cherenkov Detectors

⇡, K, p

n

n

> n

For a certain energy range of ⇡, K, p you can choose the material such that:

• pions give Cherenkov light in C₁ and C₂

• kaons give Cherenkov light only in C₂

• protons do not give Cherenkov light

• ^⇡ > _n¹

1

• _n¹₂ < _K < _n¹

1

• ^p < _n¹

2

Cherenkov Detectors

Picture from http://www.iss.infn.it/webg3/cebaf/hadron.html

https://inspirehep.net/record/884672/plots

- The Cherenkov light emitted is collected by PMTs

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References

Material heavily based on

- http://pdg.lbl.gov/2006/reviews/passagerpp.pdf

- The Physics of Particle Detectors (Erika Garutti - DESY) http://www.desy.de/~garutti/LECTURES/ParticleDetectorSS12/

Lectures_SS2012.htm

- CERN Summer Student Lecture by Werner Riegler

- IITM Lectures by Gagan Mohanty

- An Introduction to Charged Particle Tracking by Francesco Ragusa

Backup slides

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Laplace Transform and Landau

Probability f(E) for loosing energy between E’ and E’+dE’

in a single interaction is given by the differential crossection which is given by the Rutherford crossection at large energy transfers

1 (E)

d (E, E⁰) dE⁰

Energy loss by a particle

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Poisson Distribution

The Poisson distribution is popular for modelling the number of times an event occurs in an interval of time or space.

P (n) = µ

n! e

The probability to observe n events in over an interval of time/space is given by

µ is the expected mean over that time/space interval

Photoelectric Effect