Charged Particles

Nuclear Physics

• Charged particles can come from nuclear decay.

• Nuclear physics figures into particle detection.

• Use terminology from nuclear physics.

– Isotopes share Z

– Isotones share N

• Nucleus consists of protons and neutrons.

– Protons: Z (atomic number)

– Neutrons: N

– Nucleons: A = Z + N (atomic mass)

– Full notation shows A, Z

Fe5626 Fe58

26 Ni6028

Energy Measurement

• Energy measurements for nuclear an particle physics are built on the electron volt (eV)

– Energy to move one electron through a volt

– 1 eV = 1.6 10-19 J

• Mass is expressed in terms of the rest energy

– Also atomic mass unit (u)

– 1 u = 931.5 MeV/c2

• Proton, p

– 938.3 MeV/c2

– 1.007 u

• Neutron, n

– 939.6 MeV/c2

– 1.009 u

• Electron, e

– 0.511 MeV/c2

– 5.546 10-4 u

Mass Difference

• The mass (M) in u is nearly equal to the atomic number (A).

• Tables of isotope data frequently list = M – A.

– Often converted into MeV

• Data used to calculate energy of decay products.

• 1H; = 7.29 MeV

• 4He; = 2.42 MeV

• 56Fe; = – 60.60 MeV

• 214Pb; = – 0.15 MeV

• 218Po; = 8.38 MeV

• 222Rn; = 16.39 MeV

• 226Ra; = 23.69 MeV

Alpha Particles

• Alpha particles are 4He nuclei.

– Mass approximately 4 AMU

– Charge is +2

– Generally from the decay of heavy nuclei

• The energy of the alpha particle is due to the mass difference of the daughter nuclei.

Typical Problem• Calculate the energy of the

alpha particle from 222Rn.

Answer• Get the reaction equation.

• The energy released is

– Q = MRn222MPo218MHe4

– Q = 12.89 MeV

• Most will go to the alpha.

HePoRn 42

21884

22286

Beta Particles

• Electron decay

– Nucleus emits an electron and antineutrino

– Atomic number increases

– Energy goes to e and n

– Some include photon as well

• Positron decay

– Nucleus emits a positron and a neutrino

– Atomic number decreases

– Kinematics like electron decay

– Same result as electron capture – no beta out

00

01

6028

6027 NiCo

e 00

01

2210

2211 NeNa e

00

2210

2211

01 NeNa

e

Table of Isotopes

Decay Rates

• The number of particles decaying in a short period of time is proportional to the number of particles.

• The decay constant is .

• The decay rate or activity is the rate of change.

– Activity decreases as time increases

NdtdN

Ndt

dNA

Half-Life

• The differential equation for decay gives rise to an exponential relation.

– Decay constant is fixed for a decay reaction

• Decay is usually expressed as a half-life.

– Time for half a sample to decay

– Remains constant

dtN

dN

0lnln NtN teNN 0

Te 21

693.02ln

T

Measured Activity

• The SI unit of activity is the Becquerel (Bq).

– equals one decay/sec (s-1)

• The older unit is the curie (Ci).

– Based on the decay of 226Ra

– Once activity of one gram

– Now defined by Bq

– 1 Ci = 3.7 1010 Bq

Typical Problem• A source of 24Na is marked at

1.16 MBq. How many 24Na atoms are there in the sample?

Answer• First thing is to look up the

half-life for 24Na:

– T = 15 h = 5.4 104 s

10100.92ln

ATA

N

Specific Activity

• Physical variables are often normalized to the mass.

– Described as “specific”

• Specific activity is the activity of a sample divided by the mass.

– Units Bq g-1 or Ci g-1

– In solution expressed per unit volume: pCi L-1

• For a pure radionuclide:

• Normal soil has a few pCi/g

• Drinking water has a recommended limit of 5 pCi/L of 226Ra + 228Ra.

MTMm

NSA

2323 1017.41002.6

Particle Physics

• Charged particles are measured in particle physics.

– Energy scale > 1 GeV

• Energetic particles are the results of acceleration or decays.

Particle Lifetime

• Unstable particles have a characteristic lifetime.

• The lifetime is related to the probability that a particle will survive a given period of time.

• The survival time is affected by relativity.

• The probability is an exponential relation:

/)( tetP

2/ mcE

Quarks

• Quarks are fundamental building blocks, but are not detected directly.

– Binding force too great

– Stable quarks bind to others

• Quarks exist in hadrons.

– Baryons are three quarks

– Mesons are a quark-anti quark pair.

• Some baryons

– proton, p: uud

– neutron, n: udd

– lambda, 0: uds

– lambda-b, b0 : udb

• Some mesons

– pi-minus, : ud

– k-plus, K+: us

– J/psi, : cc

Hadrons

• Protons are stable hadrons.

– Charged particles

– Interact strongly

– Easy to detect

• Any other baryon will eventually decay into a proton and other particles.

• Charged pions are unstable, but relatively long-lived hadrons.

– Lifetime 26 ns

– Interact strongly

– Detectable like protons

• Pions frequently accompany the decay of other hadrons.

Jets

• Hadrons that collide at high energy can eject a quark.

• When the quark emerges it hadronizes forming a jet of particles.

– Most emerging particles are pions

High energy pion interaction, Fermilab 1973

Leptons

• Leptons are fundamental particles.

– Interact weakly

– Able to exist in isolation

• Detection of charged leptons is important in many particle physics experiments.

• Charged leptons:

– electron, e: 0.511 MeV/c2 = 1/1836 mp

– muon, : 0.1057 GeV/c2 = 1/9 mp

– tau, : 1.776 GeV/c2 = 1.9 mp

Electrons

• Electrons are perhaps the most important particle for detection.

– Stable

– Charged

– Lightest charged particle

• Electrons result from nuclear and particle decays.

• Electron from W decay

eeW

Muons

• Muons are charged, long-lived and weakly interacting.

– Lifetime 2.2 s

• Heavy version of the electron.

– Mass provides greater penetration

• Muons are naturally created by cosmic rays.

• Muon from top decay

jje

qWqWtt

e