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
56
26
Fe
58
26
Fe
60
28
Ni
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 D = M – A.
– Often converted into MeV
• Data used to calculate energy of
decay products.
D = 7.29 MeV
4He; D = 2.42 MeV
56Fe; D = – 60.60 MeV
•
•
•
1H;
•
•
•
•
214Pb;
D = – 0.15 MeV
218Po; D = 8.38 MeV
222Rn; D = 16.39 MeV
226Ra; D = 23.69 MeV
Alpha Particles
• Alpha particles are 4He nuclei.
– Mass approximately 4
AMU
– Charge is +2
– Generally from the decay of
heavy nuclei
Typical Problem
• Calculate the energy of the
alpha particle from 222Rn.
Answer
• Get the reaction equation.
• The energy of the alpha particle
is due to the mass difference of
the daughter nuclei.
• The energy released is
– Q = MRn222-MPo218-MHe4
– Q = 12.89 MeV
• Most will go to the alpha.
222
86
4
Rn 218
Po

84
2 He
Beta Particles
• Electron decay
– Nucleus emits an electron
and antineutrino
– Atomic number increases
– Energy goes to e and n
– Some include photon as
well
60
27
0 - 0
Co60
Ni

28
-1 e  0 
• Positron decay
– Nucleus emits a positron
and a neutrino
– Atomic number decreases
– Kinematics like electron
decay
– Same result as electron
capture – no beta out
22
11
0  0
Na 22
Ne

10
1e  0 
22
0
e  22
Na

Ne

11
10
0
0 -1
Table of Isotopes
Decay Rates
• The number of particles
decaying in a short period of
time is proportional to the
number of particles.
dN  -lNdt
• The decay constant is l.
• The decay rate or activity is the
rate of change.
– Activity decreases as time
increases
dN
A lN
dt
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
dN
 -ldt
N
ln N  -lt  ln N 0
N  N 0 e - lt
1
2
 e - lT
T
ln 2
l

0.693
l
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
A
AT
N 
 9.0 1010
l ln 2
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 mCi g-1
– In solution expressed per
unit volume: pCi L-1
• For a pure radionuclide:
lN
6.02 10 23 l 4.17 10 23
SA 


m
M
MT
• Normal soil has a few pCi/g
• Drinking water has a
recommended limit of 5 pCi/L
of 226Ra + 228Ra.
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 t 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:
P(t )  e -t / t
  E / mc2
Quarks
• Quarks are fundamental
building blocks, but are not
detected directly.
– Binding force too great
– Stable quarks bind to others
• Some baryons
– proton, p: uud
– neutron, n: udd
– lambda, L0: uds
– lambda-b, Lb0 : udb
• Quarks exist in hadrons.
– Baryons are three quarks
– Mesons are a quark-anti
quark pair.
• Some mesons
– pi-minus, p-: ud
– k-plus, K+: us
– J/psi, Y: 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, m-: 0.1057 GeV/c2 =
1/9 mp
– tau, t- : 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
W   e   e
Muons
• Muons are charged, long-lived
and weakly interacting.
– Lifetime 2.2 ms
• Heavy version of the electron.
– Mass provides greater
penetration
• Muons are naturally created by
cosmic rays.
• Muon from top decay
tt  W  q  W  q
 e  e  m  m  j  j