Nuclear Transformations
Yoichi Watanabe, Ph.D.
Office: Masonic Cancer Center M10-M
Telephone: (612)626-6708
E-mail: watan016@umn.edu
http://www.tc.umn.edu/~watan016/Teaching.htm
Outline
I. Introduction
II. Radioactivity
III.Modes of Radioactive Decays
IV.Nuclear Reactions
Structure of Nucleus
Nucleus contains protons (p) and
neutrons (n).
 π-mesons (pions) act as the combining
force of p and n.
 p and n are trapped in a nuclear energy
potential and those are in discrete energy
states.
 The binding energy is in the range of
MeV instead of eV in atoms.

http://education.jlab.org/itselemental/index.html
Chart of Nuclides or Isotopes
Isotones
Z = atomic number
N = neutron number
A = mass number
A=Z+N
A
Z
X
Nucleus
Nuclei
Nuclide
Nucleon
Isotope
http://www.medicalphysics.org/apps/medicalphysicsedit/Ch13.pdf
Energy unit




1 eV is the energy that an electron or a particle
with one electron charge gains in an electric
potential of 1 V.
1 eV = 1.602x10-19 J.
1 MeV = 106 eV.
Mass can be represented by eV (<= E=mc2).
Electron mass = 511.003 keV
Proton mass = 938.280 MeV
Neutron mass = 939.573 MeV
π0-meson (pion) mass = 134.96 MeV
1 amu = 931.502 MeV
Binding Energy
The nuclear binding energy is the energy
needed to separate nucleons from nuclei.
 The binding energy in an atom is in the
range of eV.
 The binding energy in nuclei is in the
range of MeV.

Binding Energy: Example

How much energy is needed to separate a
neutron from a deuterium nuclei?
2
1
H→ H + n+Q
1
1
Deuteron mass = 2.0140177 amu = 1876.013 MeV
Q = 2.014018 - (1.007825+1.008665)
= -0.002472 amu
= -2.303 MeV (endoergic)
Note: Atomic mass includes the mass of electrons.
12
Energy Level of Nucleus:
6C
18.4
12B 13.4
5
12N 17.67
7
12.7
7.7
4.4
γ
12C
6
http://www.tunl.duke.edu/nucldata/index.shtml
Outline
I. Introduction
II. Radioactivity
III.Modes of Radioactive Decays
IV.Nuclear Reactions
Antonio Henri Becquerel

Henri Becquerel (1852-1908) noticed black spots on
a photographic plate with uranium salts and pure
uranium metal in 1896.
Marie and Pierre Curie



Pierre Curie (1859-1906) and Marie Curie (1867-1934)
coined the term Radioactivity.
They studied radioactivity using uranium ore after the
discovery of Becquerel.
They discovered Polonium and Radium.
Radioactivity
All elements with Z greater than 82 are
radioactive => natural radioactivity.
 There is at least one stable configuration
in atoms lighter than Z = 82. (82Pb)
 Radioactive isotopes can be produced by
bombarding stable nuclei with particles,
(i.e., neutrons, high energy protons, etc.)
=> artificial radioactivity.

Radium




Radium is the sixth member of the naturally occurring
uranium series.
Radium nuclides contain 88 protons (Z=88). The most
stable radium isotope is 226Ra, which contains 138
neutrons (A=226).
226Ra disintegrates to form Radon.
Radium was used to treat cancer by placing it near or in
contact with a tumor soon after the discovery of Radium by
the Curies.
226
88
Ra 
→ Rn
222
86
Decay Constant, λ

The number of nuclides disintegrating per
unit time (∆N/∆t) is proportional to the
number of radioactive nuclides (N):
dN
= −λN
dt
Activity

The rate of decay is the activity, A, of a
radioactive nuclide.
A = λN
The unit of activity is Becquerel (Bq). One Bq
means one disintegration per second (dps).
1 Ci is 3.7x1010 dps and it is based on the
activity of 1 g of radium.
A Solution of Decay Equation
N (t ) = N (0)e
A(t ) = A(0)e−λt
− λt
Acitivity, MBq
Carbon 10
1000
900
800
700
600
500
400
300
200
100
0
T1/2 = 19.3 s
0
5
10
15
20
Time, Seconds
25
30
Half-life

Time for activity to decrease to a half.
A(T1/ 2 ) = A(0)e
A(0)
1
=
A(T1/ 2 ) 2
−λ T1 / 2
T1/ 2 =
0.693
ln( 2)
λ
Mean life

The number of disintegrations in the mean (or
average) life is equal to the number of
disintegrations in the infinite time.
∞
∫0
A(t )dt = A(0)Ta
Ta = 1.44T1/ 2
Specific Activity
Activity per unit mass, Ci/g.
 Radioactive isotopes with high specific
activity are preferable as radioactive
tracers .
 Co-60 source has higher specific mass
than Cs-137.

Radioactivity Example 1
1.
2.
The number of atoms in 1 g of 226Ra.
The activity of 1 g of 226Ra.
(A1) The atomic weight is the mass in gram of NA atoms. Here NA is the
Avogadro number.
N A M 6.022 ×10 23 ×1
=
= 2.664 ×10 21
N=
226.025
AW
(A2) T1/2 of 226Ra=1600 years.
0.693
= 1.373 ×10 −11 s −1
1600 × 365 × 24 × 60 × 60
A = λN = 3.658 ×1010 dps ≅ 1 Ci
λ=
Radioactivity Example 2
1.
2.
The decay constant of 60Co in months.
The activity of a 5000 Ci 60Co source after
4 years.
(A1) T1/2 of 60Co = 5.272 years = 5.272x12=63.264
months. λ=0.693/63.264=0.01095 1/month.
(A2)
−0.01095×12×4
A = 5000 × e
= 5000 × 0.5912 = 2956 Ci
Radioactive Series


The product of parent radioactive nuclide,
daughter, may be also radioactive.
There is a chain of decaying nuclides.
λ1
λ2
λ3
N1 ⇒ N 2 ⇒ N 3 ⇒
What is the relation between activities of three
nuclides?
Decay Series Diagram
Isotope T1/2 [years]
238U
4.5x109
234U
2.5x105
230Th
7.5x104
226Ra
1600
222Rn
3.82 days
206Pb
stable
http://www.medicalphysics.org/apps/medicalphysicsedit/Ch13.pdf
Radioactive Equilibrium:
Transient equilibrium
if T1 > T2
T1
A2 (t )
=
A1 (t ) T1 − T2
The daughter nuclide decays with the decay
constant of the parent.
A
Molybdenum-99 generator
Mo99
Tc99m
Tc99m after "milking"
100
90
80
70
60
50
40
30
20
10
0
T1/2:
99Mo
= 67 hours
99mTc = 6 hours
0
20
40
60
80 100 120
Hours
Notes: only 87% of Mo-99 decays to Tc-99m. 13% decays directly to Tc-99.
Radioactive Equilibrium:
Secular equilibrium
if T1 >> T2
A2 (t ) = A1 (t )
λ1 N1 = λ2 N 2 = λ3 N 3 = ....
A
Radium-226 Source
100
90
80
70
60
50
40
30
20
10
0
Ra226
Rn222
0
20
40
60
Days
80 100 120
T1/2:
226Ra
= 1600 years
222Rn = 3.824 days
Outline
I. Introduction
II. Radioactivity
III.Modes of Radioactive Decays
IV.Nuclear Reactions
Modes of Radioactive Decay


Alpha (α) particle decay
Beta (β) particle decay





Negatron (electron) emission, β− decay
Positron emission, β+ decay
Electron capture (EC)
Gamma (γ) emission
Internal conversion


Auger electron
Isomeric transition
Spontaneous fission
Alpha particle decay (1)




A nucleus emits alpha (α) particle, which is
positively charged by loosing two atomic
electrons from an helium atom.
α particle is a helium nucleus, whose atomic
number is 2 and mass number is 4. It is
composed of two neutrons and two protons.
Heavy nuclei tends to decay via α-decay.
238U, 226Ra, and 222Rn are α particle emitters.
Alpha particle decay (2)
A
A− 4
4
Z X → Z − 2Y + 2 He + Q
226
88
Ra 1622
a → Rn + He + 4.87 MeV
222
86
4
2
Energy Level Diagram: 226Ra
226Ra
88
α2 (5.5%), 4.60 MeV
γ, 0.18 MeV
222Rn
86
α1 (94.5%), 4.78 MeV
−
Beta minus decay: β decay
A
A
Z X → Z +1Y
32
15
−
+ β +ν + Q
β
ν



→
+
+
+
P 14
S
1
.
7
1
MeV
.3 days
32
16
−
Total kinetic energy of β and ν.
Proton and neutron do decay


The half-life of neutron is 886.7±1.9 s (14.77min).
The half-life of proton is longer than 1025 years.
−
n → p + e +ν
+
p → n + e +ν
Energy Level Diagram: 32P
32P
15
β− (100%), Emax=1.71 MeV
32S
16
Energy Level Diagram: 60Co
60Co
27
β1− (99.8%), Emax=0.313 MeV
β2
− (0.12%),
Emax=1.486 MeV
γ1, 1.173 MeV
γ2, 1.332 MeV
60Ni
28
Energy Level Diagram: 137Cs
137Cs
55
β1− (94.6%), Emax=0.514 MeV
137mBa ,
56
β2− (5.4%), Emax=1.176 MeV
T1/2=2.55m
γ (85%), 0.662 MeV
IC, K(7.7%), L(1.4%), M(0.5%)
137Ba
56
+
Beta plus decay: β decay
A
A
Z X → Z −1Y
22
11
+
+ β +ν + Q
Na 2

→ Ne + β +ν + 1.82 MeV
.6 years
13
7
+
22
10

→ C + β +ν + 2.21MeV
N 10
.0 min
13
6
+
Energy Level Diagram: 13N
13N
7
2 x 0.511 MeV
2.21 MeV
β+ , Emax=1.19MeV
13C
6
Energy Spectrum of β
The excess nuclear energy of the reaction
is shared between β and (anti) neutrino.
 The energy spectrum of β particles is the
bell-shaped continuous distribution with the
maximum.
 The low energy part of electron spectra is
enhanced and that of positron spectra is
held back.
 The average β particle energy is 1/3 of the
maximum energy.

Energy Level Diagram: 64Cu
64Cu
29
EC (40.5%)
T1/2=12.70 h
β- (40%),Emax=0.571MeV
EC(0.6%)
64Zn
30
β+ (19.3%), Emax=0.657MeV
64Ni
28
Beta ray spectra: 64Cu
Number of β per unit energy
5
4
β+
3
2
β-
1
0
0
0.1
0.2
0.3
0.4
0.5
Kinetic energy [MeV]
0.6
0.7
Positron Emission Tomography
PET uses 0.511 MeV photons, produced
by electron-positron annihilation.
 PET needs radioisotopes, which emit
positrons through β+ decay.
 Photons are detected by photomultiplier
tubes.
 Tomographic image is reconstructed.

Siemens PET-CT
PET Isotopes
Nuclides
T1/2
Production
Carbon-11
20.4 min
10B(d,n)11C
Nitroten-13
9.96 min
12C(d,n)13N
Oxygen-15
2.05 min
14N(d,n)15O
16O(p,pn)15O
12C(α,n)15O
Fluorine-18
110 min
18O(p,n)18F
Copper-64
12.7 hrs
64Ni(p,n)64Cu
Electron Capture (EC)




An orbital electron is captured by a nucleus.
Often EC involves the K-shell electron (K capture).
Characteristic X-ray is emitted when the orbital electron
in a higher energy level falls to the hole in the K-shell.
Characteristic X-ray photon may be absorbed by the
atom, causing emission of electrons, Auger electron.
−
p + e → n +ν
A
X
Z
A
+ e→ Z −1Y
+ν + Q
Energy Level Diagram: 7Be
7Be
4
EC (10.3%)
EC(89.7%), E=0.862 MeV
γ (0.478MeV)
7Li
3
Energy Level Diagram: 125I
125I
EC(100%)
53
60.2 d
γ or IC (0.03546MeV)
125Te
52
Energy Level Diagram: 22Na
22Na
11
β+ (90.4%),Emax=0.54MeV
2 x 0.511 MeV
EC(9.5%)
γ (1.27MeV)
β+ (0.06%), Emax=1.83MeV
22Ne
10
Gamma Emission
Upon radioactive decay (α,β,or EC), a
nucleus is left in an excited state.
 The excited state transits to the ground
state by emitting gamma ray or internal
conversion.
 The gamma emitting nuclides are the major
source of gamma rays used for radiation
therapy.

Internal conversion (1)
It is “internal photoelectric effect”.
 A nucleus in an excited state transfers the
energy to one of orbital electrons.
 The electron, conversion electron, is
ejected from the atom.
 Internal conversion causes emission of
characteristic x-ray or Auger electrons.

Internal conversion (2)
Electron
electrons
K-shell
electrons
β- decay
γ
Z, N
N-1
Z+1
β-
Energy of ejected conversion electron = Eγ - EK
Auger Electrons (1)
A hole is created in the K, L, or M shell
after an electron is ejected from an atom
by electron capture or a high energy
charged particle or internal conversion.
 The hole is filled with an electron jumping
from a higher energy shell (or level) with an
emission of characteristic x-ray.
 Instead of x-ray, an electron in a higher
energy level, Auger electron, can be
ejected.

Auger Electrons (2)
X-ray
M-shell
Auger electron
L-shell
K-shell
hole
Energy of x-ray = EK – EL
Energy of Auger electron = (EK – EL) – EM
Isomeric transition



An excited nucleus is in metastable state.
The nucleus is called isomer and it is in an
isomeric state.
The transition to the ground state is called an
isomeric transition.

99mTc
is isomer of 99Tc. Its
half life is 6 hours.
Spontaneous Fission
Heavy nuclides undergo spontaneous
fission decay. The nuclides break into two
heavy nuclides naturally.
 Cf-252 decays through spontaneous
fission process with T1/2=2.645 years. It
has been used as a neutron source. One
of medical applications is for neutron
therapy.

Chart of Nuclides (1)
Z
A
www.lbl.gov
Chart of Nuclides (2)
Outline
I. Introduction
II. Radioactivity
III.Modes of Radioactive Decays
IV.Nuclear Reactions
Nuclear Reactions
a + X → b + Y or X (a, b)Y
A lighter nuclide a bombards a heavier nuclide X.
The mass of product b is much smaller than the
mass of product Y for the energy of a below 100
MeV. (or Spallation reactions or fission).
Some physical quantities must be conserved
before and after nuclear reactions.
Energy (+mass)
Linear momentum
Angular momentum
Electric charge
Parity
Isospin
Number of nucleons
Number of leptons
Invariant under charge conjugate
Invariant under time reversal
Nuclear reaction energy, Q
a + X → b +Y +Q
Q = (M a + M X )c − (M b + M Y )c
2

Positive Q => exoergic


Fission reactions
Negative Q => endoergic

Threshold energy of reactions
2
Types of nuclear Reactions
(α,p) reactions
 (α,n) reactions
 Proton bombardment
 Deuteron bombardment
 Neutron bombardment
 Photo disintegration
 Fission
 Fusion

(α,p) reactions
4
2
He + X → H +
A
Z
1
1
A+ 3
Z +1
Y +Q
4
14
1
17
2 He + 7 N →1 H + 8 O
+Q
Mass (amu)
Mass (amu)
14N
= 14.003074
17O
4He
= 4.002603
1H
18.005677
= 16.999133
= 1.007825
18.006958
Q = -0.001281 x 931= -1.19 MeV
(α,n) reactions
4
2
He + X → n +
A
Z
9
A+ 3
Z +2
Y +Q
Be(α , n) C
12
Mass (amu)
Mass (amu)
9Be
= 9.012182
12C
4He
= 4.002603
n = 1.008664
13.014785
= 12.000000
13.008664
Q = -0.006121 x 931= -5.70 MeV
Proton bombardment
1
1
H+ X→
A
Z
7
A+1
Z +1
Y +Q
Li ( p, γ ) Be
8
Mass (amu)
Mass (amu)
7Li
8Be
= 7.016003
= 8.0053051
p = 1.007276
γ = 0.0
8.023276
8.0053051
Q = -0.006121 x 931= -16.7 MeV
Neutron bombardment
Neutron capture
 (n,p) reactions
 (n,α) reactions
 (n,γ) reactions

Thermal neutrons (E < 0.025eV)
induce fission reactions.
Fast neutrons (E=0.1 to 10MeV)
Neutron cross sections (total)
1H
208Pb
http://atom.kaeri.re.kr/endfplot.shtml
Photo disintegration
γ + X → n+ Y + Q
A
Z





A−1
Z
High energy photons can induce nuclear reactions.
(γ,n) reactions are the major source of neutrons in
accelerator rooms of radiation therapy.
(γ,n) reactions activate the material.
There is a minimum energy (threshold energy) of
photons for the reaction.
The energy spectrum of neutrons has a peak value
near 2 MeV.
Photoneutron production
Threshold energy
γ + Cu→ n+ Cu − 9.91 MeV
63
29
1
0
62
29
Element Threshold
energy [MeV]
Al
13.1
Fe
13.4
Cu
9.91 (10.86?)
W
6.19
Pb
6.74
β+, EC
T1/2=9.74 min
62
28
Ni
[Ref.] P.H.MaGinney “Shielding
Technique for Radiation Oncology
Facilities” Med Phys Publishing
Activation of Nuclides




Radioactive material can be produced by
bombarding atoms/nuclides with particles.
Radioisotopes for position emission tomography
are produced with cyclotron accelerators.
Many of radiotracers for nuclear medicine are
generated in nuclear reactors.
Radioactive sources for radiation therapy are
produced in nuclear reactors or with
accelerators.
Activation reactions
Rate equation for the activation reaction is
dN2
= φN1σ − λ2 N 2
dt
φN1σ
−λ2t
1− e
N 2 (t ) =
λ2
(
)
φ is flux (density)
[particle/cm2/s]
Saturation activity
A2 (t ) ≅ φN1σ for l arg e t
Neutron-induced radioactive isotopes
Radioisotope
Source
nuclide
Half life
Decay
mode
Average
Photon
energy
Co-60
Co-59
5.26 y
β-
Ir-192
Ir-191
74.2 d
β-, EC
1.173 MeV
1.332 MeV
0.37 MeV
I-125
Xe-124
60.2 d
EC
28.5 keV
Pd-103
Pd-102
17.0 d
EC
20.9 keV
Activation of patients

A patient treated with high energy photon beams
can be activated.
γ+ O →
15
8
16
8
O
T
↓
1/2=2.05
15
7
N +e
min
+
Emax=1.73 MeV
Nuclear Fission
235
1
236
141
92
92 U + 0 n→ 92 U → 56 Ba + 36 Kr
1
+ 3 0n + Q
Thermal neutrons induce fission
reactions. The product neutrons induce
more fission reactions (chain reactions).
The products nuclides are called fission
fragments. There are many combinations
of Z and A for the fission fragments.
The fission fragments carry most of
fission energy (about 167 MeV).
Energy Distribution per Fissioning
Type
Energy [MeV]
Kinetic energy of fission fragments
167
Prompt gamma ray energy
8
Kinetic energy of neutrons
8
Gamma ray energy from fission
products
Energy of antineutrinos
7
7
Total = 197 MeV
Prairie Island Nuclear Power Plant
http://www.nucleartourist.com/us/prairie.htm
Reactor by-products
Radioisotope
Half life
Decay
mode
Photon energy
Mo-99
65.9 h
β-
0.14,0.74 MeV
I-131
8.0 d
β-
0.606 MeV
I-132
2.3 h
β-
1.22, 2.16
Xe-133
8d
β-
0.08 MeV
Cs-137
30.0 y
β-
0.662 MeV