Lecture 12 Radioactive Decay modes : Gamma, Fission, Cluster, Delayed n/p, Double Beta decay
IV.
Gamma Decay
Analogous process to photon emission from atoms and molecules (uv, x-rays, IR …)
A X∗ ≡ Am X → 0 γ + A X where m ≡ * = excited state
Z
Z
0
Z
Eγ ≈ Qγ
(recoil energy negligible)
i.e. Nucleus changes its energy state.
E2
γ
E1
1
E0
γ
γ
I2, π
Eγ 1 = E2 − E0
2
Eγ 2 = E2 − E1
I1, π
Eγ 3 = E1 − E0
3
I0, π
[ Qγ = Eγ + ER ; ER ~ eV ]
A.
Eγ 1 = Eγ 2 + Eγ 3
M⎯ssbauer effect ]
Occurrence
1. De-excitation after nuclear reactions or radioactive decay.
t1/2 (γ) ≳ 10−14s
ELECTROMAGNETIC INTERACTION
2. t1/2 (γ) = f (Eγ, ΔI, Δπ)
Large Eγ, ΔI = 0, Δπ = NO
Short t1/2 (γ):
Small Eγ, ΔI = large, Δπ = YES
Long t1/2 (γ):
3. Isomers:
t1/2 ≳ 10−6s (arbitrary definition)
Unusually long-lived γ-ray emitters
105 y
210m
m = meta stable
⎯→
83 Bi(Iπ = 9− ) ⎯ ⎯ ⎯
210Bi(Iπ = 1− ) + γ
83
NOTE: For radioactive labeling of compounds, would like
t1/2 ~ hours – days ⇒ stable product
B. Competing Mechanisms for γ-decay
1. Photon Emission: 00 γ
Two-body decay ⇒ DISCRETE ENERGIES
2. Internal Conversion: IC
Eγ
a. Excess nuclear energy transferred to an atomic electron
e−
A +
Am
X
→
X
+
e
Z
Z
γ
2s
Ee = Eγ − BE(e−)
BE(e−) = electron binding
energy
1s
b. Electrons observed in Nuclear Decay
Distinction
IC: Ee− is monoenergetic ; Discrete spectra: Ee− ~ Eγ (MeV)
EC Auger: Ee− is monoenergetic ; Discrete peak: Ee− ~ Exray (eV)
Negatron Decay: ; Spectrum continuous: Emax ~ Qβ−
c. Atomic Rearrangement
Vacancy in inner shell (same as EC)
• IC is followed by x-rays and Auger electrons
• IC – x-rays characteristic of parent (ΔZ = 0)
• EC – x-rays characteristic of daughter (ΔZ = −1)
d. Competition between γ and IC:
• Large Z −
Favors IC; more compact orbitals; higher
probability that e− is inside nucleus
• Large ΔI −
• Low Eγ
3.
−
favors IC; since e− has mass, it can carry
away angular momentum easier.
favors IC; wavelength of γ close to that of
atomic electrons; high Eγ ⇒ short wavelength
Pair Production
A
Am
- + β- + Q
X
→
X
+
β
pp
Z
Z
REVERSE OF ANNIHILATION
a. Qpp
⎛ Am
= Δ⎜
⎝
⎞
A
X⎟ − [Δ X +
⎠
Δβ + + Δ β − ] ; Δβ+ = Δβ− = Δe−
⎛ Am ⎞
⎛A ⎞
X⎟ − Δ ⎜⎝ X⎟⎠ - 2Δ e− = Qγ
⎝
⎠
Δ⎜
Qpp = Qγ − 1.022 MeV
= Eβ+ + Eβ−
∴ Pair Production cannot occur unless Qγ ≥ 1.022 MeV
b. Momentum Conservation: p(β+) ⇒ Eβ+ = Eβ−
∴
NOTE: eventually the β+
annihilates and gives 1.022
MeV back
E − 1022
MeV
.
γ
E ± =
β
2
4. All Three Modes Compete
V.
Low Eγ
→
IC
(≲ 0.2 MeV)
Qγ − EBE
ELECTRON
Medium Eγ
→
γ
(~ 1 MeV)
Qγ
PHOTON
High Eγ
→
β±pair (≳ 2 MeV)
Qγ −1.022
β− − β+ pair
Exotic Decay Modes (i.e. rare)
Usually involve nuclei far from stability or very heavy nuclei
A.
Spontaneous Fission
A
A
A
X → Z1 B + Z 2 C + QSF
Z
1
2
1.
A1 ≈ A2 ~ A/2
Z1 ≈ Z2 ~ A/2
Mass Split
Asymmetric due to influence of nuclear shells; e.g., 132 Sn
50 82
Example: 252 Cf
98
25
. y
⎯ ⎯⎯
⎯→
140Xe* + 112 Ru* + Q
; QSF ≈ 190 MeV
SF
54
44
β−,γ
STABLE
β−,γ
STABLE
2.
Mass Yield Curve
i.e., NO SPECIFIC EQUATION Since there are many
ways the nucleus can divide, all of which move up
<BE> curve. Problem: nuclear waste management
P(A)
A
3.
QSF: Energy Release
a. Most of the energy goes into the kinetic energy of the fragments.
b. Remainder goes into heating fragments (~10%)
Bad news: copious γ and β emission
4.
Occurrence:
A > 230
232 Th (t = 1018 y)
SF
90
258 Fm (t = 0.4s)
SF
100
SF limits heavy element production in both nature and laboratory
Examples:
5.
B.
Barrier Penetration Problem: hard to get big chunks of matter to separate
unless Z is very large (large Coulomb repulsion). Odd nucleons slow down
rate; most new elements > 106 are odd-A
Cluster Decay
14
C, 18O, 22Ne have been observed from 88Ra, 90Th and 92U isotopes
Produces products near Z = 82, N = 126
closed shells
C.
Delayed Proton and Neutron Decay
1.
Decay of highly neutron- or proton-rich nuclei
2.
Binding energies must be low; usually from excited states with
E* > Bp or Bn
Example:
n
87 Kr
36 51
86 Kr
36 50
note closed
shell
D.
Double Beta Decay
Simultaneous Emission of two β− particles ; i.e., e − e ⇒ e-e
e.g.
−
130 Te → 130Xe + 2β + 2 ν + Q
; Q − Large
54
−1
52
2β
2β −
t1/2 ≳ 1021y
VI.
Summary of Decay Modes