22.02
INTRODUCTION TO
APPLIED NUCLEAR
PHYSICS
Lecture 2
1
SEMI-EMPIRICAL MASS FORMULA
M (Z, A) = Zm(1 H) + N mn − B(Z, A)/c2
With binding energy given by:
B(A, Z) = av A − as A2/3 − ac Z(Z − 1)A−1/3
(A − 2Z)2
+ δap A−3/4
−asym
A
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2
SEMI-EMPIRICAL MASS FORMULA
M (Z, A) = Zm(1 H) + N mn − B(Z, A)/c2
With binding energy given by:
Surface
Coulomb
B(A, Z) = av A − as A2/3 − ac Z(Z − 1)A−1/3
{
Volume
(A − 2Z)2
+ δap A−3/4
−asym
A
symmetry
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3
pairing
CHART of NUCLIDES (Z vs. A)
Z
Z
Z=A/2
)
o
U
Z
A
Z
4
Z
CHART of NUCLIDES (Z/A vs. A)
Z/A
N-
N- N
N-.
N-.N
N-
A
N
NN
N
5
NN
N
B/A: MAXIMUM
(binding energy per nucleon)
B/A [MeV]
9
8
7
Fusion
6
Fission
α-decay
5
4
3
0
50
100
150
Maximum B/A for 50 < A < 100
6
A
(Mass number)
200
250
RADIOACTIVE DECAY CHAIN
( −λ t
)
−λ2 t
1
λ1 e
−e
N2 (t) = N0
λ2 − λ 1
N1 (t) = N0 e−λ1 t
(
N3 (t) = N0
λ1 1 − e
(
)
−λ1 t
− λ2 1 − e
λ1 − λ 2
−λ2 t
)
7
MASS PARABOLA
M(Z,A=cst): Mass of nuclides at constant mass # A
A=125
56Ba
49In
b+
b-
55Cs
50Sn
51Sb
53I
52Te
8
54Xe
MASS PARABOLA
A=128
49In
b+
b50Sn
51Sb
53I
52Te
55Cs
54Xe
9
57La
56Ba
MASS PARABOLA
M(Z,A=cst): Mass of nuclides at constant mass # A
A
b
Odd A
A = 135
Even A
A = 102
?
?
ββ+
β-
β-
Even Z, even N
Atomic Mass (M)
Atomic Mass (M)
Odd Z, odd N
?
2δ
β+
ββ-
β-
EC
β+
Xe Cs
Ba La Ce
Nb Mo Tc Ru
Rh Pd Ag Cd
52 53 54 55
56 57 58
41 42 43 44
45 46 47 48
Te
Z
I
Z
ZA = 55.7
ZA = 44.7
Figure by MIT OpenCourseWare. After Meyerhof.
10
MIT OpenCourseWare
http://ocw.mit.edu
22.02 Introduction to Applied Nuclear Physics
Spring 2012
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