Transcript LiCAS - University of Oxford

Lecture 3
nuclear stability, decays and
natural radioactivity
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
1
3.1 Overview

3.2 The Valley of Stability
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3.3 Decays
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11 Nov 2004, Lecture 3
interpreting the table of nuclides
SEMF and the valley of stability
SEMF and the iron mountain
classification
a-decay
b-decay
g-decay
fission and the rest
3.4 Natural Radioactivity
Nuclear Physics Lectures, Dr. Armin Reichold
2
Z
Z
N
b stable
Neutron
longlived
9 yrs)
Magic
(>10
Numbers
Even A=const.
Even
155
Even
Odd
53
3
Even
N=Z
Odd
Odd
50
3
4
5
Odd
11
Z=92 (U)
Proton
Magic
Numbers
• Even A stable nuclides
• Odd A stable nuclides
• odd-even summary
• Magic Proton Numbers
• Magic Neutron Numbers
• N=Z
A=58
(Fe58, Ni58)
• A=const @ 58
N
• Z=92 (Uranium)
• SEMF binding energy
3
Z
Z
N
b stable
Neutron
longlived
9 yrs)
Magic
(>10
Numbers
Even A=const.
Even
155
Even
Odd
53
3
Even
N=Z
Odd
Odd
50
3
4
5
Odd
11
Z=92 (U)
Proton
Magic
Numbers
• Even A stable nuclides
• Odd A stable nuclides
• odd-even summary
• Magic Proton Numbers
• Magic Neutron Numbers
• N=Z
A=58
(Fe58, Ni58)
• A=const @ 58
N
• Z=92 (Uranium)
• SEMF binding energy
4
3.2 The Valley of Stability
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
5
3.2 The Valley of Stability

Observation: stable nuclei not on a straight line in NZ plane. The SEMF predicts this:
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Rich structure in location of stable elements
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Coulomb term pulls them down (prefers Z<N) and …
… wins over Asymmetry term (prefers Z=N)
more stable isotopes of e-e then o-o nuclei (see b-decay)
No “life” beyond Z=92 (U) and a big gap from Z=82 to 92
(the region of natural radio activity)
Funny magic numbers for Z and N (see shell model)
But what about simple Ebind per nucleon
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
6
3.2 The Iron Mountain
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
7
3.2 The Iron Mountain
Binding Energy vs. A for odd-A nuclei
Iron
Not smooth because Z
not smooth function of A
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
8
3.3 Classification of Decays
Protons
a-decay:
b-
•
•
•
•
b+
emission of Helium nucleus
ZZ-2
NN-2
AA-4
b--decay
EC
•
•
•
•
emission of e- and n
ZZ+1
NN-1
A=const
b+-decay
a
Neutrons
g-decay
• emission of g
• Z,N,A all const
• emission of e+ and n
• ZZ-1
• NN+1
• A=const
Electron Capture (EC)
• absorbtion of e- and emiss n
• ZZ-1
• NN+1
• A=const
9
3.3 b-decay
or
Into the valley of stability along the const. A direction
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Q: How does nucleus “move” along constant A?
A: Via b-decay: nucleus emits e-,ne=(b-) or e+,ne=(b+)
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DMnucl > me for bDMatom> me for b-
& DMnucl > me for b+
& DMatom>2me for b+
or via EC: like (b+) but swallow atomic e- instead instead of
Z
emitting e+
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valley
DMnucl>-me
or
DMatom>0
unstable to
β+ decay
(or K capture)
Note: DMx = Mx(mother) – Mx(daughter)
Observe: e+- has continuous energy spectrum
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unstable to
maximum of Ekin(e+-) = Qb-Erecoil(daughter) ≈ Qb
β- decay
1<Qb/MeV<15
ne carries the rest of Qb solving long standing puzzle of energy
conservation in b-decay
N
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 b-decay
or
Into the valley of stability along the const. A direction

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Q: How does nucleus “move” along constant A?
A: Via b-decay: nucleus emits e-,ne=(b-) or e+,ne=(b+)
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& DMnucl > me for b+
& DMatom>2me for b+
or via EC: like (b+) but swallow atomic e- instead instead of
emitting e+
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DMnucl > me for bDMatom> me for b-
DMnucl>-me
or
DMatom>0
Note: DMx = Mx(mother) – Mx(daughter)
Observe: e+- has continuous energy spectrum
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maximum of Ekin(e+-) = Qb-Erecoil(daughter) ≈ Qb
1<Qb/MeV<15
ne carries the rest of Qb solving long standing puzzle of energy
conservation in b-decay
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 b-decay
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Q: Where do e+- and ne (ne) come from?
A: Can’t be “in” the nucleus because nucleus is to
small a box for electrons of this energy
2 2
2
 Ebox=n h /8mea = 0.37 TeV @ n=1, a=1fm (i.e. n decay)
e and n produced during decay (particle physics)
Think of b-decay as n-decay inside the nucleus
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n  p + e- + ne
Think of n-decay as quark decay inside the neutron
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d-1/3  u+2/3 + Wfollowed by W-e- + ne
d
u
u
n
d
u
d
p
eW-
11 Nov 2004, Lecture 3
n( e)
12
3.3 b-decay and SEMF
av=15.56 MeV
ac=0.697 MeV
2
EBind = av A - as A - ac
3
Z
A
as=17.23 MeV
2
1
3
e=even
o=odd
+ 12 MeV (e-e)
ap= 0 MeV (o-e or e-o)
- 12 MeV (o-o)
(N - Z )
1
- aa
+ ap
A
A
2
aa=23.285 MeV
• Q: How do we find SEMF predictions for b-decay
• A: We need the optimum Z (max binding energy) at fixed A.
To make this easier lets consider A=odd i.e. ap=0 (even-odd or odd-even)
 2ac 8a A 
 dE bind 
 dZ  = 4a A - Z  1 3 + A  = 0

A
A

11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 b-decay and SEMF


A  ac 2 3
A A 3
Z = 
A + 1  
+ 1

2  4aa
2  133.63

-1
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This yields:
evaluate:
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2

-1

A2/3<< 133  Z≈A/2≈N
A=105  Z=3/4 N (Z=45; N=60):
Quite close to reality. The nearest nuclei are:
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A=103; Z=45; N=58: 10345Rh ,even-odd, stable
A=106; Z=46; N=60: 10646Pd ,even-even, stable
A=105; Z=46; N=59: 10546Pd ,odd-even, stable
A=105; Z=45; N=60: 10545Rh ,odd-even, meta-stable,
decays via b- to 10646Pd in 38h
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 b-decay and SEMF
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Odd A. A=135
Odd A:
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Single parabola
even-odd and odd-even
single parabolic minimum
only one b-stable nucleus for
each odd A
nearly only single b-decays
double b-decay is 2nd order
weak process and very rare
β-
ββ+
ββ54
52
Te
11 Nov 2004, Lecture 3
I
Nuclear Physics Lectures, Dr. Armin Reichold
Xe
EC
56
Cs
Ba
58
La
Ce
Pr
15
3.3 b-decay and SEMF
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Even A:
two parabolae for o-o & e-e
lowest o-o nucleus often
has two options for decay
since double b-decay
extremely weak most e-e
nuclei have two stable
isotopes
nearly no stable o-o nuclei
Even A. A=102
Two parabolae separated by 2δ,
odd-odd and even-even
β+
ββ+
ββ+
44
42
Mo
11 Nov 2004, Lecture 3
β-
Tc
Nuclear Physics Lectures, Dr. Armin Reichold
Ru
Rh
46
Pd
Ag
48
Cd
16
3.3 b-decay and SEMF
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Consequence: 2 or more even A, 1 or no odd A
11 Nov 2004, Lecture 3
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3.3 a-decay
Observation:
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emits a with Ekin≈4 MeV
RTh≈1.2*2321/3 fm = 7.36 fm
a has Epot(RTh)=24 MeV
a has negative kinetic energy
up to R=8*RTh
232
90Th
Conclusion:
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a must tunnel out of the
nucleus
half lifes should have exp(Ekin)
dependence (true over 24
orders, see Geiger-Nuttal plot)
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 a-decay
DEsep≈6MeV per nucleon for heavy nuclei
DEbind(42a)=28.3 MeV > 4*6MeV
Neutrons
11 Nov 2004, Lecture 3
Protons
Alphas
Nuclear Physics Lectures, Dr. Armin Reichold
19
3.3 a-decay
(energetics)
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What can SEMF say about a-decay?
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E
a
bind
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Decay is possible if Mnucl(N,Z)-Mnucl(N-2,Z-2)>M(a)
SEMF as function of A only (dA=dN+dZ & dN=dZ) and ignoring pairing
term (odd A only)
a
Ebind/A
E bind
= E bind  Z=2,A=4
  E bind (Z , A) - E bind (Z - 2, A - 4)
[MeV]

dE bind
dE bind
 d E bind A  E bind
= 28.3 MeV  4
4
= 4 A
+
dA dZ =dN
dA
dA
A


Slope in Ebind/A (A≥120) is 7.7*10-3 MeV
E bind 

-3
28.3 MeV  4  A  7.7  10 MeV +

A 






slope:
7.7x10-3 MeV
E bind
 7.075 MeV + A  7.7  10 -3 MeV  Aacritical  151
A
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 a-decay
(energetics)
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What can SEMF say about a-decay?
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E
a
bind
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Decay is possible if Mnucl(N,Z)-Mnucl(N-2,Z-2)>M(a)
SEMF as function of A only (dA=dN+dZ & dN=dZ) and ignoring pairing
term (odd A only)
a
E bind
= E bind  Z=2,A=4  E bind (Z , A) - E bind (Z - 2, A - 4)

dE bind
dE bind
 d E bind A  E bind
= 28.3 MeV  4
4
= 4 A
+
dA dZ =dN
dA
dA
A







Slope in Ebind/A (A≥120) is 7.7*10-3 MeV
E bind 

-3
28.3 MeV  4  A  7.7  10 MeV +

A 

E bind
 7.075 MeV + A  7.7  10 -3 MeV  Aacritical  151
A
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 a-decay
(energetics-but)
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but the world is full of isotopes with A>151
and only 7 natural a-emitters observed with
A<206 because …
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barrier penetration has t~exp(-Ea)
energies are too low to get t << age of earth
(4*109 years)
Note: Shell effects O(1 MeV) make the life
times of –emitters deviate by several orders of
magnitude from SEMF predictions
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 a-decay
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SEMF says they should not exist
It is a shell effect, see next lecture
(the 3-odd ones out)
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 a-decay
(the fine print)
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To compute decay rates one needs

a lecture from Dr. Weidberg …
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
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3.3 g-decay
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Very similar to atomic physics transitions
Egatomic<100 keV ; Egnuclear<O(1 MeV)
But: heavy nuclear rotational states can have
Egnuclear, rot<O(10 keV)
Q: When do nuclear g-decays happen?
A: When there is not enough E to emit a
strongly interacting particle (Nucleon), often
after other nuclear decays
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
25
3.3 g-decay
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Q: What if J=0 nucleus needs to loose Energy
A: It can’t loose it via g

it could loose it via pair-creation if E>2me (virtual g
does not have to have S=1 and converts to pair in
e
1
emitted electron
g*
J=0 S0 state)
nucl.

e+ emitted positron
if E<2me could do internal conversion (a’la Auger
- emitted electron
e
in atomic)
g*
nucl.
11 Nov 2004, Lecture 3
e- absorbed atomic electron
Nuclear Physics Lectures, Dr. Armin Reichold
26
3.3 Fission and the Rest
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Fission in the liquid drop model:
Yet another tunneling
process
Complicated dynamics
Coulomb repulsion
fights surface term
Call it surface barrier
Theoretical limit:
Z2/A>18 (9842Mo) could
But does not because
……
11 Nov 2004, Lecture 3
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3.3 Fission and the Rest

It would take forever
15
Fission is mainly asymmetric
10
log10(t/1 year)

5
0
-5
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
Z2/A
28
3.3 Fission and the Rest
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Fission barrier changes
with Z2/A (and via
SEMF this is a change
with A)
Thus the huge lifetime
variation observed
Beyond Z2/A=43
(which does not exist)
there would be no
fission barrier
11 Nov 2004, Lecture 3
Epot [MeV]
Nuclear Physics Lectures, Dr. Armin Reichold
29
3.3 Fission and the Rest
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t=0
Fission products:
too rich in neutrons (valley is
curved ) emit neutrons
(needed for reactors)
highly excited  g-decay
still away from valley of
stability  b-decay
tunneling: tfis~exp(-Efis)
excited nuclei (n-capture)
decay much faster via
fission (reactors)
11 Nov 2004, Lecture 3
t≈10-14 s
t>10-10 s
Nuclear Physics Lectures, Dr. Armin Reichold
30
3.3 Others
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Best to emit something with very large
binding energy  12C has been observed
Anything else is just asymmetric fission
And then there is fusion (separate chapter)
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
31
3.4 Natural Radioactivity
• Three “chains” of natural radioactivity parents:
232Th, 235U, 238U (made by last super nova, t>age
of earth)
• 40K (odd-odd, Z=19, N=21, t=1.3*1019 years, b- or
EC)
• short-lived but naturally regenerated radioactive
nuclei, eg 14C (radio-carbon)
• natural life times O(1s)<t<age-of-universe
• all types of decays present
11 Nov 2004, Lecture 3
Nuclear Physics Lectures, Dr. Armin Reichold
32
Protons
93
α
89
α
87
α
85
α
206Pb
83
β-
α
91
210Po
238U
234U
ββ-
α
β-
β-
214Po
α
β-
α
β-
230Th
α
234Th
226Ra
222Rn
218Po
214Pb
81
210Tl
79
126
128
130
132
134
238U
11 Nov 2004, Lecture 3
136
138
series
Nuclear Physics Lectures, Dr. Armin Reichold
140
142
144
146
Neutrons
33