decay. w. udo schröder, 2007 alpha decay 2 nuclear particle instability-decay types there are many...
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Decay
Heavy Particle Decay
Alp
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eca
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W. Udo Schröder, 2007
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Nuclear Particle Instability-Decay Types
There are many unstable nuclei - in nature Nuclear Science began with Henri Becquerel’s discovery (1896) of uranium radioactivity
and man-made:
+30 30 30 J oliot &Al( ,n) P Si ,1934
Th source
Curi
, E
e
6 MeV
Types of decay:
1 1
1 1 1
A A 4Z N Z 2 N 2
A AZ N Z 1 N 1 e
A AZ N Z 1 N 1 e
A AZ N Z 1 N 1 e
A A A x yAZ N Z N Z Z y N x
decay : X Y
decay : X Y e
decay : X Y e
e capture : X Y ( e )
Fission : X F F xn yp
Various rare heavy particle(cluster ) decays
“weak” decays
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Discovery of a Radioactivity
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Marie & Pierre Curie (1897-1904) studied “pitchblende” Ra: powerful a emitter
Heavy nuclides (Gd, U, Pu,..) spontaneously emit a particles.Mass systematics energetically allowed
electrometer
A A 4Z N Z 2 N 2decay : X Y
a particles energetically preferred (light particles)
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Energy Release in a Decay
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“Q-Value” for a Decay:
Q=B(4He)+B(Z-2,A-4)-B(Z,A)
Shell effect at N=126, Z=82Odd-even staggering
Z=82
Geiger-Nuttall Rule:Inverse relation between a-decay half life and decay energy for even-even nuclei
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Examples: Alpha Decay Schemes/Spectra
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Short-range a particles Long-range a particles
Many a emitters: E a ~ 6 MeV (short range)Heavy emitters also: Ea~ 8 MeV (long range)
25124710098 FmCf
251 247100 98Fm Cf
spectrum
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Solution to a Puzzle: Tunneling the Coulomb Barrier
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Nuclear Potential
a-Nucleus Coulomb Potential
Answered Puzzle: If nucleus stable : t1/2 ∞If nucleus unstable : t1/2 0Not found in nature
Resolution of Puzzle Quantum meta-stability(if nucleus has intrinsic a structure, Pa=1):
Gamov: Intrinsic a wave function “leaks” out
Superposition of repulsive Coulomb potential + attractive nuclear potential creates “barrier”
RaTh=9 fm
UaTh= 28 MeV
ya Ea=
4MeV
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Quantal Barrier Penetration
Particle escape probability (system decay) depends on
barrier height & thickness the number of states
E, UGeneral solution of Schrödinger Equ.: Lin. Comb. of exponentials
1 11 1 1
2 22 2 2
13 3
( ) 0
( ) ( ) 0
( )
ik x ik x
x x
ik x
x A e B e x
x x A e B e x d
x A e x d
0 d x
21 3U
1 1 3
2 2 2
( ) 2 2
( ) 2 ( )
p x mK mE k k
p x m E U k i
122 2 23 21 2
221 21
11 sinh ( )
4
A kT d
kA
E
22 ( )
:
16(1 ) e
dm U E
E U
E ET
U U
E
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Barriers of Arbitrary Shape
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Approximate by step function
diN N m U Eii
i i
Rm U r E dr
RG
T T
T e
Gamo Gv factor
22 ( )
1 1
222 ( ( ) )
1
e
e
RRm e Z Z
G E dr G fRrR
f x arc x x x thick barrier f x R R
e Z ZCoulomb potential U r R R E U
r
me Z Z
E
21 2
1 2
222 2 22 11 2 ( )1 2 21
( ) : cos 1 ( ) ( ) 2 1 2
: ( ) /
2
Ui
U(r
)
R1 R2
Application: Z1=2, Z2=Z-2
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The Geiger-Nuttal Rule
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a half life vs. a energy
(years
)
tE
1 21
log
Gt e
T
EG f
U
t
me Z Z
E
E
1 11 2
221 2
1 2
2
1log
RG f
R
me Z Z
E
22 1( )1 2 2
2
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Angular Momentum and Parity in a Decay
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0
eff r m r m r m
eff
r m m
m
V r r E r
m mV r U r red mass
m mr
r
r j r Y
spheric
Moment ofi ne
al harmonics
rtia orbital
wave function
Y
2
, , , , , ,
21 2
21 2
2
, ,
( ) ( , , ) ( , , )2
( ) ( ) 1 .2
:
( , , ) ( ) ( , )
ˆ
)
:
(
(
mY
:
, ) ( ) ( , )
Solve 1-D Schrödinger Equ. For a-daughter system with effective radial potential (Coulomb + centrifugal) conserved angular momentum
Spin/parity selection rule for a transitions:
= 0 most probable a decayHigher values hindered significantly because of small T
Estimate range of -values from Ea and nuclear radii !
i fi fI I ( )
Nuclear Potential
a-Nucleus effective Potential
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a Decay Patterns
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1
From Krane, Introductory Nuclear Physics
0 keV
Guess some final nuclear spins Ip
Fm h
251100
9, 5.3 ,
2
Cf h
24798
7, 3.11 ,
2
479 keV
a Decay of 251Fm
a1
a7
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Cluster Decay
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2
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Experimental Data
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Br
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Alternative
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