Transcript Interaction of Charged Particles with Matter

Decay
Discovery of a Radioactivity
a decay :
A
Z
XN 
A 4
Z 2 N 2
Y
a
Alpha Decay
2
Heavy nuclides (Gd, U, Pu,..)
spontaneously emit a particles.
Mass systematics  energetically allowed
Marie & Pierre Curie (18971904) studied “pitchblende”
Ra: powerful a emitter
electrometer
a particles energetically preferred (light particles)
W. Udo Schröder, 2007
Energy Release in a Decay
Z=82
“Q-Value” for a Decay:
Q=B(4He)+B(Z-2,A-4)-B(Z,A)
Alpha Decay
3
Shell effect at N=126, Z=82
Odd-even staggering
Geiger-Nuttall Rule:
Inverse relation between
a-decay half life and decay
energy for even-even nuclei
W. Udo Schröder, 2007
Examples: Alpha Decay Schemes/Spectra
Short-range a particles
Alpha Decay
4
Long-range a particles
100
251
Many a emitters:
Ea ~ 6 MeV (short range)
Heavy emitters also: Ea~ 8 MeV (long range)
251
100
247
Fm  98
Cf
a spectrum
W. Udo Schröder, 2007
Fm  98
Cf
247
Solution to a Puzzle: Tunneling the Coulomb Barrier
Answered Puzzle:
If nucleus stable : t1/2  ∞
If nucleus unstable : t1/2  0
George Gamov
Low stability  high a energy
a-Nucleus
Coulomb
Potential
Alpha Decay
5
Not found
in macroscopic nature
UaTh= 28 MeV
Gamov: Intrinsic a wave function “leaks” out
Ea=
4MeV
RaTh=9 fm
Nuclear
Potential
W. Udo Schröder, 2007
Resolution of Puzzle Quantum meta-stability
(if nucleus has intrinsic a structure, Pa=1):
Superposition of
repulsive Coulomb potential + attractive
nuclear potential creates “barrier” which is
penetrable for a particle
Quantal Barrier Penetration
1
E, U
General solution of Schrödinger Equ.:
Lin. Comb. of exponentials
3
2
 1( x )  A1eik1  x  B1e  ik1  x

 x
  x

( x )    2 ( x)  A2e 2  B2e 2

ik1  x

(
x
)

A
e
3
3

U
E
6
E
x0
0xd
xd
W. Udo Schröder,
2007
p1( x )  2mK  2mE  k1  k3
0
d
p2 ( x )  2m(E  U )  k2  i2
x
A3
2
Particle escape probability l l 
2
A1
(system decay) depends on
barrier height & thickness
the number of states
E
2


2
2 

1 k1  2


 1  
sinh2 (2d)

 k  
4


 1 2 
U:

16E
E
l  f T 
(1  )  e
U
U
Alpha Decay
1
2d
2m(U  E )
Barriers of Arbitrary Shape
Approximate by step function
N
N
i 1
i 1
U(r)
T   Ti   e
7

Ui
T  e G  e

2di
R
2 2

2m(Ui  E )
2m(U (r ) E )dr
R1
Alpha Decay
Gamov factor G
R1
R2
Application: Z1=2, Z2=Z-2
e2 Z1Z2
Coulomb potential : U(r ) 
 R1 R2  E / U
r
G 
2 2m
R2

R1
e2Z1Z2
 E dr  G 
r
f ( x ) : arc cos x 
W. Udo Schröder, 2007
2
e Z1Z2
2
2m R1
f(
)
R
2
E
x 1 x   (thick barrier ) f ( x )   2 
R1 R2
The Geiger-Nuttal Rule
t1 2  
Ea
a half life vs. a energy
G 
e2 Z1Z2
2m R1
f(
)
R
2
E
2
8
log
1
(years)
Alpha Decay
1
t1 2 
l
G 
e
e2 Z1Z2
log
W. Udo Schröder, 2007
1
T
 
t1 2
2
G
2m
f
Ea
 A
 Ea 


 U 
B
Ea
What are the Z dependent scaling factors A?
Decay Dynamics
Classical considerations/order of magnitude:
9
a
1. Pre-existence of a particle in nuclear medium, Pa
(Nuclear cluster structure  “Spectroscopic Factor S”)
2. Finite probability for barrier encounters, frequency, fa
(velocity, effective mass)
3. Barrier penetration, Ta (geometry of Coulomb barrier)
4. Angle of incidence on barrier, angular momentum, a
Great uncertainties in absolute decay rates
Alpha Decay
a-Nucleus
Potential
a
la  Pa  fa  Ta
UaTh= 28 MeV
Ea=4MeV
0
Ua
W. Udo Schröder, 2007
RaTh=9 fm
Nuclear
Potential
r
fa 
a

2 Ua  Ea  
2R
10 21 s 1
Pa  ??
2R
Angular Momentum and Parity in a Decay
Solve 1-D Schrödinger Equ. For a-daughter system with effective radial
potential (Coulomb + centrifugal)  conserved angular momentum
10
 2

  Veff (r ) r ,

 2

Veff (r )  U(r ) 
,m (r ,  ,  )
2
2  r 2

 1
 Er ,
,m
 r,
reduced
mass
,m (r ,  ,  )

m1m2
m1  m2
Alpha Decay
Moment of inertia (orbital ) :     r 2
a  wave function :
 r,
,m (r ,  ,  )
 j (r )  Ym( ,  )
ˆ Ym ( ,  )  () Ym ( ,  )
Spherical harmonics 
:
Spin/parity selection rule for a transitions:
W. Udo Schröder, 2007
Ii  If 
 i  ()   f
 = 0 most probable a decay
Higher  values hindered significantly because of small T
Estimate range of -values from Ea and nuclear radii !
-Dependent a Transmission Coefficients
 ≠ 0 but not very large: a-daughter effective radial potential
(Coulomb + centrifugal)  Linearization at barrier
UCoul (r ) 
2

 1
2  R2
2
Ueff ( , r )  UCoul (r ) 

 1
2  r

2
a
11
 dependent barrier : B  Ueff ( , r  R)
Ea
e2 Z1Z2 
1  1  1
R 
2Ea 
Ea


 1 
  R 0 1  1
4Ea
2  R2 


2

 1 

2  R2 
2

Alpha Decay
UCoul
R
R
r
G

2 2m
R

R
Absolute
values not
very good, by
orders of
magnitude
la  Pa  fa  Ta
W. Udo Schröder, 2007
2 1 
 e2Z Z
    E dr  G
1 2

0
2  a
r

2

r



2 1 
G 0
 

T  T  0  exp 

 2Ea
2  R2 



1 


T  T0  exp 2.027

1
3


ZA



2 1 
 
1 1
 2Ea 2  R2 


Can decrease T by
factors 5-10 for
=+1
Pocket formula
Loveland et al., Modern Nuclear
Chemistry, Wiley Interscience, 2006
a Decay Patterns
Guess some final nuclear spins I
a Decay of
251Fm
12
251
100 Fm,
Alpha Decay
a7
479 keV
a1
0 keV
247
98 Cf ,
W. Udo Schröder, 2007
From Krane, Introductory Nuclear Physics
3.11h,
7
2

5.3h,
9
2

Spontaneous Nucleon Decay
13
New: The “Drip” lines:
More limits to nuclear
stability
Alpha Decay
Sp
Sn
Near drip lines: nucleons can be
emitted from excited states.
Need secondary beams to explore
regions far off stability
Adapted from NSCL ISF White Paper, 2006
W. Udo Schröder, 2007
Sp
Sn
Proton Decay
Near proton drip line, nuclei become p-unstable at E* ~ 1 MeV.
Coulomb+centrifugal barrier  long lifetime (isomeric state)
58
Ni( 40 Ca, p3n) 94 Ag, N
14
dN/dEp
Alpha Decay
p-g
coincid.
Si
singles
I. Mukha et al., PRL 95, 22501 (2005)
W. Udo Schröder, 2007

94

Ag  2s 1
0.39 s
Alpha Decay
15
Di-Proton Decay
W. Udo Schröder, 2007
Alpha Decay
16
Spontaneous Neutron Decay
W. Udo Schröder, 2007
Spontaneous Cluster Decay
Solenoid Magnet Spectrometer
Telescope
ID(Z, E )
E-E
223Ra
Source
B 
Spectrometer Transmission
(acceptance)
17
Alpha Decay
Baffle
Gales et al., PRL 53 (1984)
W. Udo Schröder, 2007
Observed for 221Fr – 242Cm:
Cluster radioactivity (14C-34Si)
223
Ra  208 Pb  14C
Q  mRac 2   mPb  mC  c 2
 32.1MeV
energetically possible.
Magnetic spectrometer:
adjustable acceptance,
remove unwanted particles,
here: strong a lines
Can use very strong sources,
0.2 Ci 223Ra
Results:
223Ra
Decay Products
Measured Branching (Telescope in focus):
14C
  5.5  2.0  10 10
a
18
Expected from
Gamov factor:
Alpha Decay
T14C
Ta
10 3  10 4
Very different
preformation
factors ?
a
Gales et al., PRL 53 (1984)
W. Udo Schröder, 2007
E (MeV)
Structure Effects in Cluster Decay Half Lives
Reduced width g 02 
Ra
Isotopes
Alpha Decay
19
x.s.
g.s. x.s.
t1 2 
g.s.
g02
Daughter
222Ra
7.08· 10-6
208Pb
223Ra
8.91· 10-9
209Pb
224Ra
3.31· 10-6
210Pb
l  P  f T
f  5  10 21 s 1
Log t1 2  Log 0.6932  Log P  Log f  
Due to barrier
penetrabilities T
LnT  G
Hussonnois et al., PRC 42 R495 (1990)
W. Udo Schröder, 2007
2T
Parent
Ln 2
l
l
LnT
Ln 10
 const.  LnT  const.  G
Unpaired neutron suppresses
cluster emission from g.s.,
not from excited states
Theoretical Ambiguity
Prompt 1  step process
a  like cluster decay : lcl  Pcl  fcl  Tcl
20
Pcl  spectroscopic factor
Slow (viscous) shape deformation
Alpha Decay
Fission  like cluster decay : lfiss  ffiss  Tfiss
Fission and a approach
need different barriers 
map barrier shape by
inverse (fusion) process at
different energies.
A.A. Ogloblin et al., NPA 738, 313(2004)
W. Udo Schröder, 2007
Barrier for
cluster decay