Transcript Log ft values in Beta Decay

Log ft values in Beta Decay
Filip G. Kondev
[email protected]
2nd Workshop for DDEP Evaluators, Bucharest, Romania
May 12-15,2008
Some useful references
Books
“Week interaction and nuclear beta decay”, H.F. Schopper, 1966
“Handbook of nuclear spectroscopy”, J. Kantele, 1995
“Radiation detection and measurements”, G.F. Knoll, 1989
“Alpha-, Beta- and Gamma-ray Spectroscopy”, Ed. K. Siegbahn, 1965
Journal Articles
W. Bambynek et al., Rev. Mod. Phys. 49 (1977) 77
N.B. Gove and M.J. Martin, Nuclear Data Tables 10 (1971) 205
S. Raman and N.B. Gove, Phys. Rev. C7 (1973) 1995
B. Singh et al., Nuclear Data Sheets 84 (1998 487
Plenty of information available on the Web
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Introduction
Beta Decay: universal term for all weak-interaction
transitions between two neighboring isobars
Takes place is 3 different forms
b-, b+ & EC (capture of an atomic electron)
b+: p  n + e+ + n
EC: p + e-  n + n
~
b-: n  p + e- + n
a nucleon inside the nucleus is transformed into another
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Classification of b decay transition
Iipi
I iI f + L b +S b
Eb
Ifpf
L b l b -( b + ) +ln~ (n )
p ip f  (-1)
Lb

S b s b -( b + ) + sn~ (n ) 
0

1 or 
Lb = n defines the degree of forbiddenness (n)
allowed
when Lb=n=0 and pipf=+1
I  I i- I f  0,1
forbidden
when the angular momentum
conservation requires that
Lbn >0 and/or pipf=-1
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Classification of allowed decay
(p ip f  +1)
Fermi
Gamow-Teller
0+
0+
0+
Eb
1+
I  I i- I f  1
L b  0 S b 1 or 
I  I i - I f  0
Lb  0
S b  0 
2+
2+
Eb
Eb
mixed Fermi & Gamow-Teller
I  I i - I f  0
I i 0
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Classification of b decay transitions
Type of transition
I
pipf
0,+1
+1
1
2
3
4
.
k2
k3
k4
k5
.
-1
+1
-1
+1
.
1
2
3
4
.
0, k1
k2
k3
k4
.
-1
+1
-1
+1
.
Order of
forbiddenness
Allowed
Forbidden unique
Forbidden
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Some useful empirical rules
The fifth power beta decay rule:
the speed of a b transition increases approximately in
proportion to the fifth power of the total transition
energy (if other things are being equal, of course)
Ii
If
Eb
1

 [M ( Z ) - M ( Z  1) c 2 ]5
 depends on spin and parity changes between the initial
and final state
 additional hindrance due to nuclear structure effects –
isospin, “l-forbidden”, “K-forbidden”, etc.
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b decay lifetime
t  T1b/ 2i
T1exp
 / 2 partial half-life of a given b- (b+,EC) decay branch (i)
Pb i
ln 2
g2

n
T1/ 2 2p 3
W

1
peWe (W0 - We ) 2 F ( Z ,We )Cn dWe
g – week interaction coupling constant
pe – momentum of the b particle
We – total energy of the b particle
W0 – maximum energy of the b particle
F(Z,We) – Fermi function – distortion of the b particle wave function by the
nuclear charge
Cn – shape factor
Z – atomic number
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b decay Hindrance Factor
bi
2 2

T
g
 
n
1/ 2
 f nt
HFb  n   3
T1/ 2  2p ln 2 
W
f n   peWe (W0 - We ) 2 F (Z ,We )(Cn /  2 )dWe
1
statistical rate function (phase-space factor):
the energy & nuclear structure dependences
of the decay transition

2
contains the nuclear matrix elements
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Log ft values
log ft  log f + logt
coming from calculations
Decay
Mode
Type
I (pipf )
ballowed
EC + b+
0, +1 (+)
bEC + b+
1st-forb
unique
k2 (-)
coming from experiment
log f
log f 0log( f0EC + f0+ )
log f0- + log( f1- / f0- )
log[( f1EC + f1+ ) /( f 0EC + f 0+ )]
N.B. Gove and M. Martin, Nuclear Data Tables 10 (1971) 205
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Log f
 ENSDF analysis program LOGFT – both Windows & Linux distribution
http://www.nndc.bnl.gov/nndcscr/ensdf_pgm/analysis/logft/
 LOGFT Web interface at NNDC http://www.nndc.bnl.gov/logft/
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Log t
t  T1/ 2
bi
T1exp
 /2
Pb i
Pbi  [I tot (out) - I tot (in)]
I tot (out / in)   I i (1 + T i )
i
 T ( M 1) +  2 T ( E 2)
T ( M 1 + E 2) 
1+  2
 What we want to know accurately
T1/2, I, T & 
In
I tot (521+ 721)  0.086(16)
I tot (416+ 619)  0.78(10)
= 0.69(10)
(net)
Out
  0.0022 t  2.056106[s]  logt  6.31  log f  2.386  log ft  8.7
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Rules for Spin/Parity Assignments
 There are only a few
cases where unambiguous
assignment can be made
~1000 cases
 “pandemonium effect” –
neutron rich nuclei – log ft
is a just lower limit!
 needs to know the decay
scheme and its properties
accurately!
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Log ft values – latest review
~3900 cases -> gives
centroids and widths
B. Singh, J.L. Rodriguez, S.S.M. Wong & J.K. Tuli
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Implications for DDEP evaluations
log ft  a
t  T1/ 2
bi
T1exp
 /2
Pb i
log f + logT1exp
/ 2 - log Pb i  a
log f + logT1exp
/ 2 - a  log Pb i
a  log ft  9.5(8)
from systematics
log f  2.39
logT1exp
/ 2  2.49
from calculations
from experiment
1.5 10-2  Pb i  3.8 10-4
Pb i (expt )  0.012(8)
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…but be careful, nuclear structure is important
j2
j1
First forbidden  5 < log ft <10
j
7-
T1/2 =3.8x1010 y
log ft =20
K=7
8+
log ft =19
large angular momentum
re-orientation
K-forbidden decay
w
6+
4+
j=R
2+
K~0
0+
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