Experimental techniques to deduce J
Joint ICTP-IAEA Workshop on
Nuclear Structure and Decay Data Theory and Evaluation
28 April - 9 May 2008
Tibor Kibédi
p
Outline:
Lecture I: Experimental techniques to deduce Jp from
• Internal Conversion Coefficients
• Angular distributions and correlations
• Directional Correlations from Oriented nuclei (DCO)
Lecture II: New developments in characterizing nuclei
far from stability
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Electromagnetic Decay and Nuclear Structure
Energetics of g-decay:
p
Ji
Ei
Eg,
L, Dp
Ei = Ef + Eg + Tr
0 = pr + pg,
where Tr = (pr)2/2M; usually Tr/Eg ~10-5
Ef
Angular momentum and parity selection rules; multipolarities
p
Jf
|Ji - Jf| ≤ L ≤ Ji + Jf; L ≠ 0
Multipolarity known
DJ may not be unique
Dp = no;
E2, E4, E6
M1, M3, M5
Dp = yes;
E1, E3, E5
M2, M4, M6
Ji = Jf
E0
unique Dp
Mixed multipolarity
d(p`L`) = Ig(p`L`) / Ig(pL)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Electromagnetic decay modes
 Angular distribution
with spins oriented
 Angular correlations
 Polarization effects
g-ray
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Electromagnetic decay modes
 Angular distribution
with spins oriented
 Angular correlations
 Polarization effects
g-ray
M
 Electron conversion
coefficients
 E0 transitions: DL=0
electron conversion
L
K
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Electromagnetic decay modes
 Pair conversion
coefficients
 E0 transitions: DL=0
 Angular distribution
with spins oriented
 Angular correlations
 Polarization effects
e- - e+ pair
g-ray
M
 Electron conversion
coefficients
 E0 transitions: DL=0
electron conversion
L
K
Higher order effects: for example 2 photon emission is very weak
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Angular distributions of Gamma-rays
W ( )  1  A22 P2 (cos  )  A44 P4 (cos  )
1.2
2→
transition
2→
2 2transition,
Mixed,L`=1,
L=1, L`=2
mixed,
L=2
0.8
0.4
Max
A2
0.0
Max
A4
-0.4
-0.8
-1.2
-100
Mixing ratio d(pL/p`L`) = Ig(p`L`) / Ig(pL)
-80
-60
-40
-20
0
20
40
60
80
100
|d|
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Angular distributions of Gamma-rays
W ( )  1  A22 P2 (cos  )  A44 P4 (cos  )
1.2
2→
1 transition
2→
1 transition,
Mixed,L`=1,
L=1, L`=2
mixed,
L=2
0.8
A4Max
0.4
0.0
A2Max
-0.4
-0.8
-1.2
-100
Mixing
Mixing
ratio
ratio
d(pL/
d(p`L`)
p`L`) = Ig(p`L`) / Ig(pL)
-80
-60
-40
-20
0
20
40
60
80
100
|d|
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Angular distributions of Gamma-rays
Attenuation due to relaxation of nuclear orientation
0  Akk  Akmax ( J i , J f , L, L' ); k  2,4...
Akmax ( J i , J f , L, L' ) 
Fk ( LLJ f J i )  2d  Fk ( LL' J f J i )  d 2  Fk ( L' L' J f J i )
1 d 2
For Fk(LL`JfJi) see E. Der Mateosian and A.W. Sunyar, ADNDT 13 (1974) 391
Akk  Bk ( J i )  Akmax ( J i , J f , L, L' )
Nuclear orientation can be achieved
 by interaction of external fields (E,B) with the static moments of the nuclei at
low temperatures
 by nuclear reaction
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Angular distributions of Gamma-rays
(n,n )‘reaction on 92Zr
Sample (41 gr)
n`
Pulsed Proton beam 
θ = 40° - 150 °
Gas Cell
3H(p,n) @ E = 4.9 MeV
p
En = 3.9 MeV
Figure courtesy of S.W. Yates
C. Fransen, et al., PRC C71, 054304 (2005)
at Univ. of Kentucky
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Angular distributions of Gamma-rays
(n,n )‘reaction on 92Zr
92Zr(n,n`)
reaction
12 angles and
Eg = 2123.0 keV
12 hours / angle
g-spectrometer at 1.4 m
Fit to data
C. Fransen, et al., PRC C 71, 054304 (2005), at Univ. of Kentucky
W ( )  A0  A22P2 (cos  )  A44P4 (cos  )
Deduced
A2=A22/A0
A4 = A44/A0
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
Typical values
A2
A4
DJ=2 (stretched quadrupole)
+0.3
-0.1
DJ=1 (stretched dipole)
-0.2
0
+0.5 to -0.8
>0
DJ=1, D+Q
ICTP-IAEA Workshop 7-May-2008
Angular distributions – mixing ratio
‘
Beam defines a symmetry axis
W ( )  1  k 2,4 Bk ( J i )  Akmax ( J i , J f , L, d )
where Bk(J) is the statistical tensor
Bk ( J i ) 
 Ji
 (1)
J i m
m J i
Eg = 2123.0 keV
(2k  1)( 2 J i  1) 
 J i J i k  Exp( m 2 / 2 2 )

  J i

m
m
0


 Exp(m2 / 2 2 )
m  1
Approximation with
Gaussian distribution
Mixing ratio, d deduced from 2 of
Wexp ( )
Wcalc ( )
d= 0.69(16) (D+Q)
as a function of d
But no information on Electric or Magnetic character: E1+M2 or M1+E2
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Directional Correlations from Oriented nuclei (DCO)
‘
zk
J1
g1(k1)
L1 L`1 d1
2
1
g2(k2)
J2
L2 L2` d2
J3
xk
1
yk
2
For a J1 → J2 → J3 cascade (see A.E. Stuchbery, Nucl. Phys. A723 (2003) 69)
 k1 k k2 

W (1 ,1 ,2 , 2 )    k1q1 (J1 )( 1)
(2k  1)( 2k1  1) 

k ,q ,k1 ,q1 ,k2 ,q2
  q1 q q2 
 Akk2k1 (dg 12 LL' J 2 J1 )Qk ( Eg 12 ) Dqk0 (1 ,1 ,0)
k1  q1
 Ak 2 (dg 23LL' J 3 J 2 )Qk2 ( Eg 23 ) Dqk220 ( 2 , 2 ,0)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Directional Correlations from Oriented nuclei (DCO)
example
‘
184Pt
from natGd + 29Si @ 145
MeV CAESAR array (ANU)
2.0
M.P. Robinson et al., Phys. Lett B530
(2002) 74
1 0
1.5
1
48
1
97
10+
6+
4+
2+
g2 (□)
1.0
W 1 2
8+
g1
0.5
g2 (●)
1.5
g2 (○)
1.0
0+
0.5
1
0
146
90
2
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
1800
90
180
2
ICTP-IAEA Workshop 7-May-2008
Directional Correlations from Oriented nuclei
DCO ratio
zk
J1
L1 L`1 d1
g1(k1)
2
1
g2(k2)
J2
L2 L2` d2
J3
By ignoring  dependence we get
W (1 , g 1 , 2 , g 2 )
DCO 
W (1 , g 2 , 2 , g 1 )
W (1 , g 1 )  W ( 2 , g 2 )

W (1 , g 2 )  W ( 2 , g 1 )
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
xk
1
yk
2
For stretched transitions
DCO
L 1 = L2
1
L1=1 & L2=2
~2
ICTP-IAEA Workshop 7-May-2008
Conversion electrons (CE)
Radial distribution of EWF
g-ray
M
L
Electron conversion
K
r
 ie bound state electron
 ef* free particle electron
Energetics of CE-decay (i=K, L, M,….)
Ei = Ef + Ece,i + EBE,i + Tr
g- and CE-decays are independent; transition probability
lT = lg + lCE = lg + lK + lL + lM……
Conversion coefficient
ai = lCE,i / lg
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
The physics of conversion coefficients
le,K
aK 
lg
le 
2p
m fi
2
d
dE
Fermi’s golden rule
Density of the final electron state
(continuum)
m fi   Nf *  ef* F,m  iN ie

Electron
Nuclear
Multipolar source
Same for g and CE
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
 ie bound state electron
 ef* free particle electron
ICTP-IAEA Workshop 7-May-2008
100
1000
Energy (keV)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
-
-
E5
-
10-4
aK NOT SELECTIVE
-
10-3
-
E4
-
10-2
ai depends on
1) Transition energy (Eg)
2) Atomic number (Z)
3) Multipol order (L;
the angular momentum
carried away)
4) Electric (El) or
magnetic (Ml)
character
5) The shell or subshell
the electron is
ejected
6) Atomic screening
7) Nuclear structure
effects (penetration)
-
E3
-
10-1
-
M5
E2
E1
-
100
-
ICC(K)
101
M3
M2
M4
M1
-
102
-
Pb
207Pb 569.698 E2202Pb 786.99 E5 204Pb 911.78 E5
207Pb 1063.656 M4+E5
-
-
-
103
-
Sensitivity to transition multipolarity
NOTE (3) and (4) often
referred as
multipolarity (pL)
ICTP-IAEA Workshop 7-May-2008
Mixed multipolarity and E0 transitions
d 
2
I g ( E 2)
I g ( M 1)
a M 1/ E 2
a M 1  d 2a E 2

1 d 2
In some cases the mixing ratio can be deduced
exp
a

a
d 2  Mexp1
a aE2
E0 transitions – pure penetration effect; no g-rays (Ig=0)
a
I CE

Ig
• Pure E0 transition: 0+ → 0+ or 0- → 0• J → J (J≠0) transitions can be mixed E0+E2+M1
a
I CE ( E 0)  I CE ( E 2)  I CE ( M 1)
Ig ( E 2) Ig ( M 1)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
134.363(18) keV M1+E2 transition in 172Yb
2(MR) hyper surface
CE data
1968Ka01 K
0.63(16)
1968Ka01 L1/L2 0.62(19)
1968Ka01 L2/L3 1.3(3)
MR=1.3(3) (ENSDF)
MR=1.52(24) (BrIccMixing from Chi-squared fit)
MR=1.5(+12-4) (BrIccMixing from Χ2(MR) hyper surface)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
104
M1-shell
103
-
-
-
-
-
-
-
105
-
More on conversion coefficients
Z=30 (Zn) E2
L1-shell
102
K-shell
101
10-1
Electronpositron pair
production
10-2
10-3
Conversion coefficient
ai = lCE,i / lg
10-4
10-5
1
10
100
Energy (keV)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
1000
-
-
-
-
-
-
10-7
-
10-6
-
Total conversion coefficient
aT aK aL aM + ….+ap
Fewer electrons than g-rays
ICC
100
ICTP-IAEA Workshop 7-May-2008
Measuring conversion coefficients - methods
 NPG: normalization of relative CE (ICE,i) and g (Ig) intensities via
intensities of one (or more) transition with known a
I CE ,i
ai 
Ig
 I g*

*
  * a 
 I CE
 KNOW N
 CEL: Coulomb excitation and lifetime measurement
aT 
2.829  1011  Eg5 (keV )
B( E 2)  (e b )  T1 / 2 (ns )
2 2
1
 XPG: intensity ratio of K X-rays to g-rays with K-fluorescent yield, K
I KX
1
aK 

Ig  K
And many more, see Hamilton`s book
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Internal Conversion Process – the Pioneers
E. Seltzer & R. Hager
E.F. Zganjar
T.R. Gerholm
M.E. Rose
J.H. Hamilton
M. Sakai
May 1965, Vanderbilt University, Nashville, Tennessee
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Conversion electron spectroscopy with PACES
Based on new data, favoured interpretation is that isomer is not a
high-K, but Kp=0+
Electrons are vital!
K/L(E3) ~ 0.3
Built by E. Zganjar,
LSU
Figure courtesy of P.M.
Walker (Surrey) and P.
Garrett (Guelph)
channel number (0.6 keV/ch)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Magnetic spectrometers
Superconducting solenoid
 Broad-range mode – 100 keV up to a few MeV
 Lens mode – finite transmitted momentum bandwidth
(Dp/p~15-25%) – high peak-to-background ratio
Mini-orange (looks like a peeled orange)
 transmission > 20%
 small size and portability, but
poorer quality
ATOMKI,
Debrecen
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Super-e Lens (ANU)
Si(Li)
M
etic
agn
d
fiel
CE
Target
Beam
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
gammas
delayed (35 - 550 ns)
@ 76 MeV
Pulsed beams (~1 ns) with 1.7 ms
separation
10+
11-
293.2
679.1
= 23 ns
9-
= 28.8 ns
3038.8+
3033.9+
142.7
436.1432.5427.5
= 133 ns
2606.4+
2602.7+
385.7
2217.0+
912.1
counts
12+
+
2896.0+11
11-
912.1
385.7
400
526.2
194Pt(12C,4n)202Po
571.2
800
x102
676.8
202Po
442.7
Super-e Lens
(ANU)
0
electrons
442.7E2
915.7
571.2E2
526.2
= 168 ns
8+
6+
1690.7+
1690.7
676.8 E2
4000
442.7
4+
202Po
84 118
1248.0
571.2
2+
676.8
E3
2000
E2
676.8
0+
385.7
912.1
E1
526.2
0.0
0
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
400
600
800
transition energy (K) in Po [keV]
1000
ICTP-IAEA Workshop 7-May-2008
The SACRED Electron Spectrometer
(Liverpool-JYFL)
H. Kankaanpää et al., NIM A534 (2004) 503
see also P.A. Butler et al., NIM A381 (1996) 433
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
The SACRED array
example
208Pb(48Ca,2n)254No
S. Eeckhaudt, et al.,
Eur. Phys. J. A 25, 605 (2005)
P.A. Butler, et al.,
Phys. Rev. Lett. 89, 202501 (2002)
Sacred + RITU
recoil tagged CE
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Super-e & Honey (ANU)
liquid helium
reservoire
vacuum
feedthrough
Electrons from atomic
collisions are the major
difficulty in low energy
CE spectroscopy using
ion induced reactions
superconducting
coils
coaxial
cable
HPGe
electron trajectory
-50 kV barrier
target
Honey
array
B
PTFE insulator
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
Super-e Honey (ANU)
eeg coincidences
total CE gate
Gate on ALL CE
569.9
970.2
996.0
873.3
906.3
823.2
862.4
896.2
510.1
538.2
602.9
614.2
800
529.9
565.1
1600
337.9
counts
aT(M1) = 7.3!
2400
262.5
291.6
Eg=63.1 keV transition not
visible in the gamma spectrum
Bi X-rays
275.3
3200
6000
0
63.1 g:aT(M1)7.3
K-shell conversion not allowed
BEK=90.5 keV
totalgammas
Gamma gate
Gate on ALL
4000
counts
63.1 LM
2000
208Pb(p,n)208Bi
x4
@ 9 MeV
K.H. Maier et al,
Phys. Rev. C 76, 064304 (2007)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
0
200
400
600
Energy [keV]
800
1000
ICTP-IAEA Workshop 7-May-2008
873.3
Super-e Honey (ANU)
eeg coincidences
970.2
996.0
906.3
862.4
896.2
823.2
614.2
602.9
510.1
529.9
400
565.1
538.2
538.2
291.6
800
337.9
counts
Bi X-rays
1200
569.9
262.5 275.3
63L+M+N CE gate
Gate on
on 63
63 LM
LM CE
CE
Gate
0
538 keV Gamma gate
63.1 g:a
g:aT(M1)7.3
(M1)7.3
63.1
T
Gate
Gate on
on 538.2
538.2 keV
keV
gammas
gammas
80
counts
63.1
LMLM
63.1
40
0
200
400
600
800
1000
Energy [keV]
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
ICC from total intensity balances –example 1
t
Out-of-beam (or decay) coincidence data
Igtoti  Ig i  (1  a itot )  Igtoto  Ig o  (1  a otot )
a otot  ( Ig  o / Ig  i )  (1  aitot )  1
i
o
a tot (350)  0.05
228/463
1085/463
IN
OUT
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
ICC from total intensity balances – when to use
1014
1013
Ta
Total ICC (Z=73)
1012
1011
1010
109
• Be careful near energies close to shell
binding
106
105
M3
104
103
aotot  ( Ig  o / Ig  i )  (1  aitot ) 1
M2
i
o
E3
102
101
E2
M1
100
10-1
E1
10
L
K
100
1000
-
1
M
-
N
-
dIg/Ig ~ 10%
10-2
10-3
10-4
• Accuracy of gamma-ray measurements
controls the range of its use
-
ICC(total)
108
107
Log10(Egamma)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
ICC from total intensity balances –example 2
In-beam: only when gating from “above”
Igtoti  Ig i  (1  a itot )  Igtoto  Ig o  (1  a otot )
I gtoti  I gtoto  I sf
577/611
Side
feeding
207/311
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
ICC from X- and g-ray intensities
Vacancies in the atomic shell give rise to rearrangements in the shells which are
accompanied by the emission of
• X-rays
•
Auger electrons
K x-rays:
Ka(K-L shells)
Kb (K-M, K-MN, etc. shells)
I KX  I K  K
B Schönfeld and h. Jansen, Nucl. Instr. and Merh. in Phys. Res. A 369 (1993) 527.
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008
ICC from X- and g-ray intensities
Singles gamma measurement
• No other photon and/or contaminates
• Well calibrated spectrometer
• Correct treatment of the photon attenuation,
scattering, etc.
• Knowledge of the fluorescence yield
N. Nica, et al. Phys. Rev. C75 (2007) 024308
N KX  g
a K K 

N g  KX
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
Ba-KX
661.657g
ICTP-IAEA Workshop 7-May-2008
Acknowledgements
G.D. Dracoulis , G.J. Lane, P. Nieminen, H. Maier (ANU)
F.G. Kondev (ANL)
P.E. Garrett (University of Guelph and TRIUMF)
S.W. Yates (Univ. of Kentucky)
Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University
ICTP-IAEA Workshop 7-May-2008