issues on -decay total absorption spectroscopy j.l. tain [email protected] instituto de...
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Issues on -Decay Total Absorption Spectroscopy
J.L. Tain
[email protected]://ific.uv.es/gamma/
Instituto de Física Corpuscular
C.S.I.C - Univ. Valencia
IAEA Specialists Meeting Vienna, 12-14 December, 2005
• Total absorption spectroscopy: how, why
• How reliable are the results from TAS ?
• -delayed neutron emission: a problem for TAS?
-decay
• Total absorption gamma-ray spectroscopy is the best technique to measure the -decay strength distribution over the entire energy
window in particular for nuclei far from the stability.
• Total absorption spectroscopy, using large 4 scintillation detectors, aims to detect the full -ray cascade rather than individual -rays as in high resolution spectroscopy, using Ge detectors.
• Total absorption spectroscopy avoids the “Pandemonium effect” (misplacement of -strength) when constructing level schemes in high resolution spectroscopy.
CLUSTER-CUBE at GSI
The Pandemonium effect in 150Ho decay:
CLUSTER-CUBE: 6 EUROBALL Clusters in cubic geometry
CLUSTER: 7 Ge detectors, 60% each
Efficiency
P
T
• How do we extract the -strength from the measured TAS spectra?• How reliable is the result?
Relation between TAS data and the -intensity distribution:
j
jiji orfRd fRd
k
kii ffI
21)( TEQf
IS
i
ii
Relation between -strength S and -intensity I:
Statement of the problem:
-decay
Rij: probability that for decay to level j
we register a count in channel i
Solution: f=R-1·d
The response matrix R can be constructed by recursive convolution:
kjkj RgR
1
0
j
kjkb
0
1
2
3
gjk: -response for j k transitionRk: response for level kbjk: branching ratio for j k transition
Problem: • number of levels 104-106
• also: spectrometer resolutionSolution: rebin the levels into ENew problems:• bjk cannot be rebinned• mismatch on energies
Problem: bjk are in general unknownSolution: bjk as externally introduced parameters
Caution: convolution of discretized continuous distributions
ASUME VALIDITY & CHECK SYSTEMATIC DEVIATIONS
Monte Carlo simulation of TAGS -ray (and -ray,…) response
GEANT3 and Geant4 simulations with detailed geometry, light production and PMT response
NIM A430 (1999) 333NIM A430 (1999) 488
Solution of linear inverse problems: d = R · f
is not f = R-1 · d
Problem: • statistical nature of the problem• numerical difficulties of the inversionSolution: • reproduce the data in 2 or maximum-likelihood sense• use a priori information on the solution
ill-posed or ill-conditioned problems
Solution of linear inverse problems: d = R · f
Linear Regularization (LR) method: • solution must be smooth: polynomial 22:min fBf
: Lagrange multiplier, B: regularization matrix, Vd: data covariance
Algorithm: dVRBBRVRf 1d
T1T1d
T λ
Maximum Entropy (ME) method:• solution must maximize entropy ff 21
)(:max
S
S(f): entropy,
iii
i
ii hfh
ffS ln)(f
Algorithm:
ii
k
skikiij
sj
sj fRdRff 2)()()1( 2
exp
Expectation Maximization (EM) method:• modify knowledge on causes from effects
jjji
jjiij fPfdP
fPfdPdfP
|
||
Algorithm:
ik
skik
isjij
iij
sj fR
dfR
Rf
)(
)()1( 1
NIM A, submitted
Results of the EM algorithm
Comparison of the three algorithms
LINEAR REGULARIZATIONMAXIMUM ENTROPYEXPECTATION-MAXIMIZATION
• LR gives strong oscillations and negative values for low statistics• uncertainties for LR and ME depend on Lagrange multiplier• ME and EM give very similar results• differences in averaged and/or accumulated strengths are bellow few percent
In the case of a real decay how much depends the solution on: • approximations used in the construction of the response matrix?• the assumption on branching ratios?
Use the nuclear statistical model to define a realistic decay:• level density formula + Wigner fluctuations: nuclear levels• -ray strength functions + Porter-Thomas fluctuations: branching ratios• -strength function + Porter-Thomas fluctuations: feeding probability
Average branching ratio matrix (based on statistical model parameters)
ME algorithm
Results:
LR, ME and EM algorithms
Average branching ratio matrix “Flat” branching ratio matrix
: average b.r.: flat b.r.: reference strength
• For decay-heat problems we want to measure the -strength of - decaying nuclei
• To clean spectra from isobar contamination at on-line separators we can use half-lifes, chemical selectivity or laser ionization
• A particular challenge is the application of this technique at the neutron rich side, due to the beta delayed neutrons
The beta-delayed neutronsneutrons and the subsequently emitted gamma-raysgamma-rays (may) become a contamination source
The main source of systematic uncertainty in TAS are contamination/background signals
Grand-daughter -rays are prompt with daughter -rays
Solution: “subtract” from data
• Measure them with high resolution (Ge array + neutron-detector array)
• Measure them with low resolution (TAS + neutron detector): MC simulations + test measurements planned
n
implantation
NE213
moderator +3He count
Neutrons interact through:
• elastic scattering
• inelastic scattering -rays
• capture -rays
• Recoils with very low energies and -rays
• Long interaction times (>s) delayed signals
MC simulations
Are the neutrons a problem ?
Available MC codes do not treat properly the generation of secondaries in inelastic and capture processes
BaF2 scintillator:
Rocinante (Surrey-Valencia)
-rays
neutrons
Pulse shape
Direct neutron interaction:
•pulse shape depends on particle
• recoils have low energies ( Emax
=4A/(A+1)2En )
• their light is quenched (~3-5)
ETHR=100 keV 20 MeV n
Inelastic & capture interaction time distribution
~10 ns
capture0.5 %
inelastic30 %
BaF2 scintillator:
19F
135Ba
134Ba136Ba
NaI30keV
(mb)
th
(mb)
EC (MeV)
E1stEx (MeV)
23Na 2 530 6.9 0.44
127I 635 6200 6.8 0.06
BaF2
30keV
(mb)
th
(mb)
EC (MeV)
E1stEx (MeV)
19F 6 10 6.6 0.11
natBa 52 1150 4.7-9.1 0.2
LaBr3
30keV
(mb)
th
(mb)
EC (MeV)
E1stEx (MeV)
79,81Br 472 6900 7.9,7.6 0.2
139La 38 9000 5.2 0.17
LaCl3
30keV
(mb)
th
(mb)
EC (MeV)
E1stEx (MeV)
35,37Cl 8 33100 8.6,6.1 1.2
139La 38 9000 5.2 0.17
638
63
145
46
2