Issues on -Decay Total Absorption Spectroscopy

J.L. Tain

Jose.Luis.Tain@ific.uv.eshttp://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