Issues on  -Decay Total Absorption Spectroscopy J.L. Tain Instituto de Física Corpuscular C.S.I.C - Univ. Valencia IAEA Specialists Meeting Vienna, 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 150 Ho decay: CLUSTER-CUBE: 6 EUROBALL Clusters in cubic geometry CLUSTER: 7 Ge detectors, 60% each Efficiency PP T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: Relation between  -strength S  and  -intensity I  : Statement of the problem:  -decay R ij : 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: g jk :  -response for j  k transition R k : response for level k b jk : branching ratio for j  k transition Problem: number of levels also: spectrometer resolution Solution: rebin the levels into  E New problems: b jk cannot be rebinned mismatch on energies Problem: b jk are in general unknown Solution: b jk 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) 333 NIM 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 inversion Solution: 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 : Lagrange multiplier, B : regularization matrix, V d : data covariance Algorithm: Maximum Entropy (ME) method: solution must maximize entropy S( f ): entropy, Algorithm: Expectation Maximization (EM) method: modify knowledge on causes from effects Algorithm: NIM A, submitted

Results of the EM algorithm

Comparison of the three algorithms LINEAR REGULARIZATION MAXIMUM ENTROPY EXPECTATION-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 neutrons gamma-rays The beta-delayed neutrons and the subsequently emitted gamma-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 + 3 He 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

BaF 2 scintillator: Rocinante (Surrey-Valencia)  -rays neutrons Pulse shape Direct neutron interaction: pulse shape depends on particle recoils have low energies ( E max =4A/(A+1) 2 E n ) their light is quenched (~3-5)  E THR  =100 keV  20 MeV n Inelastic & capture interaction time distribution ~10 ns

capture 0.5 % inelastic 30 % BaF 2 scintillator: 19F 135Ba 134Ba 136Ba

NaI  30ke V (mb)  th (mb) E C (MeV) E 1stEx (MeV) 23 Na I BaF 2  30ke V (mb)  th (mb) E C (MeV) E 1stEx (MeV) 19 F nat Ba LaBr 3  30ke V (mb)  th (mb) E C (MeV) E 1stEx (MeV) 79,81 Br , La LaCl 3  30ke V (mb)  th (mb) E C (MeV) E 1stEx (MeV) 35,37 Cl , La