The two-step (and multiple-step) γ cascade method as a tool for studying γ-ray strength functions. Milan Krtička

Transcription

1 The two-step (and multiple-step) γ cascade method as a tool for studying γ-ray strength functions Milan Krtička

2 Outline The method of two-step γ-cascades following thermal neutron capture (setup at Rez near Prague) Two-step (multi-step) γ-cascades following resonance neutron capture (DANCE - LANL) Data processing - DICEBOX code Examples / Results (Enhancement of PSFs at low energies, Scissors mode)

3 The method of two-step γ-cascades following TNC Geometry: 6 m long neutron guide HPGe #1 γ 1 Target n γ 2 HPGe #2 4 mm Data acquisition: Three-parametric, list-mode - Energy E γ1 - Energy E γ2 - Detection-time difference

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5 TSC spectra Spectrum of energy sums A n E γ1 B n Quasi-continuum E γ2 B n -E f E f A+1 G.S. Time response function Energy sum E γ1 + E γ2 Detection-time difference i=-1 i=0 i=+1 j=-1 j=0 j=+1 Accumulation of the TSC spectrum from, say, detector #1: The contents of the bin, belonging to the energy E γ1, is incremented by q = α ij, where α ij is given by the position and the size of the corresponding window in the 2D space detection time energy sum E γ1 +E γ 2. List-mode data background-free spectrum

6 TSC spectra Spectrum of energy sums A n E γ1 B n Quasi-continuum E γ2 B n -E f E f A+1 G.S. Energy sum E γ1 + E γ2 TSC spectrum - taken from only one of the detectors i=-1 i=0 i=+1 Time response function Detection-time difference j=-1 j=0 j=+1 TSC Intensity (arb. units) X List-mode data Gamma-Ray Energy (kev)

7 Example of sum-energy spectra ( 57 Fe) TSC from thermal 56Fe(n,γ)57Fe reaction Gamma-ray energy sums Counts per 1 kev Gamma-ray energy sum (kev)

8 Example of a TSC spectrum Annih. Two-step γ cascades terminating at the 57 Fe ground state Counts per 1keV bin kev kev Dynamic range 1:1000 Gamma-ray energy (kev) Annih. Annih kev Annih kev Gamma-ray energy (kev)

9 Example of a TSC spectrum 9000 J π = 5/2 +, 251 kev terminal level in 163 Dy TSC intensity (relative units) Gamma-ray energy (kev)

10 Results of GEANT3 simulations - 95 Mo(n,γ) 96 Mo Annih. Backscattering Backscattering Annih. Annih. Backscattering Backscattering Number of GEANT Events per 10 kev Backscattering Annih. Doublet lev Annih. Backscattering Backscattering Annih. Annih. Backscattering kev kev Bremsstrahlung 0.96 % Annih % 0.57 % 0.54 % Bremsstrahlung Bremsstrahlung Gamma-Ray Energy (kev)

11 Two-step (multi-step) γ-cascades following neutron capture with higher energies (in the region of resolved or unresolved resonances) Measured with BaF 2 detector array (DANCE LANL, n_tof)

12 LANSCE Moderated W target gives white neutron spectrum, ~14 n s/proton DANCE is on a 20 m flight path / ~1 beam after collimation repetition rate 20 Hz pulse width 125 ns DANCE consists of 160 BaF 2 crystals

13 What can be checked? B n +E n E γ1 Neutron capturing states Intensity (arb. units) Multiplicity Gd Multiplicity = Multiplicity = 1 Multiplicity = Multiplicity = 2 Multiplicity > 4 Intensity (arb. units) E γ2 E γ Energy sum (kev) Energy sum (kev) Energy sum (kev) E γ4 Ground state 10 Multiplicity = 1 50 Multiplicity = Multiplicity = 4 Intensity (arb. units) 0 10 Multiplicity = Energy (kev) Multiplicity > Energy (kev) Energy (kev) E γ 1 E γ 2 E γ 3 E γ 4

14 What can be checked? We can gate on strong resonances (spectra from different resonance spins can be compared) unresolved region

15 How to process data from these experiments? Result of interplay of level density and γ-ray SF Comparison with predictions from decay governed by different level density formulas and γ-ray strength functions Code DICEBOX is used for making these simulations Simulates gamma decay of a compound nucleus within extreme statistical model

16 Simulation of γ cascades - DICEBOX algorithm Main assumptions: For nuclear levels below certain critical energy spin, parity and decay properties are known from experiments Energies, spins and parities of the remaining levels are assumed to be a random discretization of an a priori known level-density formula A partial radiation width Γ iγf (XL), characterizing a decay of a level i to a level f, is a random realization of a chi-square-distributed quantity the expectation value of which is equal to f (XL) (E γ ) E γ 2L+1 /ρ(e i ), where f (XL) and ρ are also a priori known Selection rules governing the γ decay are taken into account Any pair of partial radiation widths Γ iγf (XL) is statistically uncorrelated

17 Modelling within ESM Simulation of the decay: nuclear realization (10 6 levels Γ λγf ) precursors are introduced fluctuations originating from nuclear realizations cannot be suppressed Deterministic character of random number generators is exploited Level Number α c 1 2 α 1 α 2 0 s s s 3 1 Precursor Excitation Energy ζ αc ζ α1 ζ α2 E αc B n E α1 E α 2 α 3 0 s 4 1 E crit E α 3 Outcomes from modelling are compared with experimental data α n 0

18 Main feature of DICEBOX There exists infinite number of artificial nuclei (nuclear realizations), obtained with the same set of level density and γ-ray SFs models that differ in exact number of levels and intensities of transitions between each pair of them leads to different predictions from different nuclear realizations DICEBOX allows to treat predictions from different nuclear realizations The size of fluctuations from different nuclear realizations depend on the (observable) quantity - in our case intensity of TSC cascades - and nucleus Due to fluctuations only integral quantities can be compared In principle, simulation of detector response must be applied (very simple in the TSC setup, GEANT simulations for DANCE)

19 Example of a TSC spectrum Wide-bin TSC spectra

20 Examples of spectra Spectrum of energy sums Simulation Experiment B n -E f Energy sum E γ1 + E γ2

21 Normalization of experimental spectra Knowing intensity of one γ-ray cascade simulated/experimental TSC intensities to all final levels can be normalized Corrections to angular correlation and vetoing must be done

22 Enhanced PSF at low energies - 96 Mo

23 Enhanced PSF at low energies - 96 Mo

24 Enhanced PSF at low energies - 96 Mo Pictures with comparison similar but correct statistical analysis excludes also this model at 99.8 % confidence level Krticka et al., PRC (2008) the enhancement is very weak if any analysis of data from DANCE confirm this

25 Enhanced PSF at low energies - 96 Mo Experiment Simulations

26 Enhanced PSF at low energies - 96 Mo S. Sheets et al., Phys. Rev. C 79, (2009)

27 TSCs in the 162 Dy(n,γ) 163 Dy reaction deformed nuclei M1 1/ E1 E1-M1 & M1-E1 E1-E1 & M1-M1 - + π f = + π f = - Řež experimental data DICEBOX Simulations Entire absence of SRs is assumed

28 TSCs in the 162 Dy(n,γ) 163 Dy reaction A pygmy E1 resonance with energy of 3 MeV assumed to be built on all levels

29 TSCs in the 162 Dy(n,γ) 163 Dy reaction SRs assumed to be built only on all levels below 2.5 MeV

30 TSCs in the 162 Dy(n,γ) 163 Dy reaction Scissors resonances assumed to be built on all 163 Dy levels E = 3.0 MeV Γ = 0.6 MeV ΣB 6.2 µ N 2 M. Krticka et al. Phys. Rev. Lett. 92 (2004)

31 TSCs in the 162 Dy(n,γ) 163 Dy reaction Scissors resonances assumed to be built on all 163 Dy levels E = 3.0 MeV Γ = 0.6 MeV ΣB 3.0 µ N 2

32 TSCs in the 159 Tb(n,γ) 160 Tb reaction Preliminary results Entire absence of SRs is assumed

33 TSCs in the 159 Tb(n,γ) 160 Tb reaction Scissors mode with E = 3.0 MeV

34 TSCs in the 159 Tb(n,γ) 160 Tb reaction Scissors mode with E = 2.7 MeV ΣB 3 µ N 2 Very similar results also for E = 3.5 MeV ΣB 2-7 µ N 2 J. Kroll, diploma thesis, Prague 2009

35 157 Gd(n,γ) 158 Gd reaction deformed nuclei Experimental spectra

36 Experiment: TSC vs. DANCE

37 157 Gd(n,γ) 158 Gd reaction deformed nuclei No SR

38 157 Gd(n,γ) 158 Gd reaction E = 3.0 MeV ΣB 2.5 µ N 2

39 154 Gd(n,γ) 155 Gd reaction Experimental spectra

40 154 Gd(n,γ) 155 Gd reaction E = 2.6 MeV ΣB 2 µ N 2

41 Conclusions Two-step and multi-step γ cascade methods are very powerful tools for studying γ-ray SF Spectra from presented experiments cannot be processed without simulations DICEBOX code allows to keep inherent uncertainties due to statistical character of the decay under control

42 TSC meausurements Prague - F. Bečvář, M. Krtička, J. Kroll Řež - I. Tomandl DANCE LANL - T.A. Bredeweg, R. Haight, J.M. O Donnell, R.S. Rundberg, J.L Uhlmann, D. Vieira, J.M. Wouters, J.B. Wilhelmy, A. Chyzh, B. Baramsai LLNL - U. Angvaanluvsan, J.A. Becker, W. Parker, C.Y. Wu, D. Dashdorj NCSU - G.E. Mitchell Prague - F. Bečvář, M. Krtička Dubna - E.I.Sharapov

43 Thank you for your attention