1. “Nuclear structure” from TOF measurements
Milan Krtička
Charles University in Prague

2. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Outline
Photon (g-ray/radiative) strength functions and level density from TOF measurements
Measurements of g-ray spectra from radiative neutron capture with 4p balls
Needed for calculation of cross section in reactions involving photons
Influence of “non-statistical” effects observed in neutron capture on the decay of nucleus (on level density, calculated cross sections)
Observed effect for neutron widths
Measurement of intensities of primary transitions with Ge detectors
Needed for calculation of cross section
Prospects of TOF, Darmstadt, Mar 18-20, 2013

3. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Introduction
Main problems with description of atomic nucleus:
Interaction (nuclear Hamiltonian) is not known precisely
“Many body” problem
How do we describe the nucleus?
At low excitation energies – well separated levels – people try to describe the nucleus with “microscopic” models (nuclear structure)
At higher excitation energies – “statistical approaches”  use of average quantities and fluctuation properties
Niels Bohr - Nature (1936)
Prospects of TOF, Darmstadt, Mar 18-20, 2013

4. Photon Strength Functions}
Average quantities – level density (LD) and photon strength functions (PSFs) for different types of transitions (E1, M1, E2,…)
PSFs give the average probability of photon emission from “highly-excited” states or photoexcitation (in absolute units)
needed in all cases where one deals with g decay/photoexcitation a b
Prospects of TOF, Darmstadt, Mar 18-20, 2013

5. Photon Strength Functions
Above neutron separation energy measured in (g,xn) experiments in many nuclei
Experiment does not distinguish multipolarity, dominance of E1 assumed
Giant Dipole Electric Resonance is observed (and predicted) in all nuclei
The shape seems to be well described by single, or double (or triple?) Lorentzian
What is the PSF shape below neutron separation energy and for transitions between excited states?
From B.L. Berman, S.C. Fultz, Rev. Mod. Phys. 47 (1975) 713
Prospects of TOF, Darmstadt, Mar 18-20, 2013

6. Brink hypothesis n,g Brink hypothesis: generalization “g.s.”  “f” n,g
A target in photonuclear/photoabsorption experiment is in the ground state i
g.s. γ
n,g
“equivalent to”
Quasicontinuum
Identical !
Brink hypothesis: generalization “g.s.”  “f” i f γ
n,g
“equivalent to”
Fictitious (γ,γ‘) and (γ,x) experiments
g.s.
NRF experiments
Photoexcitation pattern of
an excited target nucleus
Prospects of TOF, Darmstadt, Mar 18-20, 2013

7. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Brink hypothesis
The energy dependence of the photoeffect is independent of the
detailed structure of the initial state
 dependence on g-ray energy but not on excit. energy (T), Jp,…
validity of the hypothesis?
at least approximately - from (n,g) reaction and hot nuclei
some weak signs of temperature (excitation energy) dependence
LANL, June 27, 2012
Prospects of TOF, Darmstadt, Mar 18-20, 2013

8. Different PSFs shapes from different reactions
Main unresolved problems
Exact shape of E1 at low energy tail of GDER
Dependence of low-energy tail of GDER on temperature (excitation energy)
Inconsistency of PSFs derived from different experiments
Contribution of M1 strength …
Prospects of TOF, Darmstadt, Mar 18-20, 2013

9. Prospects of TOF, Darmstadt, Mar 18-20, 2013
How to process data?
Spectra of photons usually given by a complicated interplay of PSFs for different types of transitions (E1, M1, E2,…) and LD
A problem with “disentanglement” of PSFs and LD also in (n,g)
Probably the only solution (at the moment) is a comparison of experimental spectra with outcome of simulations
We use the DICEBOX code for making these simulations
Simulates gamma decay of a compound nucleus within extreme statistical model
Prospects of TOF, Darmstadt, Mar 18-20, 2013

10. Simulation of  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 if (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)(Eγ) Eγ2L+1/(Ei),
where f (XL) and ρ are also a priori known
Selection rules governing the  decay are taken into account
Any pair of partial radiation widths if (XL) is statistically uncorrelated
Prospects of TOF, Darmstadt, Mar 18-20, 2013

11. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Modelling within ESM
Simulation of the decay:
“nuclear realization” (106 levels Ţ 1012 Glgf)  “precursors” are introduced
fluctuations originating from nuclear realizations cannot be suppressed
Deterministic character of random number generators is exploited
Outcomes from modelling are compared with experimental data
Prospects of TOF, Darmstadt, Mar 18-20, 2013

12. Main features of DICEBOX
There exists infinite number of artificial nuclei (nuclear realizations) obtained with the same set of LD and PSFs 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 (NRs)
DICEBOX allows to treat predictions from different NRs – fluctuations can be treated correctly
The size of fluctuations from different nuclear realizations depend on the (observable) quantity and nucleus
Due to fluctuations only “integral” quantities can be compared
Simulation of detector response must be applied (GEANT simulations for DANCE,…)
Prospects of TOF, Darmstadt, Mar 18-20, 2013

13. Spectra from 4p ball – MSC spectra
Eg1
Eg2
Eg3
Eg4
Prospects of TOF, Darmstadt, Mar 18-20, 2013

14. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Spectra from 4p ball
BaF2 detector arrays used so far
“The only” problem might be due to a background from neutron capture on Ba isotopes in crystals
Background is small for strong resonances and often can be subtracted
Spectra from isolated neutron resonances (DANCE, n_TOF)
Spins and parities of initial states known
Spectra from unresolved resonance region (Karlsruhe, FRANZ,…)
A mixture of different spins (and parities) – can be reasonably estimated at low neutron energies (up to several hundred keV of En - neutron strength functions must be known)
Prospects of TOF, Darmstadt, Mar 18-20, 2013

15. Spectra from 4p ball – unresolved resonances
Prospects of TOF, Darmstadt, Mar 18-20, 2013

16. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Resolved resonances
TOF spectrum from 95Mo(n,g) from DANCE
Only events corresponding to strong resonances are used
Prospects of TOF, Darmstadt, Mar 18-20, 2013

17. Spectra from 4p ball – resolved resonances
In some cases – isotope dependent
Different shapes (multiplicity distributions) of MSC spectra for different Jp
Can be used for Jp assignment / Jp needed in simulations
Prospects of TOF, Darmstadt, Mar 18-20, 2013

18. Spectra from 4p ball – resolved resonances
Another illustration of difference of spectra from resonances with different Jp
Experiment
Simulations
Prospects of TOF, Darmstadt, Mar 18-20, 2013

19. Spectra from 4p ball – resolved resonances
Experiment
Predicted fluctuations from simulations
Prospects of TOF, Darmstadt, Mar 18-20, 2013

20. Prospects of TOF, Darmstadt, Mar 18-20, 2013
151Eu spectra
M=1
M=2
M=3
M=4
M=5
M=6
M=7
M=2
M=1
M=3
M=4
M=5
M=6
M=7
Predicted shapes from all s-wave resonances (2+ and 3+) identical
The same for simulations
Prospects of TOF, Darmstadt, Mar 18-20, 2013

21. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Results
Only restricted regions of nuclei have been/are planed to be probed
Rare-earth nuclei (mainly deformed)
Actinides (deformed)
Presence of so-called scissors mode tested
Mo region
Test of the presence of enhancement of PSF at low Eg – proposed from Oslo method in A< nuclei
Sn/Cd region
In addition to the enhancement, tests of presence of pygmy resonance
Pt/Au region
Shape of PSF is probably very different from other regions (pygmy)
Almost all results obtained at DANCE
Some results for actinides at n_TOF – only sum-energy spectra published, MSC spectra are processed
Prospects of TOF, Darmstadt, Mar 18-20, 2013

22. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Results
Only restricted regions of nuclei have been/are planed to be probed
Rare-earth nuclei (mainly deformed)
Actinides (talks of J. Ullmann and C. Guerrero)
Presence of so-called scissors mode tested
Mo region
Test of the presence of enhancement of PSF at low Eg – proposed from Oslo method in A< nuclei
Sn/Cd region
In addition to the enhancement, tests of presence of pygmy resonance
Pt/Au region
Shape of PSF is probably very different from other regions (pygmy)
Almost all results obtained at DANCE
Some results for actinides at n_TOF – only sum-energy spectra published, MSC spectra are processed
Prospects of TOF, Darmstadt, Mar 18-20, 2013

23. Fe, Mo + other light nuclei – softpole
Data from Oslo  strong enhancement of PSF at low g-ray energies
In the case of Fe a support from TSC measurements
arbitrary normalization of exp. data
Prospects of TOF, Darmstadt, Mar 18-20, 2013

24. MSC spectra of 96Mo (2+ resonaces)
Strong PSF enhancement at low Eg leads to strong change in predicted MSC spectra – shift in multiplicity distribution, spectral shape
Prospects of TOF, Darmstadt, Mar 18-20, 2013

25. MSC spectra of 96Mo (3- resonaces)
Strong PSF enhancement at low Eg leads to strong change in predicted MSC spectra – shift in multiplicity distribution, spectral shape
Prospects of TOF, Darmstadt, Mar 18-20, 2013

26. Prospects of TOF, Darmstadt, Mar 18-20, 2013
MSC spectra of 96Mo 2+ 3-
Prospects of TOF, Darmstadt, Mar 18-20, 2013

27. Prospects of TOF, Darmstadt, Mar 18-20, 2013
(n,g) data on 96Mo
Predicted MSC spectra similar for T-dependent PSFs from the figures
But correct statistical analysis of TSC spectra excludes the model on right figure at 99.8 % confidence level Krticka et al., PRC (2008)
 the enhancement is “very weak” if any
Prospects of TOF, Darmstadt, Mar 18-20, 2013

28. Rare-earth region – “scissors mode”
A mode observed in (e,e’) and (g,g’) at excitation energy near 3 MeV
In (g,g’) problems with exp. threshold  relation between exp. and actual strength? – important especially in odd nuclei
Data from two-step cascades (TSC) in 163Dy and Oslo data, (3He,a), on several isotopes indicated that the strength at similar energy is needed also for transitions between excited states – a mode in a PSF
TSC spectra clearly showed that the excitation is in M1
M1 strength is “comparable to/ stronger than” E1 near 3 MeV
H. Maser et al., PRC 53 (1995) 2749
Ge detectors: allows to resolve individual GS transitions (in even-even nuclei)
Prospects of TOF, Darmstadt, Mar 18-20, 2013

29. Rare-earth region – “scissors mode”
Neutron separation energy in odd products makes the bumps more pronounced than in even-even products
No resonance structure in PSF postulated
Prospects of TOF, Darmstadt, Mar 18-20, 2013

30. Rare-earth region – “scissors mode”
Resonance structure postulated in E1 PSF Confirms conclusion from TSC spectra
Prospects of TOF, Darmstadt, Mar 18-20, 2013

31. Rare-earth region – “scissors mode”
Resonance structure postulated in M1 PSF only on states with excitation energy of lower than 3 MeV
Prospects of TOF, Darmstadt, Mar 18-20, 2013

32. Rare-earth region – “scissors mode”
Resonance structure postulated in M1 PSF only on states with excitation energy of lower than 3 MeV
Prospects of TOF, Darmstadt, Mar 18-20, 2013

33. Rare-earth region – “scissors mode”
Resonance structure postulated in M1 PSF on all states
Prospects of TOF, Darmstadt, Mar 18-20, 2013

34. Rare-earth region – “scissors mode”
Resonance structure must be postulated in M1 PSF at all energies (we are sensitive up to about 4 MeV) – Brink hypothesis valid
Odd-even effect seems to be seen in the strength of the mode - strength reproducing 157,159Gd is about 3x higher than in 156,158Gd
Energy near 3 MeV in rare-earth nuclei (what is the energy in other regions (actinides)?)
Half-width is about 1 MeV
Some inconsistencies in parameters between Oslo and (n,g)
Prospects of TOF, Darmstadt, Mar 18-20, 2013

35. Rare-earth region – “scissors mode”
3-MeV bumps in spectra seen also in even-even nuclei
Prospects of TOF, Darmstadt, Mar 18-20, 2013

36. Rare-earth region – “scissors mode”
One can make additional gates on spectra – a peak in 156Gd comes from decay of about 5 states with excitation MeV  transitions to these states can be checked  gated MSC spectra
Prospects of TOF, Darmstadt, Mar 18-20, 2013

37. Pygmy resonance in 198Au data obtained before 1980 ?
197Au(n,)198Au reaction
Photonuclear data
Isolated neutron resonances
Fast n-capture, CTF
Fast n-capture, BSFG
Lorentzian GDR
“Depressed”
Lorentzian GDR ?
Is there, indeed, an E1 pygmy resonance at 5.5 MeV?
… or a mere deficiency and/or a redistribution of E1 photon strength?
Redrawn from S. Joly, D. M. Drake and L. Nilsson, PRC 20 (1979) 2072
GSI, January 15, 2013
Prospects of TOF, Darmstadt, Mar 18-20, 2013

38. Pygmy resonance in 198Au data from the Karlsruhe 4 BaF2  calorimeter
No pygmy resonance postulated
Pygmy resonance at 5.5 MeV
Suppression of PSF below 5 MeV
No difference in fits
… but postulating a pygmy resonance leads to too large total radiation width
Prospects of TOF, Darmstadt, Mar 18-20, 2013

39. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Pygmy resonance in 198Au
Exactly the same results obtained also from also TSC spectra
Prospects of TOF, Darmstadt, Mar 18-20, 2013

40. Fluctuation properties
Inherent part of the statistical model/calculations
It is assumed that wave functions at high excitation energies are “very complicated” and the distribution of their overlaps (via EM operator) <y|T(EM)|y> are “random” – create Gaussian distribution
This assumption least to the Porter-Thomas distribution (PTD) (c2 distribution with one degree of freedom n) of reduced neutron widths, partial radiation widths, …
Prospects of TOF, Darmstadt, Mar 18-20, 2013

41. Fluctuation properties
Recently, a strong indication of a violation of the Porter-Thomas distribution (PTD) (n = 1.0) of reduced neutron widths was found in odd Pt isotopes
From analysis of neutron widths measured at ORELA P. Koehler PRL 105, (2010)
Maximum-Likelihood (ML) analysis yielded: 192Pt: n = 0.57± Pt: n = 0.47± Pt: n = 0.60±0.28
No indication of the PTD violation in 232Th (target) not yet published
There are more nuclei showing some problems with PTD P. Koehler, Phys. Rev. C 76, (2007), Phys. Rev. C 84, (2011)
More detailed investigation needed
Prospects of TOF, Darmstadt, Mar 18-20, 2013

42. Prospects of TOF, Darmstadt, Mar 18-20, 2013
ORELA Measurements
Transmission as well as capture cross section measured
Resonance parameters deduced using SAMMY
Prospects of TOF, Darmstadt, Mar 18-20, 2013

43. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Testing the PTD Using 192,194Pt+n ORELA Data
Several statistics to test the consistency with PTD used
Combining them for two nuclei:
PTD rejected at % confidence level
Prospects of TOF, Darmstadt, Mar 18-20, 2013

44. Fluctuation properties
A violation of PTD might have “strong” consequences:
If distributions were “wider” (n < 1) – there would be higher number of levels with small widths - either unobserved or difficult to be distinguished from p-wave resonances
Resonance spacing can be different
Prospects of TOF, Darmstadt, Mar 18-20, 2013

45. Fluctuation properties
A violation of PTD might have “strong” consequences:
If distributions were “wider” (n < 1) – there would be higher number of levels with small widths - either unobserved or difficult to be distinguished from p-wave resonances
Resonance spacing can be different
Prospects of TOF, Darmstadt, Mar 18-20, 2013

46. Fluctuation properties
Is there any problem also with gamma widths?
Primary transitions from neutron resonances can be, in principle, measured
A few measurements were performed at GELINA (thesis of F. Gunsing and L. Zanini) and Dubna (F. Bečvář)
Test of the PTD and/or correlations with some quantum numbers (K) would be perfect
A huge amount of material needed – about 100 g
Prospects of TOF, Darmstadt, Mar 18-20, 2013

47. Prospects of TOF, Darmstadt, Mar 18-20, 2013
Example:
Spectra of primary transitions from several Jp = 1- resonances in 107Ag(n,g) as measured at GELINA
Thesis of L. Zanini
Prospects of TOF, Darmstadt, Mar 18-20, 2013

48. Thank you very much for your attention!