Spallation Neutron Energy Spectrum Determination with Yttrium as a Threshold Detector on UPbassembly

1
Spallation Neutron Energy Spectrum Determination
with Yttrium as a Threshold Detector on
U/Pb-assembly Energy plus Transmutation

• S. Kilim1, E. Strugalska-Gola1, M. Szuta1, A.
  Wojciechowski1, M. Bielewicz1, M.I.
  Krivopustov2, A.D.Kovalenko2, I. Adam2,3, A.
  Krasa3, M. Majerle3, V. Wagner3
• 1. Institute of Atomic Energy, 05-400
  Otwock-Swierk, Poland
• 2. Joint Institute of Nuclear Research, 141980
  Dubna, Russia
• 3. Nuclear Physics Institute of CAS, 25068 Rez,
  Czech Republi

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Energy plus Transmutation project

• International research project realised in JINR
  Dubna.
• Michail I. Krivopustov project leader
• 12 states take part in
• Started 1999
• Purpose of the project is to study transmutation
  on U/Pb-assembly driven by accelerator NUKLOTRON.
• Transmutation samples 129I, 237Np, 238Pu, 239Pu
• Activation detectors Al, Ti, V, Mn, Fe, Co, Ni,
  Cu, Y, Nb, In, Dy, Lu, W, Au, Bi
• 3He counter
• SSNTD

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U-Pb assembly in Energy plus Transmutation
project
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Experiments with Energy plus Transmutation
set-up

• Proton beam
• Ep 0.7 GeV
• Ep 1.0 GeV
• Ep 1.5 GeV
• Ep 2.0 GeV

• Deuteron beam
• Ed 1.6 GeV
• 0.8 GeV/nucleon
• Ed 2.52 GeV
• 1.26 GeV/nucleon

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Yttrium samples location during irradiation
PLANE 2
R 3 cm
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Yttrium-89 activation reactions
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Y-89(n,?) reaction cross sections available in
ENDFs
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Y-88 and Y-87 production spatial distribution
comparison
P2,R3
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Y-86 production spatial distribution comparison
P2,R3

• Distribution summary
• Radial maximum in beam axis
• 1.6 GeV axial maximum on plane 2 (11.8 cm)
• 2.52 GeV axial maximum in between plane 2 and 3
• 2.52 GeV axial maximum wider than 1.6 Gev one

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How to get neutron energy spectrum from these
results?

• Use MCNPX code for independent calculation not
  a subject of this presentation.
• Use spectral indexes quotient of various
  isotope production 2. Many reactions, many
  isotopes needed. We lack them.
• Use/create special function representing isotope
  k production dependence on reaction threshold
  energy and then

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Basic definitions

• Isotope k production per one Y89 gram
• N 6.77?1021 nuclei/g
• Ethr,k reaction k threshold energy MeV
• ?(E) neutron energy spectrum n/cm2/d/MeV
• ?k(E) reaction k cross section cm2

• Spectral Index (SI)
• E87,E88 reaction threshold energies MeV

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Spectral Index SI87/88 and SI86/88 spatial
distribution comparison between the experiments
P2,R3
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Spectral Index spatial distribution summary

• Beam area to be rejected
• Very similar pictures for both 1.6 and 2.52 GeV
  experiment
• Excluding front and rear planes, the spectral
  index spatial distribution is very uniform,
  almost flat throughout the entire EpT setup. No
  dependence on radius. Very little growth with
  axis.
• This suggests the neutron spectrum not to change
  much throughout the entire setup body.
• This doesnt say what the neutron spectrum is
  like.

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Purpose of the work

• Look for possibility to determine neutron energy
  spectrum directly from activation method results
• The idea was to transform the activation formula
• into Volterras integral equation of the first
  kind
• and solve it.
• It meant ?(E,Ethr) and I(Ethr) to be known and
  continuous functions.

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Looking for Y89(n,xn) reaction cross section
analytical form

• Basic assumptions come from compound nucleus
  reaction model
• Neutron energy range 0-20 MeV Y89(n,2n) reaction
  cross section has a form of Ee-E/T 3, where T
  is a temperature of a resulting nucleus or rather
  calibration factor.
• The same approximation is valid for higher
  energies as well.

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Y89(n,xn) reaction cross section basic
assumptions continued

• The only difference between Y89(n,2n), (n,3n) and
  (n,4n) reactions is threshold energy. This makes
  all three reaction cross section functions to
  have the same shape but shifted along energy axis
• Assuming this, for any threshold energy Ethr
  reaction cross section form becomes

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Looking at Y89 interactions in one point P2,R3
and looking for analytical function I(Ethr)

• Corrected experimental results for Yttrium
  isotope production are shown on upper right
  picture.
• Production values (Ik) fit very well with an
  analytical function

Y88
Y87
Y86
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Looking at Y89 interactions in one point P2,R3
and looking for analytical function I(Ethr) -
continuation

• Ik values fit very well with the whole class of
  functions
• with ?, ? and ? as parameters.

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I(Ethr) function for Y89 interactions in various
points along R3 axis for two different
experiments 1.6 and 2.52 GeV

• Both graphs show that approximation of Yttrium
  isotope production from reaction Y89(n,xn) with
  function
• makes sense despite of fact of being only a
  mathematical representation without any physical
  meaning.

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Spallation neutron energy spectrum ?(E)
representation basing on experimental data I(Ethr)
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Solving a Volterras integral equation for
Yttrium isotope production

• Using the mentioned earlier functions for
  ?(E,Ethr) and I(Ethr) the equation
• becomes Volterras integral equation of the first
  kind
• with nucleus K(E,Ethr) (E-Ethr)e-?E and
  solution

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Solving a Volterras integral equation for
Yttrium isotope production - continuation

• To fulfill request ?(E ? 0) 0 and ?(E ? ?) ? 0
  must be
• and ?(E) becomes

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Spallation neutron spectrum function properties
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Spallation neutron spectrum function properties -
continuation
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1.6 and 2.52 GeV spallation neutron spectra
comparison in various axial positions at R3 cm
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1.6 and 2.52 GeV spallation neutron spectra
comparison in various axial position at R3 cm -
continuation

• Comparison summary
• Spectrum width growths with axial position growing

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1.6 and 2.52 GeV spallation neutron spectra
comparison in various axial position at R3 cm -
continuation

• Comparison summary - continuation
• Spectrum maximum moves toward higher energies
  with axial position growing
• Ed 1.6 GeV maximum in front of target larger
  than 2.52 GeV one. Axial distribution of the
  maxima has a maximum then both maxima decrease
  with axial position growing but 1.6 GeV one
  decreases faster and at rear of the target 2.52
  GeV maximum is larger.
• Spectrum maximum values comparison says that 2.52
  GeV d neutrons penetrate dipper than 1.6 GeV d
  ones.

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Parametr ? determination
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Surprising

• Surprising is that using threshold detector with
  threshold energies 11.598, 20.5 i 32.7 MeV one
  can say so much about the spectrum in the entire
  energy range.

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Exception

• Spectrum maximum position is about 10 MeV while
  it should be 1.5 MeV

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Is there anything interesting in this method?

• I think yes, despite of a lot of work to be done
  to verify it. First of all the method is simple.

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Recommendations

• Error analysis to be done.
• Compare deuteron beam results with proton ones.
• Explain why the maximum is moved to high
  energies.
• Is the determination error responsible for it?
• Is the reaction cross section bad approximation
  responsible?
• The same analysis should be done for the other
  activation detectors Au, In.

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References

• 1. M.I. Krivopustov et al., JINR Preprint
  R1-2000-168, Dubna, 2000// Kerntechnik 2003, 68,
  p.p. 48-55// JINR-Preprint E1-2004-79, Dubna,
  2004.
• Martsynkevich B. A. et al. Unfolding of Fast
  Neutron Spectra in the Wide Energy Range (up to
  200 MeV) in Heterogeneous Subcritical Assembly of
  an Electronuclear System Energy plus
  Transmutation in Russ. JINR preprint
  R1-2002-65.
• ANL/NDM-94 Evaluated Neutronic Data File for
  Yttrium, A.B. Smith, D.L. Smith, P. Rousset,
  R.D. Lawson, and R.J. Howerton, January 1986