The Nuclear Level Densities in Closed Shell 205208Pb Nuclei

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The Nuclear Level Densities in Closed Shell
205-208Pb Nuclei
Syed Naeem Ul Hasan
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Introduction

• Nuclear level density Bethe Fermi gas model in
  1936. For many years, measurements of NLD have
  been interpreted in the framework of an infinite
  Fermi-gas model.
• Gil. Cam. CTF, BSFG were later proposed
  accounting shell effects etc.
• Shell Model Monte Carlo (SMMC)

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• Experimental NLD,
• Counting of neutron (proton) resonances
• Discrete levels counting
• Evaporation spectra
• OSLO METHOD
• Method has successfully been proven for a No. of
  nuclei.
• However in cases where statistical properties are
  less favorable the method foundation is more
  doubtful.
• A test at the lighter nuclei region has been made
  already for 27,28Si.
• The limit of applicability of method on closed
  shell nuclei was also required.

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Experimental details

• MC-35 cyclotron at OCL,
• 38 MeV 3He beam bombarded on 206Pb and 208Pb
  targets having thickness of 4.707 and 1.4
  mg/cm2.
• Following reactions were studied,
• 206Pb(3He, 3He)206Pb
• 206Pb(3He, ?)205Pb
• 208Pb(3He, 3He)208Pb
• 208Pb(3He, ?)207Pb
• The particle-? coincidences were recorded
  while the experiment ran for 2-3 weeks.

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Oslo Cyclotron Lab
CACTUS
Concrete wall
http//www.physics..no/ocl/intro/
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• Detector Arrangement
• The charged ejectiles ----gt 8 collimated Si at
  45o to the beam.
• The ?-rays detection -----gt CACTUS 28 NaI(Tl)
  5x5
• detection ? 15 of 4p.
• Particles ?-rays are produced in rxns are
  measured in both particle-? coincidence
  particle singles mode by the CACTUS
  multi-detector array.

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Data Analysis
Unfolding of coincidence spectra
Raw Data
Particle Spectra Calibration
?-spectra calibration and alignment
Extracting Primary- ? spectra
Data Reduction
Particle - ? coincidences
thickness spectrum Gating on particles
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Coincidence Spectra
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Unfolding

• Detector response of 28 NaI detectors are
  determined 11 energies and interpolation is made
  for intermediate ?-energies.
• Folding iteration method is used
• Unfolded spectrum is starting point, such that,
  f R u.
• First trial fn as, uo r
• First folded spectrum, fo R uo
• Next trial fn, u1 uo (r - fo)
• Generally, ui1 ui (r - fi)
• Iteration continues until fi r
• Fluctuations in folded spectra Compton
  background are subtracted.

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Test of method
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Primary ?-matrix

• Assumption
• The ?-decay pattern from any Ex is independent
  of the population mechanism
• The nucleus seems to be an CN like
  system prior to ?-emission.
• Method The f.g. ?-spectrum of the highest Ex is
  estimated by,
• f1 f.g. ?-spectrum of highest Ex bin.
• g weighted sum of all spectra.
• wi prob. of decay from bin 1 - i.
• ni ?i / ?j

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• Multiplicity Normalization
• Algorithm
• Apply a trial fn wi
• Deducing hi fi - ? g
• Transforming hi to wji (i.e. Unfold h, make h
  having same energy calibration as wi, normalize
  the area of h to 1).
• If wji (new) wji (old) then the calculated hi
  would be the Primary-? function for the level Ei,
  else proceed with (2)

Some experimental conditions can introduce severe
systematic errors, like pile-up effects,
isomers etc.
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Testing of an Experimental spectrum
Ex 4.5-5.5 MeV.
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Extraction of NLD GSF

• Brink-Axel Hypothesis
• Transforming
• A, B, ? are free parameters.
• A. Schiller et al./ Nucl. Instr. Methods in
  Physics Research A 447 (2000) 498-511

fEdiff
?Ef
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• Gamma transition probability
• Theoretically
• Minimizing

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Nuclear Level Density

• At low Ex
• comparing the extracted NLD to
• At Bn deducing NLD from resonance spacing data.
• BSFG level density extrapolation
• where a level density parameter,
• U E-E1 and E1 back-shifted parameter,

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Experimental NLD
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Entropy

• ?o is adjusted to give S ln ? 0 close to
  ground state band
• The ground band properties fullfil the Third law
  of dynamics
• S(T 0) 0

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Gamma Strength Function

• The fitting procedure of P(Ei, E?) determines the
  energy dependence of T(Ei, E?) .
• The fitting of B must be done here.
• Assumptions
• The decay in the continuum E1, M1.
• No of states with ? is equal
• Radiative strength function is,

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Collaborators

• Magne Guttormsen University of Oslo
• Suniva Siem University of Oslo
• Ann Cecilie University of Oslo
• Rositsa Chankova University of Oslo
• A. Voinov Ohio university, OH, USA
• Andreas Schiller MSU, USA
• Tom Lønnroth Åbo Akademi, Finnland
• Jon Rekstad University of Oslo
• Finn Ingebretsen University of Oslo

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• Thank You

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