presentation of the phd thesis “statistical properties in the quasi-continuum of atomic nuclei”
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Presentation of the PhD thesis“Statistical properties in the quasi-
continuum of atomic nuclei”
Presentation of the PhD thesis“Statistical properties in the quasi-
continuum of atomic nuclei”
Ann-Cecilie LarsenMay 20, 2008
Ann-Cecilie LarsenMay 20, 2008
May 20, 2008 Ann-Cecilie Larsen 2
The atomic nucleusThe atomic nucleus
May 20, 2008 Ann-Cecilie Larsen 3
Quantum energy levels Quantum energy levels
Nuclear level density = number of energy levels within one energy unit
Nuclear level density = number of energy levels within one energy unit
May 20, 2008 Ann-Cecilie Larsen 4
Decay probabilityDecay probability
Transition between quantum levels Fermi’s golden rule: Gamma-ray transmission coefficients and
strength functions
Transition between quantum levels Fermi’s golden rule: Gamma-ray transmission coefficients and
strength functions
€
λ=2π
hf ˆ H i
2
ρ(E f )
Giant dipole resonance, 98Mo
i
f
May 20, 2008 Ann-Cecilie Larsen 5
ApplicationsApplications
Nucleosynthesis in supernovae Transmutation of nuclear waste
Nucleosynthesis in supernovae Transmutation of nuclear waste
May 20, 2008 Ann-Cecilie Larsen 6
MotivationMotivation
Level density and gamma-ray strength function in medium-mass nuclei: 44,45Sc, 50,51V, 93-98Mo
Shell effects? Decay probability in the quasi-continuum?
Level density and gamma-ray strength function in medium-mass nuclei: 44,45Sc, 50,51V, 93-98Mo
Shell effects? Decay probability in the quasi-continuum?
May 20, 2008 Ann-Cecilie Larsen 7
The Oslo Cyclotron LaboratoryThe Oslo Cyclotron Laboratory
Reactions: inelastic scattering (3He,3He’), and pick-up (3He,)
Low spin and high intrinsic excitation energy CACTUS: 28 5”x5” NaI (~15% eff.) Eight E-E Si particle telescopes
Reactions: inelastic scattering (3He,3He’), and pick-up (3He,)
Low spin and high intrinsic excitation energy CACTUS: 28 5”x5” NaI (~15% eff.) Eight E-E Si particle telescopes
May 20, 2008 Ann-Cecilie Larsen 8
Particle-gamma coincidencesParticle-gamma coincidences
Si E-E telescope
45o
NaI(Tl)
3He
Target nucleus
May 20, 2008 Ann-Cecilie Larsen 9
The Oslo method in a The Oslo method in a
Unfold -ray spectra Apply first-generation subtraction method Ansatz: decay probability(Ex-E)T(E)
Unfold -ray spectra Apply first-generation subtraction method Ansatz: decay probability(Ex-E)T(E)
44Sc
May 20, 2008 Ann-Cecilie Larsen 10
Quality of the extraction, 44ScQuality of the extraction, 44Sc
May 20, 2008 Ann-Cecilie Larsen 11
Experimental level densitiesExperimental level densities
May 20, 2008 Ann-Cecilie Larsen 12
Shell effects in the Mo isotopesShell effects in the Mo isotopes
Back-shifted Fermi gas:
Calc. from neutron res. data
May 20, 2008 Ann-Cecilie Larsen 13
Comparison with theory, 51VComparison with theory, 51V
Fermi gas? Fermi gas?
May 20, 2008 Ann-Cecilie Larsen 14
ThermodynamicsThermodynamics
Microcanonical vs. canonical ensembleMicrocanonical vs. canonical ensemble
€
S(E) = k lnΩ
1
T=
∂S
∂E
⎛
⎝ ⎜
⎞
⎠ ⎟N
€
Z(T) = Ω(E)e−E / kT
E
∑
E = kT 2 ∂
∂TlnZ
F = −kT lnZ
S = −∂F
∂T
⎛
⎝ ⎜
⎞
⎠ ⎟V
€
Ω(E) = ρ (E) /ρ 0
May 20, 2008 Ann-Cecilie Larsen 15
Microcanonical entropyMicrocanonical entropy
May 20, 2008 Ann-Cecilie Larsen 16
Combinatorial modelCombinatorial model
Combining all possible proton and neutron configurations
Nilsson energy scheme BCS quasiparticles
Combining all possible proton and neutron configurations
Nilsson energy scheme BCS quasiparticles
Ω
J
May 20, 2008 Ann-Cecilie Larsen 17
Calculated level densities, average number of broken pairs
Calculated level densities, average number of broken pairs
May 20, 2008 Ann-Cecilie Larsen 18
Parity asymmetryParity asymmetry
Defining the parity asymmetry: Defining the parity asymmetry:
€
=+ −−
+ +−
May 20, 2008 Ann-Cecilie Larsen 19
Experimental gamma-ray strength functions
Experimental gamma-ray strength functions
May 20, 2008 Ann-Cecilie Larsen 20
Comparison with theoryComparison with theory
Anomalous strength functions? Anomalous strength functions?
TXL(E) = 2 E2L+1 fXL
fXL(E) = E-(2L+1) XL(E)/D
Assuming only dipole radiation:
f(E) T(E) / 2E3
May 20, 2008 Ann-Cecilie Larsen 21
Papers included in the thesisPapers included in the thesisPublication My contributionRadiative strength functions in 93-98Mo
[Phys. Rev. C 71, 044307 (2005)]
Discussions of the results, suggestions to and proof-reading of the manuscript.
Level densities and thermodynamic quantities of heated 93-98Mo isotopes
[Phys. Rev. C 73, 034311 (2006)]
Discussions of the results (mainly level densities and microcanonical results), suggestions to and proof-reading of the manuscript.
Microcanonical entropies and radiative strength functions of 50,51V
[Phys. Rev. C 73, 064301 (2006)]
Main author. Performed the data analysis and calculations. Wrote the manuscript.
Nuclear level densities and gamma-ray strength functions in 44,45Sc
[Phys. Rev. C 76, 044303 (2007)]
Main author. Performed the data analysis and calculations. Wrote the manuscript.
Level densities of 44Sc and 47Ti from different experimental techniques
[Phys. Rev. C 77, 034613 (2008)]
Provided data and info for the OCL exp. (44Sc). Suggestions to and proof-reading of the manuscript. Participated in the Ohio exp.
May 20, 2008 Ann-Cecilie Larsen 22
HighlightsHighlights
The Oslo method works well for medium-mass nuclei
Pronounced shell effects Single quasi-particle entropy constant, but
vanish near shell closures Enhancement of low-energy gamma decay
probability established for all nuclei studied
The Oslo method works well for medium-mass nuclei
Pronounced shell effects Single quasi-particle entropy constant, but
vanish near shell closures Enhancement of low-energy gamma decay
probability established for all nuclei studied
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