22
Presentation of the PhD thesis “Statistical properties in the quasi-continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008

Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

Embed Size (px)

Citation preview

Page 1: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 2: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 2

The atomic nucleusThe atomic nucleus

Page 3: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 4: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 5: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 5

ApplicationsApplications

Nucleosynthesis in supernovae Transmutation of nuclear waste

Nucleosynthesis in supernovae Transmutation of nuclear waste

Page 6: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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?

Page 7: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 8: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 8

Particle-gamma coincidencesParticle-gamma coincidences

Si E-E telescope

45o

NaI(Tl)

3He

Target nucleus

Page 9: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 10: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 10

Quality of the extraction, 44ScQuality of the extraction, 44Sc

Page 11: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 11

Experimental level densitiesExperimental level densities

Page 12: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 13: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 13

Comparison with theory, 51VComparison with theory, 51V

Fermi gas? Fermi gas?

Page 14: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 15: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 15

Microcanonical entropyMicrocanonical entropy

Page 16: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 17: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 17

Calculated level densities, average number of broken pairs

Calculated level densities, average number of broken pairs

Page 18: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 18

Parity asymmetryParity asymmetry

Defining the parity asymmetry: Defining the parity asymmetry:

=+ −−

+ +−

Page 19: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

May 20, 2008 Ann-Cecilie Larsen 19

Experimental gamma-ray strength functions

Experimental gamma-ray strength functions

Page 20: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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

Page 21: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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.

Page 22: Presentation of the PhD thesis “Statistical properties in the quasi- continuum of atomic nuclei” Ann-Cecilie Larsen May 20, 2008 Ann-Cecilie Larsen May

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