Challenges on phase transitions and gamma-strength functions Magne Guttormsen
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Challenges on phase transitions and gamma-strength functions
Magne GuttormsenDepartment of Physics, University of Oslo
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
• Oslo method• Thermodynamics• Electromagnetic transitions• Challenges
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Spin-energy diagram
Spin2-6 ħ
Ex
T = 1 MeV
Yrast line(no levels)
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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The first generation method
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
F0
F1
F2
F3
€
1
Nsingles
or M
Ncoinc
-
=
F0
G
W
M
M-1
1€
G = w iFii
∑
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Gamma-ray multiplicity
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
€
M statγ = M tot
γ −M yrastγ
= (E − Eentry ) Eγ >E 0
M totγ = E Eγ
Spin
Spin
E
E
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The Brink Axel hypothesis
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P(E i,Eγ )∝ ρ(E f ) ⋅T (Eγ )
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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Does it work?
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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Nuclear entropy
€
S(E) = kB lnΩ(E)
Ω(E) = ρ (E) /ρ 0
ρ 0 = 2.2 MeV -1
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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canonical - canonical ensemble
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
€
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
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Rare-earth region, case erbium
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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Proton number Z = 50Neutron Cooper pairs
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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€
Structural transition when :
FC (E1) = FC (E2) for a given TC
Linearized free energy :
FC (E) = E −TC ⋅S(E)
J.Lee and J.M.Kosterlitz, Phys. Rev. Lett. 65, 137 (1990)
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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€
T(E) =∂S(E)
∂E
⎛
⎝ ⎜
⎞
⎠ ⎟−1
€
T(E) =∂S(E)
∂E
⎛
⎝ ⎜
⎞
⎠ ⎟−1
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
Challenges, new thermodynamic
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T(E) =∂S(E)
∂E
⎛
⎝ ⎜
⎞
⎠ ⎟−1
Isolated E
€
E(T) = kT 2 ∂
∂TlnZ(T)
HeatbathHeatbath T
S = S0 + S* + S1
Negative Cv(E) and T(E) Smoothed (up to E = 100 MeV)
T
€
ΩR +S = ΩRΩS = ΩR (E0 − E)
= exp S0 +∂S
∂E(−E) +
1
2
∂ 2S
∂E 2 E2 + ...
⎡
⎣ ⎢
⎤
⎦ ⎥
Boltzmann factor
€
e−E /T
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€
f (Eγ ) =1
2π
T (Eγ )
Eγ3
€
f (Eγ ) =1
2π
T (Eγ )
Eγ3
Loved child, many names
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
• Radiative strength function (RSF)
• Photon strength function (PSF)
• Gamma-ray strength function
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Simulation tests of the Oslo method
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
Event-by-event datagenerated in Praguewith DICEBOX
Sorted in Oslo into(Ex, E) matrix
First generationprocedure
Axel-Brinkfactorizationinto and f
2 4 6 8
2
5
8
Ex
E
2 4 6 8
2
5
8Ex
E
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Results from the blind test
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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€
f (Eγ ) =1
2π
T (Eγ )
Eγ3
€
f (Eγ ) =1
2π
T (Eγ )
Eγ3
Radiative strength functions
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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f py (Eγ ) =1
3π 2h2c 2
σ pyEγΓpy2
(Eγ2 − E py
2 )2 + Eγ2Γpy
2
€
f py (Eγ ) =1
3π 2h2c 2
σ pyEγΓpy2
(Eγ2 − E py
2 )2 + Eγ2Γpy
2
Pygmy resonance
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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€
π ν
€
B(M1↑) =9hc
32π 2
σΓ
E
⎛
⎝ ⎜
⎞
⎠ ⎟py
= 6.5(15)μN2
€
Pygmy resonance in 172Yb at Eγ = 3.3 MeV
Scissors mode
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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€
fE1(Eγ ) =1
3π 2h2c 2
0.7σ E1ΓE12 (Eγ
2 + 4π 2T 2)
EE1(Eγ2 − EE1
2 )2
€
fE1(Eγ ) =1
3π 2h2c 2
0.7σ E1ΓE12 (Eγ
2 + 4π 2T 2)
EE1(Eγ2 − EE1
2 )2
Kadmenskii, Markushev and Furman (KMF) model
Giant dipole resonance
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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Physics News Update
Unexpected RSF upbend
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
Voinov et al., Physical Review Letters,1 October 2004.
Also observed in: Mo, V, Sc, Ni, Ti (3He, 3He) and (3He, 4He) reactions
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Upbend in iron
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
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Temperature dependence?
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
€
96Mo( 3He, 3He′ γ )96Mo
€
×31
€
×32
€
×33
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Subatomic and Astrophysics Division Annual Meeting 2007
€
Bn = Eγ1 + Eγ 2Verifications
Budapest Research Reactor(n, ) reaction
INPP, Ohio University(d,n) reaction
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Challenges
-canonical or canonical ensemble - or another theory?
Critical T, how to interpret and measure?
Single quasi-particle entropy
Workshop onLevel Density andGamma Strength in Continuum, Oslo, May 21 - 24, 2007
Understand the difference in quantities observed in different experiments Pygmy resonance GEDR-tail match Low energy -strength
Spin distribution Parity asymmetry Thermalization