to the QuasiContinuum of E xcited N uclei Magne Guttormsen Department of Physics and SAFE University of Oslo Oslo Seminar Oslo 6 December 2012 The Oslo Method Oslo Seminar Oslo 6 December 2012 ID: 356055
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Slide1
The Oslo Method Applied
to the Quasi-Continuum
of
Excited NucleiMagne GuttormsenDepartment of Physics and SAFE University of Oslo
Oslo Seminar, Oslo, 6 December, 2012Slide2
The Oslo Method
Oslo Seminar, Oslo, 6 December, 20121) M. Guttormsen et al., NIM A374 (1996) 3712) M. Guttormsen et al., NIM A255 (1987) 5183) A. Schiller et al., NIM A447 (2000) 498Analysis of possible systematic errors of the Oslo methodA.C. Larsen et al.,
Phys. Rev. C 83, 034315 (2011)Measure particle-g coincidencesUnfold spectra at each E 1)
Apply the first-generation method 2)Ansatz: First-generation matrix P(E, E) (E - E) T(E) 3) Normalization
Examples of
level
densitySlide3
Experiments at OCL
12 MeV d on 232Th 24 MeV 3He on 232Th g3He –beam 3He, a,d
,t
5”x5” NaIM.Guttormsen
, A.Bürger, T.E.Hansen, N.Lietaer
, NIM A648(2011)168
∆E-E
Backwards:
J
= 40
o
– 54
o
Oslo Seminar, Oslo, 6 December, 2012Slide4
∆E-E bananas
(d,d’)232Th (d,p)233Th(3He,t)232Pa (3He,d)233Pa(
3He,a)231Th
Oslo Seminar, Oslo, 6 December, 2012Slide5
Assumption for the extraction of
first-generation g-spectraOslo Seminar, Oslo, 6 December, 2012
(
d,p)(d,p)
The
g
-energy distribution is the same
if the decay starts at E after
g
-emission or
starts after the direct reaction into E.
E
gSlide6
Gamma-multiplicity
Oslo Seminar, Oslo, 6 December, 2012Slide7
From total to primary g-ray matrix
s
pin
2-6
ħ
E
x
232
Th(
d
,p
)
233
Th
Oslo Seminar, Oslo, 6 December, 2012Slide8
Primary g-ray matrix P(Ex,Eg) Level density
Trans. coeff.r(Ef) T(Eg)
P(Ex,Eg) Oslo Seminar, Oslo, 6 December, 2012Slide9
Multiplicative factorsOslo Seminar, Oslo, 6 December, 2012
Brink
hypothesis
Fermi’s
golden
ruleSlide10
P(Ex,Eg) = r(Ef) . T(Eg) ?
Oslo Seminar, Oslo, 6 December, 2012Slide11
Normalization
Oslo Seminar, Oslo, 6 December, 2012A. Gilbert and A.G.W. Cameron, Can. J. Phys. 43, 1446 (1965)T. von Egidy and D. Bucurescu, Phys. Rev. C 72, 044311 (2005), Phys. Rev. C 73, 049901(E) (2006)S. Goriely, HF+
BCS Demetriou and Goriely, Nucl. Phys. A695 (2001) 95 44Sc
Average level spacings D from neutron capture: Slide12
r(Ef) and T(Eg)
Oslo Seminar, Oslo, 6 December, 2012Slide13
231,232,233Th and 232,233PaInverse energy-weighted sum rule:
K. Heyde, P. von Neumann-Cosel, A. Richter, Rev. Mod. Phys., 82, 2365 (2010)Oslo Seminar, Oslo, 6 December, 2012M. Guttormsen et al., PRL 109, 162503 (2012) Slide14
Thermal quasi-particles,
the spectators of mid-shell nucleiOslo Seminar, Oslo, 6 December, 2012Slide15
Thermal quasi-particles create level density
Oslo Seminar, Oslo, 6 December, 2012
Cooper pair Broken pair
1 level 25 levelsSlide16
A simple model for level density
Oslo Seminar, Oslo, 6 December, 2012
-
Combining all possible proton and neutron configurations- Nilsson single-particle energy scheme- BCS quasi-particles
jSlide17
Nilsson level scheme
Oslo Seminar, Oslo, 6 December, 2012Model parameters: = 0.066 = 0.32 = 0.23
1p 1n
1p 3n1p 5n1p 7n
3p 1n
3p 3n
3p 5n
5p 1n
5p 3n
7p 1n
20Slide18
Level density and broken pairs
Oslo Seminar, Oslo, 6 December, 2012
Level densities Number of broken pairsSlide19
Parity asymmetry
Oslo Seminar, Oslo, 6 December, 2012
U. Agvaanluvsan, G.E. Mitchell
, J.F. Shriner Jr., Phys. Rev. C 67, 064608 (2003)Slide20
Titanium and tin
Oslo Seminar, Oslo, 6 December, 201246TiSlide21
Summary
Oslo Seminar, Oslo, 6 December, 2012Simultaneous extraction of level density and g-strength functionExamples from A = 40 – 230Number of thermal quasi-particles determines number of levelsConstant temperature level densityFluctuations for lighter even-even nucleiSlide22
Oslo Seminar, Oslo, 6 December, 2012
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