Transcript The Oslo Method

Oslo Seminar, Oslo, 6 December, 2012
Measure particle-g coincidences
Unfold g spectra at each E 1)
Apply the first-generation method
Ansatz: First-generation matrix
P(E, Eg)  (E - Eg)  T(Eg) 3)
• Normalization
• Examples of level density
•
•
•
•
2)
M. Guttormsen et al., NIM A374 (1996) 371
2) M. Guttormsen et al., NIM A255 (1987) 518
3) A. Schiller et al.,
NIM A447 (2000) 498
1)
Analysis of possible systematic errors of the Oslo method
A.C. Larsen et al., Phys. Rev. C 83, 034315 (2011)
Oslo Seminar, Oslo, 6 December, 2012
12 MeV
d on 232Th
24 MeV 3He on 232Th
Backwards:
J = 40o – 54o
5”x5” NaI
g
3He
–beam
3He,
a,d,t
∆E-E
M.Guttormsen, A.Bürger, T.E.Hansen, N.Lietaer,
NIM A648(2011)168
Oslo Seminar, Oslo, 6 December, 2012
(3He,a)231Th
(d,d’)232Th
(d,p)233Th
Oslo Seminar, Oslo, 6 December, 2012
(3He,t)232Pa
(3He,d)233Pa
(d,p)
g
E
(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.
Oslo Seminar, Oslo, 6 December, 2012
E
Mg (E) =
Eg
Mg = 3.2
Mg = 2.2
Oslo Seminar, Oslo, 6 December, 2012
Mg =1.0
232Th(d,p) 233Th
Ex
g
g
g
2-6ħ spin
Oslo Seminar, Oslo, 6 December, 2012
P(Ex,Eg)
P(Ex,Eg)
Level density
(Ef)
Oslo Seminar, Oslo, 6 December, 2012
Trans. coeff.
T(Eg)
l=
2p
2
M if × r(E f )
Fermi’s golden rule
P(E i , Eg ) µ T (Eg ) × r(E f )
Brink hypothesis
Oslo Seminar, Oslo, 6 December, 2012
,Eg)
Oslo Seminar, Oslo, 6 December, 2012
(Ef) T(Eg)
Normalization
Average level spacings D from neutron capture:
1)
2)
3)
Oslo Seminar, Oslo, 6 December, 2012
44Sc
A. 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
(Ef)
Oslo Seminar, Oslo, 6 December, 2012
T(Eg)
231,232,233Th
and
232,233Pa
M. Guttormsen et al., PRL 109, 162503 (2012)
-9
´10
232
3
231
50
Th( He,a) Th
40
30
20
10
0
-10 ´10-9
-3
RSF (MeV )
50
40
30
20
10
0
-10
50
40
30
20
10
0
-10
50
40
30
20
10
0
-10
232
Th(d,d)
232
Th
-9
´10
232
Th(d,p)
233
Th
-9
´10
232
3
Inverse energy-weighted sum rule:
232
Th( He,t)
Pa
2
3
QIV ( g p - gn ) m N2
16p
2
QIV » Q RIGID = mN r02 A 5/3 (1+ 0.31d ), r0 = 1.15fm
5
S-1 =
-9
´10
50
40
30
20
10
0
-10
0
232
3
Th( He,d)
0.5
1
233
Pa
1.5
2
2.5
3
g -ray energy E g (MeV)
3.5
4
Oslo Seminar, Oslo, 6 December, 2012
K. Heyde, P. von Neumann-Cosel, A. Richter, Rev. Mod. Phys., 82, 2365 (2010)
Thermal quasi-particles,
the spectators of mid-shell nuclei
Oslo Seminar, Oslo, 6 December, 2012
Thermal quasi-particles create level density
Cooper pair
1 level
Oslo Seminar, Oslo, 6 December, 2012
Broken pair
25 levels
A simple model for level density
- Combining all possible proton and neutron configurations
- Nilsson single-particle energy scheme
- BCS quasi-particles
j

Oslo Seminar, Oslo, 6 December, 2012
Nilsson level scheme
44
21
45
Sc 23 and 21
Sc 24
Model parameters:
 = 0.066
 = 0.32
 = 0.23
20
For Sc 23 :
44
21
1p 1n
1p 3n
1p 5n
1p 7n
3p 1n
3p 3n
3p 5n
5p 1n
5p 3n
7p 1n
Oslo Seminar, Oslo, 6 December, 2012
Level density and broken pairs
Level
densities
44
21
45
21
Sc 23
Sc 24
Oslo Seminar, Oslo, 6 December, 2012
Number
of broken
pairs
44
21
Sc 23
45
21
Sc 24
Parity asymmetry
r + - ra=
r+ + r-
a » 0.02 for
r(J = 1/2,J = 3/2)
U. Agvaanluvsan, G.E. Mitchell, J.F. Shriner Jr.,
Phys. Rev. C 67, 064608 (2003)
Oslo Seminar, Oslo, 6 December, 2012
44
21
Sc 23
45
21
Sc 24
Titanium and tin
Present experiment
Known levels
Back-shifted Fermi gas
From neutron res. data
From Ericson fluctuation data
-1
Level density r (E) (MeV )
104
46Ti
103
102
10
1
0
2
4
6
8
10 12
Excitation energy E (MeV)
Oslo Seminar, Oslo, 6 December, 2012
14
Summary
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•
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Simultaneous extraction of level density and g-strength function
Examples from A = 40 – 230
Number of thermal quasi-particles determines number of levels
Constant temperature level density
Fluctuations for lighter even-even nuclei
Oslo Seminar, Oslo, 6 December, 2012
http://tid.uio.no/workshop2013/
Oslo Seminar, Oslo, 6 December, 2012