The Oslo Method Applied to the Quasi-Continuum

of Excited Nuclei

Magne GuttormsenDepartment of Physics and SAFE

University of Oslo

Oslo Seminar, Oslo, 6 December, 2012

The Oslo Method

Oslo Seminar, Oslo, 6 December, 2012

1) M. Guttormsen et al., NIM A374 (1996) 3712) M. Guttormsen et al., NIM A255 (1987) 5183) A. Schiller et al., NIM A447 (2000) 498

Analysis of possible systematic errors of the Oslo methodA.C. Larsen et al., Phys. Rev. C 83, 034315 (2011)

• Measure particle-g coincidences• Unfold 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 density

Experiments at OCL

12 MeV d on 232Th24 MeV 3He on 232Th

g3He –beam

3He, a,d,t

5”x5” NaI

M.Guttormsen, A.Bürger, T.E.Hansen, N.Lietaer,

NIM A648(2011)168

∆E-E

Backwards: J = 40o – 54o

Oslo Seminar, Oslo, 6 December, 2012

∆E-E bananas

(d,d’)232Th (d,p)233Th (3He,t)232Pa (3He,d)233Pa

(3He,a)231Th

Oslo Seminar, Oslo, 6 December, 2012

Assumption for the extraction of first-generation g-spectra

Oslo Seminar, Oslo, 6 December, 2012

(d,p)

(d,p)

The g-energy distribution is the sameif the decay starts at E after g-emission orstarts after the direct reaction into E.

E

g

Gamma-multiplicity

Oslo Seminar, Oslo, 6 December, 2012

From total to primary g-ray matrix

spin2-6ħ

Ex

232Th(d,p) 233Th

Oslo Seminar, Oslo, 6 December, 2012

Primary g-ray matrix

P(Ex,Eg)

Level density Trans. coeff.

r(Ef) T(Eg)

P(Ex,Eg)

Oslo Seminar, Oslo, 6 December, 2012

Multiplicative factors

Oslo Seminar, Oslo, 6 December, 2012

Brink hypothesis

Fermi’s golden rule

P(Ex,Eg) = r(Ef) . T(Eg) ?

Oslo Seminar, Oslo, 6 December, 2012

Normalization

Oslo Seminar, Oslo, 6 December, 2012

1) A. Gilbert and A.G.W. Cameron, Can. J. Phys. 43, 1446 (1965)

2) T. von Egidy and D. Bucurescu, Phys. Rev. C 72, 044311 (2005), Phys. Rev. C 73, 049901(E) (2006)

3) S. Goriely, HF+BCS Demetriou and Goriely, Nucl. Phys. A695 (2001) 95

44ScAverage level spacings D from neutron capture:

r(Ef) and T(Eg)

Oslo Seminar, Oslo, 6 December, 2012

231,232,233Th and 232,233Pa

Inverse energy-weighted sum rule:

K. Heyde, P. von Neumann-Cosel, A. Richter, Rev. Mod. Phys., 82, 2365 (2010)

Oslo Seminar, Oslo, 6 December, 2012

M. Guttormsen et al., PRL 109, 162503 (2012)

Thermal quasi-particles, the spectators of mid-shell nuclei

Oslo Seminar, Oslo, 6 December, 2012

Thermal quasi-particles create level density

Oslo Seminar, Oslo, 6 December, 2012

Cooper pair Broken pair

1 level 25 levels

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

j

Nilsson level scheme

Oslo Seminar, Oslo, 6 December, 2012

Model parameters:k = 0.066m = 0.32b = 0.23

1p 1n1p 3n1p 5n1p 7n

3p 1n3p 3n3p 5n

5p 1n5p 3n

7p 1n

20

Level density and broken pairs

Oslo Seminar, Oslo, 6 December, 2012

Level densities

Number of broken pairs

Parity asymmetry

Oslo Seminar, Oslo, 6 December, 2012

U. Agvaanluvsan, G.E. Mitchell, J.F. Shriner Jr., Phys. Rev. C 67, 064608 (2003)

Titanium and tin

Oslo Seminar, Oslo, 6 December, 2012

46Ti

Summary

Oslo Seminar, Oslo, 6 December, 2012

• 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/