Oslo Seminar Oslo 6 December 2012 Measure particle

Oslo Seminar, Oslo, 6 December, 2012

Measure particle- coincidences Unfold spectra at each E 1) Apply the first-generation method Ansatz: First-generation matrix P(E, E ) (E - E ) T(E ) 3) • Normalization • Examples of level density • • 2) M. Guttormsen et al. , NIM A 374 (1996) 371 2) M. Guttormsen et al. , NIM A 255 (1987) 518 3) A. Schiller et al. , NIM A 447 (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 Me. V d on 232 Th 24 Me. V 3 He on 232 Th Backwards: J = 40 o – 54 o 5”x 5” Na. I 3 He –beam 3 He, a, d, t ∆E-E M. Guttormsen, A. Bürger, T. E. Hansen, N. Lietaer, NIM A 648(2011)168 Oslo Seminar, Oslo, 6 December, 2012

(3 He, a)231 Th (d, d’)232 Th (d, p)233 Th Oslo Seminar, Oslo, 6 December, 2012 (3 He, t)232 Pa (3 He, d)233 Pa

(d, p) E (d, p) The -energy distribution is the same if the decay starts at E after -emission or starts after the direct reaction into E. Oslo Seminar, Oslo, 6 December, 2012

Oslo Seminar, Oslo, 6 December, 2012

232 Th(d, p) 233 Th Ex 2 -6ħ spin Oslo Seminar, Oslo, 6 December, 2012

P(Ex, Eg) Level density r(Ef) Oslo Seminar, Oslo, 6 December, 2012 Trans. coeff. T(Eg)

Fermi’s golden rule Brink hypothesis Oslo Seminar, Oslo, 6 December, 2012

, Eg) Oslo Seminar, Oslo, 6 December, 2012 r(Ef) T(Eg)

Normalization Average level spacings D from neutron capture: 1) 2) 3) Oslo Seminar, Oslo, 6 December, 2012 44 Sc 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. A 695 (2001) 95

r(Ef) Oslo Seminar, Oslo, 6 December, 2012 T(Eg)

231, 232, 233 Th and 232, 233 Pa M. Guttormsen et al. , PRL 109, 162503 (2012) 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

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 Model parameters: k = 0. 066 m = 0. 32 b = 0. 23 20 1 p 1 n 1 p 3 n 1 p 5 n 1 p 7 n 3 p 1 n 3 p 3 n 3 p 5 n 5 p 1 n 5 p 3 n 7 p 1 n Oslo Seminar, Oslo, 6 December, 2012

Level density and broken pairs Level densities Oslo Seminar, Oslo, 6 December, 2012 Number of broken pairs

Parity asymmetry U. Agvaanluvsan, G. E. Mitchell, J. F. Shriner Jr. , Phys. Rev. C 67, 064608 (2003) Oslo Seminar, Oslo, 6 December, 2012

Titanium and tin 46 Ti Oslo Seminar, Oslo, 6 December, 2012

Summary • • • Simultaneous extraction of level density and -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/workshop 2013/ Oslo Seminar, Oslo, 6 December, 2012