What can we learn from nuclear level density? Magne Guttormsen Department of Physics and SAFE University of Oslo

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 2 Fermi gas and beyond ● Protons and neutrons ● The Pauli principle ● Interacting particles Fermi gas (Hans Bethe 1936): Parameters: a    

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 3 Oslo Cyclotron Laboratory

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio Er( 3 He, 3 He’) 167 Er Spin ExEx    T = 1 MeV Particle-gamma coincidences

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 5 The Oslo method

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 6 Simulations and extraction Generated in Prague: Event-by-event data with DICEBOX Sorted in Oslo: (E x, E  ) matrix First generation procedure Factorization into  and f Ex EE Ex EE

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 7 Blind test

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 8 Level density and entropy Yb 172

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 9 Modeling level density Cooper pair Broken pair 1 state 25 states ● Odd-even mass differences ● Ground-state spin J = 0 ● Abrupt increase at E x = 2∆

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 10 A simple model for level density - Combining all possible proton and neutron configurations - Nilsson single-particle energy scheme - BCS quasi-particles  j

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 11 Nilsson level scheme Model parameters:  =  = 0.32  = p 1n 1p 3n 1p 5n 1p 7n 3p 1n 3p 3n 3p 5n 5p 1n 5p 3n 7p 1n 20

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 12 Scandium, shape coexistence Level densities Number of broken pairs

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 13 Parity asymmetry U. Agvaanluvsan, G.E. Mitchell, J.F. Shriner Jr., Phys. Rev. C 67, (2003)

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 14 Iron, blocking of neutron pairs

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 15 Molybdenum, approaching N=50 93 Mo  = Mo  = Mo  = Mo  = Mo  = Mo  = d 5/2 g 9/2

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 16 Tin, proton shell gap Z=50

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 17 Tin, dominance of neutron pairs

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 18 Ytterbium, dominance of proton pairs Proton and neutron orbitals +/- 8 MeV above Fermi surface: 44(p) + 58(n) = 102 orbitals

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 19 Proton or neutron pairs p n p n p n n p 86% n 14% p 57% n 43% p

Nuclear level density reveals ● Entropy and thermodynamics (T c, C V ) ● Breaking Cooper pairs ● Parity asymmetry ● Shell gaps ● Shape coexistence New position in Oslo, Professor of Physics!

Workshop on Statistical Nuclear Physics and Applications in Astrophysics and Technology, July , Athens, Ohio 21 Extensivity in nuclei S = S* S = S* + S1 S1