4. Level densities Prof. Dr. A.J. (Arjan) Koning1,2

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Presentation transcript:

Email: A.koning@iaea.org 4. Level densities Prof. Dr. A.J. (Arjan) Koning1,2 1International Atomic Energy Agency, Vienna 2Division of Applied Nuclear Physics, Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden Email: A.koning@iaea.org EXTEND European School on Experiment, Theory and Evaluation of Nuclear Data, Uppsala University, Sweden, August 29 - September 2, 2016

THE LEVEL DENSITIES (Principle) ?

Level density definition

Fermi gas level density

(Qualitative aspects 1/2) THE LEVEL DENSITIES (Qualitative aspects 1/2) 56Mn 57Fe 58Fe E (MeV) N(E) Incident neutron energy (eV) Total cross section (b) n+232Th Exponential increase of the cumulated number of discrete levels N(E) with energy  r(E)=  odd-even effects Mean spacings of s-wave neutron resonances at Bn of the order of few eV  r(Bn) of the order of 104 – 106 levels / MeV dN(E) dE increases exponentially

(Quantitative analysis 2/2) THE LEVEL DENSITIES (Quantitative analysis 2/2) ~ a (A) 1 - exp ( - g U* ) U* 1 + dW(N,Z) a (N, Z, U*) =

(Summary of most simple analytical description) THE LEVEL DENSITIES (Summary of most simple analytical description) 1 10 - 10 3 - 10 4 - 10 5 - 10 6 - 10 2 - N(E) E (MeV) 1 2 3 4 5 6 7 8 9 Fermi gas (adjusted at Bn) Temperature law Discrete levels (spectroscopy) ( ) exp 2 aU* a1/4U*5/4 r (E) a = N(E)=exp E – E0 T ( )

MISCELLANEOUS : THE LEVEL DENSITIES (More sophisticated approaches) Superfluid model & Generalized superfluid model Ignatyuk et al., PRC 47 (1993) 1504 & RIPL3 paper (IAEA) More correct treatment of pairing for low energies Fermi Gas + Ignatyuk beyond critical energy Explicit treatment of collective effects r(U) = Kvib(U) * Krot(U) * rint(U) Collective enhancement only if rint(U)  0 not correct for vibrational states aeff  A/8 a  A/13 Several analytical or numerical options

(The combinatorial method 2/3) THE LEVEL DENSITIES (The combinatorial method 2/3) Structures typical of non-statistical feature

Towards a complete calculation for Cu-65: level density Sample case 17 contains 3 sub-cases for different level density models, for Tc-99. Apply these keywords to the case of Cu-65 and see what the effect is. talys < input >output (3 times) Retrieve experimental data for (n,p) and/or (n,n’) and/or (n,2n) from EXFOR at IAEA and compare.