1. 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
EXTEND
European School on Experiment, Theory and Evaluation of Nuclear Data, Uppsala University, Sweden, August 29 - September 2, 2016

2. THE LEVEL DENSITIES
(Principle) ?

3. Level density definition

4. Fermi gas level density

5. (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

6. (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*) =

7. (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)
Fermi gas (adjusted at Bn)
Temperature law
Discrete levels
(spectroscopy)
( )
exp aU*
a1/4U*5/4
r (E) a =
N(E)=exp
E – E0 T
( )

8. 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

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

10. 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.