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7. Gamma-ray strength functions Prof. Dr. A.J. (Arjan) Koning 1,2 1 Division of Applied Nuclear Physics, Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden 2 Nuclear Research and Consultancy Group (NRG), Petten, The Netherlands Email: koning@nrg.eu PhD course on Nuclear reactions and nuclear reaction modeling with TALYS, Uppsala University, Uppsala, Sweden, November 13 – 20, 2014
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THE COMPOUND NUCLEUS MODEL (basic formalism) Compound nucleus hypothesis - Continuum of excited levels - Independence between incoming channel a and outgoing channel b abababab= (CN) P b aaaa (CN) = T a aaaa p kakakaka 2 Pb=Pb=Pb=Pb= TbTbTbTb S TcS TcS TcS Tc c Hauser- Feshbach formula = abababab p kakakaka 2 Ta TbTa TbTa TbTa Tb S TcS TcS TcS Tc c Tb can only be a gamma-ray transmission coefficient
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Gamma transmission coefficients T k ( ) = = 2 f(k, )) 2 +1 k : transition type EM (E or M) : transition multipolarity : outgoing gamma energy f(k, ) : gamma strength function Decay selection rules from a level J i i to a level J f f : For E : For M : |J i - ≤ J f ≤ J i + f =(-1) i f =(-1) i (several models) 2 k ( ) (E) dE E E+ E Renormalisation technique for thermal neutrons = 2 (B n ) D0D0 1 experiment C T k ( ) (B n - ,J f, f ) S(,J i, i J i, f ) d = 0 BnBn Ji,iJi,i k Jf,fJf,f C
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MISCELLANEOUS : THE PHOTON EMISSION (strength function and selection rules)
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THE PHOTON EMISSION (strength function and selection rules) Improved analytical expressions : - 2 Lorentzians for deformed nuclei - Account for low energy deviations from standard Lorentzians for E1. Kadmenskij-Markushef-Furman model (1983) Enhanced Generalized Lorentzian model of Kopecky-Uhl (1990) Hybrid model of Goriely (1998) Generalized Fermi liquid model of Plujko-Kavatsyuk (2003) - Reconciliation with electromagnetic nuclear response theory Modified Lorentzian model of Plujko et al. (2002) Simplified Modified Lorentzian model of Plujko et al. (2008) Microscopic approaches : RPA, QRPA « Those who know what is (Q)RPA don’t care about details, those who don’t know don’t care either », private communication Systematic QRPA with Skm force for 3317 nuclei performed by Goriely-Khan (2002,2004) Systematic QRPA with Gogny force underconstruction
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MISCELLANEOUS : THE PHOTON EMISSION (phenomenology vs microscopic) See S. Goriely & E. Khan, NPA 706 (2002) 217. S. Goriely et al., NPA739 (2004) 331.
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Important for practical TALYS work (TALYS manual) 7 Strength function can be renormalised and fitted to neutron capture data Using gamgamadjust keyword
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Fit capture cross section for Cu-65 Channels y Filechannels y Plot (log scale) xs000000.tot Adjust ‘gamgamadjust 29 66’ until satisfied 8
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Photonuclear: Do this for Cu-65 (any exp data? If not, run for Cu-63) 9
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