Reduced Electromagnetic Transition Strengths and Recommended Upper Limits
"Title: RULER - Reduced Electromagnetic Transition Strengths and Recommended Upper Limits. Definitions isomer exp. Partial-ray half-life. Current issues with RULER. Uncertainty propagation. Details on empirical transition strengths presented by Tibor Kibdi from the Australian National University."
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RULER - Reduced Electromagnetic Transition Strengths and Recommended Upper Limits T. Kib di (ANL) F.G. Kondev (ANU) Tibor Kib di, Dep. of Nuclear Physics, Australian National University ND2010, Jeju Island , Korea, 26-30-Apr-2010
Definitions isomer exp + 2 1 2 ( 2 + ln 2 1 e )! ! b c = ( ) ( ) T E B E / 1 2 ) 1 + 2 8 ( E j + 2 1 2 ( + 2 + ln 2 1 )! b ! c = ( ) ( ) T M B M / 1 2 2 N 1 8 ( ) 1 E Relative strengths ( ) B E Weisskopf single particle estimates: exp = ( )( . .) B E W u ( ) B E . . s p + 2 1 2 ( + 2 2 2 + e + 1 3 + ln 2 1 )! R ! 3 c = 2 = ( ) B E R ( ) T E . . s p / 1 2 . . s p 4 2 2 3 b 2 ( ) 1 3 E + 2 1 2 ( + 2 2 2 2 + + 10 b 3 + ln 2 1 )! R ! 3 c = 2 2 = ( ) B M R ( ) T M . . s p / 1 2 . . s p 1 2 N 2 3 80 ( ) 1 3 E Tibor Kib di, Dep. of Nuclear Physics, Australian National University NSDD 2015, IAEA, 20-24-Apr-2015
Empirical transition strength isomer exp Partial -ray half-life: N = + k k T 1 ( ) I = j 1 k j exp j I ( ) B E Mixed transitions exp = ( )( . .) B E W u ( ) B E . . s p ( ' ) ' I = + 2 j j I ( ) 1 ( ) = 2 ( ' / ' ) ( ) + 2 1 + + 2 ( ) ( ' ) ' = j j ( ' ) ' = j ( ' / ' ) T T 2 T 2 1 Tibor Kib di, Dep. of Nuclear Physics, Australian National University NSDD 2015, IAEA, 20-24-Apr-2015
Current issues with RULER NSDD/IAEA: 3.2a (Aug-6-2007; T.W. Burrows) Isomer evaluation (ANU/ANL): 4.1c (12-Jun-2014) Problems: Complicated logic Related parameters stored at different places Uncertainty propagation: analytical approach; ad hock, nested branches based on numerical values Modifications ENSDF type: Value, uncertainties (numerical and character) stored together Simplified logic Added functionality: ICC calculated for mixed and pure multipolarities to deduce B( L) and B( L ) LaTex output for ADNDT Tibor Kib di, Dep. of Nuclear Physics, Australian National University NSDD 2015, IAEA, 20-24-Apr-2015
Uncertainty propagation isomer exp Partial -ray half-life: N = + k k T 1 ( ) I = j 1 k j exp j I + + 2 ( ) ( ' ) ' f(X) = j ( ' / ' ) T T T 2 1 X Value = f(X) Uncertainty calculated as: |DfL|= |f(X)-f(DXL)| |DfU|= |f(X)-f(DXL)| X-DXL X-DXU Tibor Kib di, Dep. of Nuclear Physics, Australian National University NSDD 2015, IAEA, 20-24-Apr-2015
Uncertainty propagation isomer exp Partial -ray half-life: N = + k k T 1 ( ) I = j 1 k j exp j I + + 2 ( ) ( ' ) ' f(X) = j ( ' / ' ) T T T 2 1 X Value = stat. mean Uncertainty calculated from distribution of f(x) X-DXL X-DXU Tibor Kib di, Dep. of Nuclear Physics, Australian National University NSDD 2015, IAEA, 20-24-Apr-2015
Uncertainty propagation using Monte Carlo Probability Density Functions NORMAL (symmetric) Skewed Gaussian (asymmetric) Square (limits; constant prob.) X 3 : - X 3 X -3 : - X -3 but X +3 : 0 X +3 Program library based on NPL report MS 7 (2010 Cox) Part of NS_lib (FORTRAN 90) shared with BrIcc, BrIccMixing, BrIccEmis, NEWRuler . Tibor Kib di, Dep. of Nuclear Physics, Australian National University NSDD 2015, IAEA, 20-24-Apr-2015
