# Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 New Theoretical Conversion Coefficients. Comparison with.

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Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 New Theoretical Conversion Coefficients. Comparison with Experimental Values and Recent Additions to the Band-Raman Internal Conversion Coefficients (BrIcc) T. Kibédi Dept. of Nuclear Physics, Australian National University, Canberra, Australia T.W. Burrows National Nuclear Data Center, Brookhaven National Laboratory, Upton, U.S.A. M.B. Trzhaskovskaya Petersburg Nuclear Physics Institute, Gatchina, Russia P.M. Davidson Dept. of Nuclear Physics, Australian National University, Canberra, Australia C.W. Nestor, Jr. Oak Ridge National Laboratory, Oak Ridge, U.S.A

Conversion Electron Process (CE) Transition probability T =  + K + L + M …… +  Selection rules (  L) |L-j i | ≲ j f ≲ L+j i  = (-1) L for EL  = (-1) L+1 for ML Tibor Kibèdi, D`ep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Energetics of CE-decay (i=K, L, M,….) E i - E f = E ce,i + E BE,i + T r K L M  -ray pair production (E tr > 1022 keV) conversion electron K M

Physical model  Calculations up to the first nonvanishing order of the perturbation theory  One electron approximation Atomic field model  Exchange term  Relativistic Hartree-Fock-Slater (HsIcc, RpIcc): approximately  Relativistic Dirac-Fock (RAINE used for BrIcc): exactly  Free neutral atom  Screening of the nuclear field by the atomic electrons  Spherically symmetric atomic potential  Experimental electron binding energies Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 How good the theoretical ICCs are?

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 How good the theoretical ICCs are? Nuclear model  Spherically symmetric nucleus; most abundant isotope  Finite nuclear size, penetration effects  203 Tl: E  =279.1955(12) keV; M1+E2;  =+1.17(5)  K (exp) =0.1642(11) from 7 measurements  Non-hindered transitions, RAINE used for BrIcc: “Static effects” approximately, but consistently (SC model, Sliv)  Non-hindered transitions, RAINE used for BrIcc: “Static effects” treated approximately, but consistently (SC model, Sliv)  Hindered transitions: correction for “dynamic effects” (Pauli) measured theoretical λ, η, ξ: depend on nuclear parameters (from fit to the experimental data) a 1i, a 2i, a 3i, a 4i, a 5i, b 1i, b 2i : depend on electronic parameters (from theoretical calculations)  K (HsIcc)=0.216(10)  K (RpIcc)=0.218(10)  K (BrIcc)=0.209(8)

Higher order effect – ignored in most models  Atomic many body correlations: factor ~2 for E kin (ce) < 1 keV  Partially filled valence shell: non-spherical atomic field  Binding energy uncertainty: 10 keV  Chemical effects: <<1% Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 How good the theoretical ICCs are? BrIcc: for i-th atomic shell  i is given for E tr ≥ BE i + 1 keV

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 “No Hole” Approximation, BTNTR Band, Trzhaskovskaya, et. al. (2002)  -ray K L M r Radial distribution of EWF bound state electron free particle electron Electron conversion Vacancy disregarded in the SCF of a neutral atom

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008  -ray K L M r Radial distribution of EWF bound state electron free particle electron Electron conversion Vacancy included in the SCF of a neutral atom in the SCF of an ion “Self Consistent” Approximation, RNIT(1) Band, Trzhaskovskaya, et. al. (2002)

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008  -ray K L M r Radial distribution of EWF bound state electron free particle electron Electron conversion in the SCF of a neutral atom Constructed from bound wave function of a neutral atom; it is NOT SCF Vacancy included “Frozen Orbital” Approximation, RNIT(2) Band, Trzhaskovskaya, et. al. (2002)

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Hole / No Hole – how sizable is it? “Frozen Orbital” vs. “No Hole” (Total ICC) (K-shell)

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Benchmark experimental ICC data Benchmark data sets  100  K and  T -  100  K and  T - S. Raman, et al., Phys. Rev. C66, 044312 (2002)  1510 ICC ratios – S. Raman, et al., Atomic Data and. Nucl. Data Tables 92, 207 (2006) New experiments – see talk by Ninel Nica   K (80 keV 193 Ir M4) Nica, et al., Phys. Rev. C 70 (2004) 054305   T (88 keV 109 Ag E3) Kossert et al., App. Rad. and Isotopes 64 (2006) 1031   K (128 keV 134 Cs E3)/  K (662 keV 137 Ba M4) Nica et al., Phys. Rev. C 75, (2007) 024308  K (128 keV 134 Cs E3) and  K (662 keV 137 Ba M4)   K (128 keV 134 Cs E3) and  K (662 keV 137 Ba M4) Nica et al., Phys. Rev. C 77, (2008) 034306

History Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008  K (experimental) (31 published value)

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 History Calculations

More than 20% of the ICC values and/or uncertainties have been changed. ENSDF  K ( 124 Te, 646 keV, E2(+M3)) 0.00340(14)  K ( 58 Co, 25 keV, M3) 1860(100) 1063.656(3) keV M4+E5 in 207 Pb  K 0.0972(23) Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 New review of high precision ICC`s  K NPG changed  K(557) XPG changed XPG changed  K Re-evaluated; 8 measurements; 1 excluded Raman 2002 --- 2030(90) 0.0945(22) Present work 0.00345(14) 1860(69) 0.0946(15)

General policies to deduce adopted ICCs  Primary data:  ≤ 15%; Adopted values:  ≤ 5%  Multipolarity: E2, M3, E3, E4, M4, E5. Excluded: E1 (hindered) and M1 (mixed), M2 (mixed)  ICCs considered:  K,  L,  Total,  K /  L  Energy (uncertainty), mixing ratio from adopted ENSDF data set  Multipolarity must determined from other quantities  When more than two measurements are known, three statistical methods used to  When more than two measurements are known, three statistical methods used to identify discrepant data points and deduce weighted mean values and assign uncertainties – Limitation of Relative Statistical Weights Method (LWM), – Normalized Residuals Method (NRM), – Rajeval Technique (RT). http://wwwrsphysse.anu.edu.au/~txk103/avetools/ Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 New review of high precision ICC`s With Thomas Burrows (NNDC) in 2005-2008

 N≥3 – no single value should have a weight >50%  Discrepant data: more than 3  away from the mean  χ 2 /(N-1) < χ 2 (critical) – weighted mean used  χ 2 /(N-1) ≥ χ 2 (critical) – weighted or unweighted average is adopted and the larger value of the internal or external uncertainty is used  Uncertainty may be increased to include the “most precise” value In most cases LWM was adopted, however the other two methods were used to identify discrepant data. Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Limitation of Relative Statistical Weight (LWM)

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Normalized Residual Method (NRM)  Normalized Residual, R i defined as: Where  Data discrepant if and its uncertainty adjusted

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Rajeval Technique (RT)   Deviant values identified (and rejected) by comparing the absolute value of to 1.96 where μ i is the unweighted average excluding the ith value and σ μi is its associated standard deviation  Uncertainties on inconsistent values are adjusted until the standardized deviate is consistent with the central deviate

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Calculating Experimental Averages (Adopted values)   If results from the three techniques agree, the input data can be considered consistent. Comparison of the detailed output from the three techniques may aid in an objective determination of deviant input data  Data is deviant if (Same criteria for comparing experiment to theory) - Marked as an outlier by LWM and RT and adjusted by NRM - Marked as an outlier by LWM and significantly adjusted by NRM and RT - Marked as an outlier by RT and significantly adjusted by NRM - Significantly adjusted by NRM and RT  Process is repeated until results from all three techniques agree or no value satisfies the above criteria  If results from the three techniques do not agree, the arithmetic mean of NRM and RT is adopted and the larger of the uncertainties from NRM and RT is used. Adopted 213 ICC values of Total, K-, L-shells and K/L ratios Summary: Adopted 213 ICC values of Total, K-, L-shells and K/L ratios

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 ENSDF (2007) ICC K =0.0904(5) Adopted LWM: 0.09102(27) Χ 2 /(N-1)=0.94 NRM: 0.09102(27) RT: 0.09110(28) DDEP (2006) ICC K =0.0896(15) HSICC: 0.09261 RPICC: 0.09285 BTNTR: 0.09068 RNIT(1): 0.09139 RNIT(2): 0.09148

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Comparing Experiment with Theory   Difference measured as:  Compared with the three Dirac-Fock calculations of BTNTR: “No hole” RNIT(1): “Self consistent” RNIT(2): “Frozen Orbital”  Data divided into subgroups based on multipolarity, shell (or ratio)  Looked for deviant data; same criteria as for calculating average experimental ICC  Adopted average differences from LWM; NRM and RT used only to identify discrepant data  Adopted average differences based on 186 ICCs

80.2 K (M4) 193 Ir How good are the internal conversion coefficients now? Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Exp. vs. “No Hole”, BTNTR +0.70 (40) % ALL +0.19(26) % Raman et al. (2002) (K-shell)

80.2 K (M4) 193 Ir Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 -1.18(24) % Raman et al. (2002) ALL -0.93 (14) % Exp. vs. “Frozen Orbital”, RNIT(2) How good are the internal conversion coefficients now? (K-shell)

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 MLShellN“No Hole” BTNTR ”Self Consistent” RNIT(1) “Frozen Orbital” RNIT(2)  2 /(N-1) All 186+0.70(40)1.82-0.61(14)1.01-0.93(14)0.87  ICC How good are the internal conversion coefficients now? (Aug 2007) χ 2 (critical)=1.25 Both negative; RNIT(1) out by 4.5  RNIT(2) out by 6.9 

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 MLShellN“No Hole” BTNTR ”Self Consistent” RNIT(1) “Frozen Orbital” RNIT(2)  2 /(N-1) All 186+0.70(40)1.82-0.61(14)1.01-0.93(14)0.87 TotAll54+0.32(25)0.79-0.55(24)0.76-0.71(24)0.73  ICC How good are the internal conversion coefficients now? (Aug 2007) χ 2 (critical)=1.51 1.3  2.3  3.0  Marginal differences

+1.50 (120) % K +0.5(5) % Raman et al. (2002) 80.2 K (M4) 193 Ir Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Exp. vs. “No Hole”, BTNTR How good are the internal conversion coefficients now? (K-shell)

-0.72 (21) % K -1.4(4) % Raman et al. (2002) 80.2 K (M4) 193 Ir How good are the internal conversion coefficients now? Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Exp. vs. “Frozen Orbital”, RNIT(2) (K-shell)

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 MLShellN“No Hole” BTNTR ”Self Consistent” RNIT(1) “Frozen Orbital” RNIT(2)  2 /(N-1) All 186+0.70(40)1.82-0.61(14)1.01-0.93(14)0.87 TotAll54+0.32(25)0.79-0.55(24)0.76-0.71(24)0.73 KAll72+1.5(12)3.14-0.18(21)1.09-0.72(21)0.80  ICC How good are the internal conversion coefficients now? (Aug 2007) χ 2 (critical)=1.43 Not favored

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 MLShellN“No Hole” BTNTR ”Self Consistent” RNIT(1) “Frozen Orbital” RNIT(2)  2 /(N-1) All 186+0.70(40)1.82-0.61(14)1.01-0.93(14)0.87 TotAll54+0.32(25)0.79-0.55(24)0.76-0.71(24)0.73 KAll72+1.50(120)3.14-0.18(21)1.09-0.72(21)0.80 K/LAll46+0.00(31)0.83-1.64(31)0.96-1.94(30)1.02  ICC How good are the internal conversion coefficients now? (Aug 2007) RNIT(1) and RNIT(2) out by >5  Unexpected

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 MLShellN“No Hole” BTNTR ”Self Consistent” RNIT(1) “Frozen Orbital” RNIT(2)  2 /(N-1) All 186+0.70(40)1.82-0.61(14)1.01-0.93(14)0.87 TotAll54+0.32(25)0.79-0.55(24)0.76-0.71(24)0.73 KAll72+1.50(120)3.14-0.18(21)1.09-0.72(21)0.80 K/LAll46+0.00(31)0.83-1.64(31)0.96-1.94(30)1.02 E2All103+0.21(23)1.01-0.77(23)0.89-0.93(23)0.90  ICC How good are the internal conversion coefficients now? (Aug 2007) RNIT(1) and RNIT(2) out by >3  RNIT(2) “follows the trend” being around -0.9 BTNTR consistent

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 MLShellN“No Hole” BTNTR ”Self Consistent” RNIT(1) “Frozen Orbital” RNIT(2)  2 /(N-1) All 186+0.70(40)1.82-0.61(14)1.01-0.93(14)0.87 TotAll54+0.32(25)0.79-0.55(24)0.76-0.71(24)0.73 KAll72+1.50(120)3.14-0.18(21)1.09-0.72(21)0.80 K/LAll46+0.00(31)0.83-1.64(31)0.96-1.94(30)1.02 E2All103+0.21(23)1.01-0.77(23)0.89-0.93(23)0.90 M4All50+0.98(68)3.87-0.51(20)1.29-0.93(20)0.72  ICC How good are the internal conversion coefficients now? (Aug 2007) χ 2 (critical)=1.53 Not favored RT adjusted 193 Ir K  from 3.4(8)% to 3.4(17)% Problems with 207 Pb K/L New data from TAMU on 193 Ir and 137 Ba!

+0.77 (51) % Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Exp. vs. “No Hole”, BTNTR How good are the internal conversion coefficients now? (K-shell)

-0.95 (17) % How good are the internal conversion coefficients now? Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Exp. vs. “Frozen Orbital”, RNIT(2) 193 Ir 80.2K M4 193 Pt 135.5K M4 197 Hg 165.0K M4 (K-shell)

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 MLShellN“No Hole” BTNTR ”Self Consistent” RNIT(1) “Frozen Orbital” RNIT(2)  2 /(N-1) All 186+0.70(40)1.82-0.61(14)1.01-0.93(14)0.87 TotAll54+0.32(25)0.79-0.55(24)0.76-0.71(24)0.73 KAll72+1.50(120)3.14-0.18(21)1.09-0.72(21)0.80 K/LAll46+0.00(31)0.83-1.64(31)0.96-1.94(30)1.02 E2All103+0.21(23)1.01-0.77(23)0.89-0.93(23)0.90 M4All50+0.98(68)3.87-0.51(20)1.29-0.93(20)0.72 ICCs known better than 1.5% rel. unc. All 25+0.77(51)8.21-0.56(26)2.12-0.95(17)1.06  ICC How good are the internal conversion coefficients now? (Mar 2008) χ 2 (critical)=1.79 Not favored Marginally larger than χ 2 (critical) Favored

BrIcc – Status and plans Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Version History Nov-2003, NSDD, Vienna: program development initiated May-2004, ICC tables, based on the “No Hole” approximation developed Oct-2004, Version 1.3 (“No Hole” ) distributed for ENSDF evaluators Nov-2004, BrIcc (“No Hole”) web interface (ANU) Feb-2005, Review of experimental ICC`s started Jun-2005, NSDD, McMaster: “Frozen orbital” approximation has been adopted Oct-2005, BrIcc v2.0 (“Frozen orbital”, Z=10-95) released Apr-2007, BrIcc adopted for the DDEP network Mar-2008, BrIcc v2.0 (“Frozen orbital” “No Hole” and, Z=5-110, updated mass and binding energy data) Future: E0 and E0+M1+E2 transitions, Atomic radiations following electron conversion, improved treatment of uncertainties

Evaluation of theoretical conversion coefficients using BrIcc Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 A general tool to obtain electron conversion coefficients:  i ; i=K, L1, L2, …R2 shells; L=1-5 Based on Band et. al.,, ADNDT 81, 1 (2002) model[2002Ba85] “Frozen Orbitals” Approximation DEFAULT & RECOMMENDED “No Hole” Approximation electron-positron pair conversion coefficients:    L=1-3 P. Schluter and G. Soff, At. Data Nucl. Data Tables 24, 509 (1979)[1979Sc31] C.R. Hofmann and G. Soff, At. Data Nucl. Data Tables 63, 189 (1996)[1996Ho21] E0 electronic factors: Ω i (K,L1,L2) and Ω  R.S. Hager and E.C. Seltzer, Nucl. Data Tables, 6, 1 (1969)[1969Ha61] D.A. Bell, et. al., Can. J. of Phys., v48, 2542 (1970) [1970Be87] A. Passoja and T. Salonen, JYFL Preprint 2/86 (1986)[1986PaZM] An ENSDF evaluation tool to calculate:  i ±Δα i for the GAMMA records for a given Z, E  and for pure or mixed multipolarities. Uncertainties in transition energy and mixing ratio can either symmetric, asymmetric including limits. Version 2.2 Z=5-110 ~40 atomic masses changed Nuclear Instr. and Meth. in Phys. Res. A 589 (2008) 202

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Integration BrIcc into other programs BrIccS “Silent” version  Called from other programs, parameters passed on the command line  ICC data returned in XML format  Simplified coding work  ICC and uncertainty evaluated according to ENSDF Example 1063.656(3) keV, M4 + E5,  =0:020(10) transition in 207 Pb. Format of the command line: briccs -Z 82 -g 1063.656 -e 3 -L M4+E5 -d 0.020 -u 10 -a -w BrIccFO

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 BrIcc on the web http://wwwrsphysse.anu.edu.au/nuclear/bricc/

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 Integration BrIcc into other programs – XML output Lead M4+E5 0.020 1063.656 0.1257 0.0942 briccs -Z 82 -g 1063.656 -e 3 -L M4+E5 -d 0.020 -u 10 -a -w BrIccFO XML parsers are readily available for many programming languages and operating systems

Tibor Kibèdi, Dep. of Nuclear Physics, Australian National University DDEP Workshop 12-May-2008 BrIcc on the web http://wwwrsphysse.anu.edu.au/nuclear/bricc/ Un-mixed (pure) ICC

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