1. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 Jagdish K. Tuli NNDC Brookhaven National Laboratory Upton, NY 11973, USA Decay Scheme Normalization

2. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 1.Relative intensity is what is generally measured 2. Multipolarity and mixing ratio (  ). 3. Internal Conversion Coefficients Theoretical Values: From BRICC

3. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 Experimental values: For very precise values (  3% uncertainty). E  = 661 keV ; 137 Cs (  K =0.0902 + 0.0008, M4) Nuclear penetration effects. 233 Pa  - decay to 233 U. E  = 312 keV almost pure M1 from electron sub-shell ratios. However  K (exp) = 0.64 + 0.02. (  K th (M1)=0.78,  K th (E2)=0.07)

4. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 For mixed E0 transitions (e.g., M1+E0). 227 Fr  - 227 Ra E  = 379.1 keV (M1+E0);  (exp) = 2.4 + 0.8  th (M1) = 0.40;  th (E2) = 0.08 675.8 296.6 379.5 ½- <10 ps 227 Ra

5. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

6. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

7. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 Decay Scheme Normalization Rel. Int.Norm. FactorAbs. Int. I  NR  BR%I  I t NT  Br%I t I  NB  BR%I  I  NB  BR%I  I  NB  BR%I  BR: Factor for Converting Intensity Per 100 Decays Through This Decay Branch, to Intensity Per 100 Decays of the Parent Nucleus NR: Factor for Converting Relative I  to I  Per 100 Decays Through This Decay Branch. NT: Factor for Converting Relative TI to TI Per 100 Decays Through This Decay Branch. NB: Factor for Converting Relative   and  Intensities to Intensities Per 100 Decays of This Decay Branch.

8. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

9. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 Absolute intensities “Intensities per 100 disintegrations of the parent nucleus” Measured (Photons from  -,  +  +, and  decay) Simultaneous singles measurements Coincidence measurements

10. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

11. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 Normalization Procedures 1.Absolute intensity of one gamma ray is known (%I  ) Relative intensity I  +  I  Absolute intensity %I  +  I  Normalization factor N = %I  / I  Uncertainty  N =[ (  I   %I  ) 2 +(  I   I      x N Then %I  l = N x I  l  I  l = [(  N/N) 2 + (  I   I       x I  l I1I1 I2I2 %I  

12. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 2.From Decay Scheme I  Relative  -ray intensity;  : total conversion coefficient N x I  x (1 +  ) = 100% Normalization factor N = 100/ I  x (1 +  ) Absolute  -ray intensity % I  = N x I   00  (1 +  ) Uncertainty  % I   = 100 x  /(1 +  ) 2    100 % II

13. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 Total intensity from transition-intensity balance 200 150 100 95 0 -- TI(  7 ) = TI(  5 ) + TI(  3 ) If  (  7 ) is known, then I  7 = TI(  7 ) / [1 +  (  7 )] I6I6 I5I5 I4I4 I2I2 I3I3 I1I1 I7I7

14. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

15. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

16. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 Equilibrium Decay Chain T 0 > T 1, T 2 are the radionuclide half-lives, For t = 0 only radionuclide A 0 exists, % I  3, I  3, and I  1 are known. Then, at equilibrium % I  1 = (% I  3 /I  3 ) × I  1 × (T 0 /(T 0 – T 1 ) × (T 0 /(T 0 – T 2 ) Normalization factor N = %I  1 / I  1 A0A0 A1A1 A2A2 A3A3 I1I1 I3I3 T0T0 T1T1 T2T2

17. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

18. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

19. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

20. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

21. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

22. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

23. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

24. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

25. Jag Tuli DDP-Workshop Bucharest, Romania, May 08

26. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 Normalization factor N = 100 / I  1 (1 +  1 ) + I  3 (1 +  3 ) % I  1 = N x I  1 = 100 x I  1 / I  1 (1 +  1 ) + I  3 (1 +  3 ) % I  3 = N x I  3 = 100 x I  3 / I  1 (1 +  1 ) + I  3 (1 +  3 ) % I  2 = N x I  2 = 100 x I  2 / I  1 (1 +  1 ) + I  3 (1 +  3 ) Calculate uncertainties in %I  1, % I  2, and % I  3. Use 3% fractional uncertainty in  1 and  3. See Nucl. Instr. and Meth. A249, 461 (1986). To save time use computer program GABS  - 100 % I3I3 I2I2 I1I1

27. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 4. Annihilation radiation intensity is known I (  +) = Relative annihilation radiation intensity X i = Intensity imbalance at the ith level = (  +ce) (out) – (  +ce) (in) r i =  i /  + i theoretical ratio to ith level X i =  i +  + i =  + i (1 + r i ), therefore  + i = X i / 1 + r i 2 [X 0 / (1 + r 0 ) + Σ X i / (1 + r i )] = I(  +) ……… (1) [X 0 + Σ I  i (  + ce) to gs ] N = 100 ………. (2) Solve equation (1) for X 0 (rel. gs feeding). Solve equation (2) for N (normalization factor).  +ce) (in) (  +ce)(out) (++)2(++)2 (++)1(++)1 (++)0(++)0 ++++

28. Jag Tuli DDP-Workshop Bucharest, Romania, May 08 5.X-ray intensity is known I K = Relative Kx-ray intensity X i = Intensity imbalance at the ith level = (  +ce) (out) – (  +ce) (in) r i =  i /  + i theoretical ratio to ith level X i =  i +  + i, so  i = X i r i / 1 + r i (atomic vacancies);  K = K- fluorsc.yield P Ki = Fraction of the electron-capture decay from the K shell I K =  K [  0 ×P K0 + Σ  i × P Ki ] I K =  K [P K0 × X 0 r 0 / (1 + r 0 ) + Σ P Ki × X i r i / 1 + r i ]…(1) [X 0 + Σ I i (  + ce) to gs] N = 100 …. (2) Solve equation (1) for X 0, equation (2) for N.  +ce) (in) (  +ce)(out) (++)2(++)2 (++)1(++)1 (++)0(++)0 ++++