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Jagdish K. Tuli NNDC Brookhaven National Laboratory Upton, NY 11973, USA

Decay Scheme Normalization. Jagdish K. Tuli NNDC Brookhaven National Laboratory Upton, NY 11973, USA. 1.Relative intensity is what is generally measured 2. Multipolarity and mixing ratio ( d ). 3. Internal Conversion Coefficients Theoretical Values: From BRICC. Experimental values:

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Jagdish K. Tuli NNDC Brookhaven National Laboratory Upton, NY 11973, USA

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  1. Decay Scheme Normalization Jagdish K. TuliNNDCBrookhaven National LaboratoryUpton, NY 11973, USA

  2. 1.Relative intensity is what is generally measured 2. Multipolarity and mixing ratio (d). 3. Internal Conversion Coefficients Theoretical Values: From BRICC

  3. Experimental values: For very precise values ( 3% uncertainty). Eg = 661 keV ; 137Cs (aK=0.0902 + 0.0008, M4) Nuclear penetration effects. 233Pa b- decay to 233U. Eg = 312 keV almost pure M1 from electron sub-shell ratios. However aK(exp) = 0.64 + 0.02. (aKth(M1)=0.78, aKth(E2)=0.07)

  4. <10 ps 675.8 ½- For mixed E0 transitions (e.g., M1+E0). 227Fr b-227Ra Eg = 379.1 keV (M1+E0); a(exp) = 2.4 + 0.8 ath(M1) = 0.40; ath(E2) = 0.08 379.5 296.6 ½- 227Ra

  5. Decay Scheme Normalization Rel. Int. Norm. Factor Abs. Int. Ig NR  BR %Ig It NT  Br %It Ib NB  BR %Ib Ie NB  BR %Ie Ia NB  BR %Ia 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 Ig to IgPer 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 B-and E Intensities to Intensities Per 100 Decays of This Decay Branch.

  6. Absolute intensities “Intensities per 100 disintegrations of the parent nucleus” Measured (Photons from b-, e+b+, and a decay) Simultaneous singles measurements Coincidence measurements

  7. Normalization Procedures b- Ig2 Ig1 %Ig Absolute intensity of one gamma ray is known (%Ig) Relative intensity Ig+DIg Absolute intensity %Ig+D%Ig Normalization factor N = %Ig / Ig Uncertainty DN =[ (D%Ig/ %Ig)2+(DIg/ Ig)2]1/2 x N Then %Igl = N x Igl D%Igl = [(DN/N)2+ (DIg1/ Ig1)2]1/2x Igl

  8. 2. From Decay Scheme b-100% Ig Ig: Relative g-ray intensity; a: total conversion coefficient N x Ig x (1 + a) = 100% Normalization factor N = 100/ Ig x (1 + a) Absolute g-ray intensity % Ig = N x Ig = 100/ (1 + a) UncertaintyD% Ig= 100 x Da/(1 + a)2

  9. Total intensity from transition-intensity balance b- 200 Ig5 Ig4 Ig6 150 Ig2 Ig3 100 Ig7 95 Ig1 0 TI(g7) = TI(g5) + TI(g3) If a(g7) is known, then Ig7 = TI(g7) / [1 + a(g7)]

  10. T0 A0 Ig1 T1 Equilibrium Decay Chain A1 T2 A2 Ig3 A3 T0 > T1, T2are the radionuclide half-lives, For t = 0 only radionuclide A0 exists, % Ig3, Ig3, and Ig1are known. Then, at equilibrium % Ig1 = (% Ig3/Ig3) × Ig1× (T0/(T0 – T1) × (T0/(T0 – T2) Normalization factor N = %Ig1/ Ig1

  11. b-100% Ig2 Ig1 Ig3 Normalization factor N = 100 / Ig1(1 + a1) + Ig3(1 + a3) % Ig1 = N x Ig1 = 100 x Ig1 / Ig1(1 + a1) + Ig3(1 + a3) % Ig3 = N x Ig3 = 100 x Ig3 / Ig1(1 + a1) + Ig3(1 + a3) % Ig2 = N x Ig2 = 100 x Ig2 / Ig1(1 + a1) + Ig3(1 + a3) Calculate uncertainties in%Ig1, %Ig2, and % Ig3. Use 3% fractional uncertainty ina1 and a3. See Nucl. Instr. and Meth. A249, 461 (1986). To save time use computer program GABS

  12. e+b+ 4. Annihilation radiation intensity is known (e+b+)2 (g+ce) (in) (e+b+)1 (g+ce)(out) (e+b+)0 I(g+) = Relative annihilation radiation intensity Xi = Intensity imbalance at the ith level = (g+ce) (out) – (g+ce) (in) ri = ei / b+itheoretical ratio to ith level Xi = ei + b+i = b+i (1 + ri), thereforeb+i = Xi / 1 + ri 2 [X0 / (1 + r0) + Σ Xi / (1 + ri)] = I(g+) ……… (1) [X0 + Σ Igi (g + ce) to gs ] N = 100 ………. (2) Solve equation (1) for X0(rel. gs feeding). Solve equation (2) for N (normalization factor).

  13. e+b+ (e+b+)2 5. X-ray intensity is known (g+ce) (in) (e+b+)1 (g+ce)(out) (e+b+)0 IK = Relative Kx-ray intensity Xi = Intensity imbalance at the ith level = (g+ce) (out) – (g+ce) (in) ri = ei / b+itheoretical ratio to ith level Xi = ei + b+i, soei = Xi ri / 1 + ri(atomic vacancies);wK=K-fluorsc.yield PKi = Fraction of the electron-capture decay from the K shell IK= wK [e0×PK0 + Σ ei× PKi] IK = wK [PK0× X0 r0 / (1 + r0) + Σ PKi× Xi ri / 1 + ri]…(1) [X0 + Σ Ii(g + ce) to gs] N = 100 …. (2) Solve equation (1) for X0, equation (2) for N.

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