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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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Decay Scheme Normalization Jagdish K. TuliNNDCBrookhaven National LaboratoryUpton, 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: 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)
<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
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.
Absolute intensities “Intensities per 100 disintegrations of the parent nucleus” Measured (Photons from b-, e+b+, and a decay) Simultaneous singles measurements Coincidence measurements
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
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
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)]
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
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
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).
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.