jagdish k. tuli nndc brookhaven national laboratory upton, ny 11973, usa
DESCRIPTION
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: - PowerPoint PPT PresentationTRANSCRIPT
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jagdish K. TuliNNDC
Brookhaven National LaboratoryUpton, NY 11973, USA
Decay Scheme Normalization
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
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
• Experimental values:
For very precise values ( 3% uncertainty).
E = 661 keV ; 137Cs (K=0.0902 + 0.0008, M4)
Nuclear penetration effects.
233Pa - decay to 233U.
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)
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
For mixed E0 transitions (e.g., M1+E0).
227Fr - 227Ra
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-
½-
<10 ps
227Ra
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Decay Scheme NormalizationRel. Int. Norm. Factor Abs. Int.
I NR BR %IIt NT Br %It
I NB BR %II NB BR %II 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.
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
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
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
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 / IUncertainty N =[ (I%I)2+(IIx N
Then %Il = N x Il
Il = [(N/N)2 + (IIx Il
I1 I2
%I
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
2. From Decay Scheme
IRelative -ray intensity; : total conversion coefficient
N x I x (1 + ) = 100%
Normalization factor N = 100/ I x (1 + )
Absolute -ray intensity % I = N x I00(1 +
)
Uncertainty % I= 100 x /(1 + )2
100%
I
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
I7 = TI(7) / [1 +
(7)]
I6I5 I4
I2 I3
I1
I7
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Equilibrium Decay Chain
T0 > T1, T2 are the radionuclide half-lives,
For t = 0 only radionuclide A0 exists,
% I3, I3, and I1 are known.
Then, at equilibrium
% I1 = (% I3/I3) × I1× (T0/(T0 – T1) × (T0/(T0 – T2)
Normalization factor N = %I1/ I1
A0
A1
A2
A3
I1
I3
T0
T1
T2
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
Normalization factor N = 100 / I1(1 + 1) + I3(1 + 3)
% I1 = N x I1 = 100 x I1 / I1(1 + 1) + I3(1 + 3)
% I3 = N x I3 = 100 x I3 / I1(1 + 1) + I3(1 + 3)
% I2 = N x I2 = 100 x I2 / I1(1 + 1) + I3(1 + 3)
Calculate uncertainties in %I1, % I2, and % I3. Use
3% fractional uncertainty in 1 and 3.
See Nucl. Instr. and Meth. A249, 461 (1986).
To save time use computer program GABS
- 100%
I3
I2
I1
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
4. Annihilation radiation intensity is known
I(+) = Relative annihilation radiation intensity
Xi = Intensity imbalance at the ith level = (+ce) (out) – (+ce)
(in)
ri = i / +i theoretical ratio to ith level
Xi = i + +i = +
i (1 + ri), therefore +i = Xi / 1 + ri
2 [X0 / (1 + r0) + Σ Xi / (1 + ri)] = I(+) ……… (1)
[X0 + Σ Ii ( + ce) to gs ] N = 100 ………. (2)
Solve equation (1) for X0 (rel. gs feeding).
Solve equation (2) for N (normalization factor).
+ce) (in)
(+ce)(out)
(++)2
(++)1
(++)0
++
Jag Tuli DDP-Workshop
Bucharest, Romania, May 08
5. X-ray intensity is known
IK = Relative Kx-ray intensity
Xi = Intensity imbalance at the ith level = (+ce) (out) – (+ce) (in)
ri = i / +i theoretical ratio to ith level
Xi = i + +i, so i = Xi ri / 1 + ri (atomic vacancies); K=K-fluorsc.yield
PKi = Fraction of the electron-capture decay from the K shell
IK= K [0×PK0 + Σ i× PKi]
IK = K [PK0× X0 r0 / (1 + r0) + Σ PKi× Xi ri / 1 + ri]…(1)
[X0 + Σ Ii( + ce) to gs] N = 100 …. (2)
Solve equation (1) for X0, equation (2) for N.
+ce) (in)
(+ce)(out)
(++)2
(++)1
(++)0
++