Transcript Gamma-Ray Emission Probabilities

g-Ray Emission Probabilities
Edgardo Browne
Decay Data Evaluation Project
Workshop
May 12 – 14, 2008
Bucharest, Romania
• Photon energy and intensity
• Transition energy and intensity
• Relative and absolute intensities
• Photon energy and intensity
Guidelines
• When possible use evaluated values:
Recommended standards for g-ray energy calibration
(1999), R.G. Helmer, C. van der Leun, Nucl. Instrum. and
Methods in Phys. Res. A450, 35 (2000)
Update of X-ray and gamma-ray decay data standards for
detector calibration and other applications. IAEA - Report,
Vienna 2007.
Guidelines
• Weighted averages of values from the same type of
measurements (e.g. with Ge detectors).
• The uncertainty on the average (recommended)
value should not be smaller than the smallest input
uncertainty.
• For discrepant data use the “Limitation of Relative
Statistical Weight” method (Program LWEIGHT).
• Transition Energy
ET = Eg + ER,
where
ER = Eg2/2 MRc2 is the nuclear recoil energy
Eg is the photon energy (in MeV)
MR ~ A is the mass of the daughter nucleus
MR c2 ~ 931.5 x A
• Transition Intensity
IT = Ig (1 + a),
where
Ig is the photon intensity,
a is the total conversion coefficient
(theoretical interpolated value)
• Relative and Absolute Intensities
• Relative intensities (relative to the intensity
of the strongest g ray, usually taken as 100).
Also called relative emission probabilities.
• Absolute intensities (per 100
disintegrations of the emitting radionuclide,
usually given in %). Also called absolute
emission probabilities, usually given “per
decay.”)
66Ga
g-ray energies
1993Al15, 1994En02
Eg (keV)
Unevaluated
2173.334 (18)
2189.631 (9)
2213.19 (11)
2265.86 (24)
2292.188 (13)
2341.691 (11)
2393.153 (10)
2422.544 (9)
2433.826 (18)
2467.99 (7)
2492.44 (3)
2537.11 (5)
2588.573 (13)
2631.46 (9)
2698.94 (5)
2713.75 (5)
2751.852 (6)
2780.12 (18)
2785.7 (3)
2802.8 (5)
2843.153 (16)
2000He14
Eg (keV)
Evaluated
2173.319 (15)
2189.616 (6)
2213.181 (9)
2393.129 (7)
2422.525 (7)
2751.835 (5)
2780.095 (16)
Fitted
Eg (keV)
2173.319 (15)
2189.616 (6)
2213.181 (9)
2265.84 (24)
2292.171 (13)
2341.673 (11)
2393.129 (7)
2422.525 (7)
2433.807 (18)
2467.97 (7)
2492.42 (3)
2537.09 (5)
2588.553 (13)
2631.44 (9)
2698.92 (5)
2713.73 (5)
2751.835 (5)
2780.095 (16)
2785.7 (3)
2802.8 (5)
2843.130 (16)
Combining evaluated and unevaluated energies
66Ga
Relative g-Ray Intensities
Absolute g-Ray Emission Probabilities
Ice(1039g)/Ib+(gs) = 2.08 (10)x10-4 (experimental, 1960Sc06)
Ib+(gs)/S Ibi+ = 0.8697 (experimental, 1960Sc06)
Ice(1039g,E2)/Ig(1039g) = 2.69 (8)x10-4 (Theory, 1978Ro22)
Therefore
Ig(1039g)/ S Ibi+ = 2.08 (10)x10-4 x 0.8697/ 2.69 (8)x10-4 =0.67(4)
Also S Ibi+/ S Iei = 1.265 (from decay scheme and theoretical
Ibi+/Iei).
Since S Ibi+ + S Iei = 100%, then S Ibi+ = 55.8 (24)%, and
Ig(1039g) = 0.67 (4) x 55.8 (24) = 37 (3)%
233Pa
b- decay
Ig(312) = 38.6 (5) % (experimental value, Gehrke et al.)
SI(g+ce) (gs) = 102 (2) %
b- 5-12%
What went wrong?
Eg(keV)
300
312
340
aT(exp.)
0.83 (2)
0.79 (2)
0.61 (2)
aT(theo. M1)
1.04
0.96
0.75
Answer: Nuclear penetration effects
Using X rays to normalize a decay scheme
231U
g-ray spectrum
Ig(25)=100 (6)
Ig(84)=50 (3)
IKX=390 (14)
EC(K)/EC(Total) = 0.59
wK = 0.972
BK=115.6 keV, thus most K-x rays originate from vacancies produced
by the electron-capture process.
Total vacancies = IKX EC(Total) / wK EC(K) = 680 (33)
Normalization factor N = 100 / 680 (33) = 0.147 (7)
Ig(25)=100 (6) x 0.147 (7) = 15 (1)%
Ig(84)=50 (3) x 0.147 (7) = 7.5 (6)%
192Ir
Eg(keV)
206
489
316
468
612
b- and electron capture decay
Ig
4.01 (6)
0.527 (9)
100.0 (5)
57.76 (20)
6.365 (25)
a
0.305 (9)
0.0242 (7)
0.085 (3)
0.0294 (9)
0.0155 (5)
Ig (1+a)
5.23 (8)
0.540 (9)
108.5 (6)
58.43 (20)
6.464 (25)
S= 5.77 (8)
S= 114.9 (6)
The normalization factor is:
N = 100 / [Ig(489) (1+a489) + Ig(206) (1+a206) + Ig(316) (1+a316) + Ig(612) (1+a612)]
= 100 / 120.7 (7) = 0.828 (5)
N = 0.828 (5)
The electron capture (e) and b- decay branchings are:
e = 100 [Ig(489) (1+a489) + Ig(206) (1+a206)] /120.7 (7) =
100 / [1 + (Ig(316) (1+a316) + Ig(612) (1+a612)/(Ig(489) (1+a489) + Ig(206) (1+a206)) =
100 / [1 + 114.9 (6)/5.77 (8)] = 100 / 20.9 (3) = 4.78 (7)%
b- = 100 – EC = 100 – 4.78 (7) = 95.22 (7)%
b- = 95.22 (7)%
e = 4.78 (7)%
125Sb
Decay Scheme
It takes about a year for the intensity of the 109-keV g ray to
be in equilibrium (within 1%) with the other g rays. The intensity
of the 35-keV g ray is also affected by the 58-year half-life of
the 144-keV 125mTc isomer.
Decay Scheme Normalization
•
•
•
[S Igi (1 + ai) (gs and 144-keV level)] N =100%
N = 0.2955 (24)
The equilibrium correction for Ig(109) is
[T1/2(125Sb) – T1/2(125mTe)/ T1/2(125Sb) ]= 0.943.
b- feeding to the 144-keV 125mTe isomer
•
Ib-=[Ig(109)(1+a109) x 0.943 – Ig(176) (1+a176) –
Ig(380)(1+a380) – Ig(497)(1+a497)]  N
•
Ib-= 13.4%
Absolute g-Ray Intensities Deduced from
Decay Scheme
Decay Branching Ratios
Assuming EC(gs) = b-(gs) = 0%
g-ray transition intensity balance
Ii(in)
Ibi
Ii(out)
Ii(gs)
0
The corresponding normalization factor is
N = 100 / S[ Ii(out) + Ii(gs) – Ii(in)] =
100 / S[ Ii(out) – Ii(in)] + S Ii(gs), but
S[ Ii(out) – Ii(in)] = 0, therefore
N = 100 / S Ii(gs)
Uncertainties of Absolute g-Ray Emission
Probabilities Deduced from Decay Scheme
b-
I1 + dI1 I2 + dI2
(I1 + I2) N = 100%
N = 100 / (I1 + I2)
The absolute emission probabilities are
I1(%) = 100 x I1/(I1 + I2)
I2(%) = 100 x I2/(I1 + I2),
Their uncertainties have the same value,
irrespective of their values in the relative
emission probabilities!!
dI1(%)2=dI2(%)2= 104 x (I12 dI22+I1dI22)/(I1+I2)2
If I1 = I2 = I, and dI1 = dI2 = dI,
then
dI1(%)/I1(%) = dI2(%)/I2(%) = [(2)1/2/2] dI/I
The fractional uncertainties are smaller than
those in the corresponding relative spectral
emission probabilities!!
See
Nucl. Instr. and Meth. In Phys. Res. A249, 461 (1986)
for general mathematical formulae.
240Am
EC Decay to 240Pu
3-
e >98%
3+
1031
988
E2
889
E2 (<1% M1)
e <1%
4+
142
e <1%
99 – E2
43
2+
0+
6561 y
240 Pu
43 – E2
0
50.8 h
240 Am
0
240Am
1972Ah07
Eg(keV)
Ig(rel)
1971LeZO
Eg(keV)
Ig(rel)
Gamma Rays
1972PoZS
Eg(keV)
Ig(rel)
Recommended Values
Eg(keV)
Ig(rel)
Ig(abs)
42.9 (1)
0.09 (1)
42.87 (4)*
0.09 (1)^
0.110 (3)
98.9 (1)
1.5 (2)
98.9 (1)#
1.5 (2)^
1.49 (3)
888.7 (1)
916.2 (3)
959.4 (3)
987.7 (1)
1033.4 (5)
1036.3 (4)
25.1 (9)
0.10 (1)
0.005 (1)
73.3 (25)
0.011 (2)
0.017 (3)
152.4 (10)
0.012 (3)
152.4 (10)†
0.012 (3)‡
0.012 (3)
249.7 (10)
0.020 (3)
249.7 (10)†
0.020 (3)‡
0.020 (3)
251.8 (10)
0.005 (2)
251.8 (10)†
0.005 (2)
0.0049 (20)
303.7 (10)
0.009 (2)
305.3 (10)
0.073
304.5 (10)&
0.009 (2)‡
0.009 (2)
343.7 (10)
0.049 (5)
343.7 (10)
0.095
343.7 (10)&
0.049 (5)‡
0.048 (5)
382.1 (10)
0.053 (5)
382.3 (10)
0.051
382.2 (10)&
0.053 (5)‡
0.052 (5)
447.8 (10)
0.013 (4)
447.8 (10)†
0.013 (4)‡
0.013 (4)
507.9 (10)
0.072 (6)
508.0 (10)&
0.072 (6)‡
0.071 (6)
555.4 (10)
0.010 (5)
555.4 (10)†
0.010 (5)‡
0.010 (5)
600.7 (10)
0.014 (6)
600.7 (10)†
0.014 (6)‡
0.014 (6)
606.7 (10)
0.070 (8)
606.9 (10)
0.055
606.8 (10)&
0.070 (8)‡
0.069 (8)
697.8
888.83 (5)
916.1 (2)
0.035 (8)
25.1 (4)
0.087 (6)
888.91 (5)
917.1 (2)
25
0.07
697.8†
888.85 (5)@
916.5 (3@)
0.035 (8)‡
25.1 (4)•
0.090 (6)•
0.035 (8)
24.7 (5)
0.089 (6)
934.6 (5)
0.025 (3)
935.7 (5)
0.032
935.2 (6)&
0.025 (3)‡
0.025 (3)
938.0 (6)
959.1 (5)
987.79 (6)
1033.5 (3)
1036.0 (3)
0.007 (3)
0.037 (4)
73.2 (10)
0.010 (1)
0.015 (2)
938.2 (10)
960.2 (2)
987.84 (6)
1034 (1)
1037 (1)
0.0054
0.022
73.2
0.0095
0.015
938.0 (5)&
959.9 (3)@
987.80 (4)@
1033.5 (2)@
1036.2 (2)@
0.007 (3)‡
0.039 (4)•
73.2 (10)•
0.010 (1)•
0.016 (2)•
0.007 (3)
0.038 (5)
72.2 (6)
0.0099 (10)
0.0157 (20)
1089.8 (10)
0.0031 (6)
1091.5 (10)
0.0029
1090.7 (8)&
0.0031 (6)‡
0.0031 (6)
508.2 (10)
0.073
Normalization Procedures
1. Assumes e(43) < 1%, e(142) < 1%, and
S Tg(GS, 43, 142) > 98% (= 99 + 1%)
Ig(988) = 72.4 + 0.9 %
2. Assumes just e(43) < 1%, and
S Tg(GS, 43) > 99% (= 99.5 + 0.5%)
Ig(988) = 72.0 + 0.6 %
Recommended value
Ig(988) = 72.2 + 0.6 %
Program GABS
INPUT: ENSDF Data Set
OUTPUT: Absolute g-Ray Intensities
REPORT FILE
Current date: 03/09/2008
240AM EC DECAY
NR= 0.984 13 BR= 1.00
FOR INTENSITY UNCERTAINTIES OF GAMMA RAYS NOT USED IN CALCULATING NR,
COMBINE THE UNCERTAINTY IN THE RELATIVE INTENSITY IN QUADRATURE
WITH THE UNCERTAINTY IN THE NORMALIZING FACTOR (NR x BR).
FOR THE FOLLOWING GAMMA RAYS:
E= 42.87 4 %IG=0.1092 24 PER 100 DECAYS.
E= 98.9
1 %IG=1.486 23 PER 100 DECAYS.(Compare with 1.49 3)
E= 152.4 10 %IG=0.012 3 PER 100 DECAYS.
E= 555.4 10 %IG=0.010 5 PER 100 DECAYS.(Compare with 0.010 5)
E= 597.40 7 %IG=0.006 3 PER 100 DECAYS.
E= 507.9 10 %IG=0.071 6 PER 100 DECAYS.
E= 606.7 10 %IG=0.069 8 PER 100 DECAYS.(Compare with 0.069 8)
E= 447.8 10 %IG=0.013 4 PER 100 DECAYS.
E= 600.7 10 %IG=0.014 6 PER 100 DECAYS.
E= 251.8 10 %IG=0.0049 20 PER 100 DECAYS.
E= 303.7 10 %IG=0.0089 20 PER 100 DECAYS.
E= 758.61 8 %IG=0.01033 13 PER 100 DECAYS.
E= 857.48 10 %IG=0.00394 5 PER 100 DECAYS.
E= 900.37 10 %IG=0.001476 19 PER 100 DECAYS.
E= 916.1 2 %IG=0.089 6 PER 100 DECAYS.(Compare with 0.089 6)
E= 249.7 10 %IG=0.020 3 PER 100 DECAYS.
E= 343.7 10 %IG=0.048 5 PER 100 DECAYS.
E= 697.8
%IG=0.034 8 PER 100 DECAYS.
E= 959.3 3 %IG=0.038 5 PER 100 DECAYS.(Compare with 0.038 5)
E= 382.1 10 %IG=0.052 5 PER 100 DECAYS.
E= 888.85 5 %IG=24.7 5 PER 100 DECAYS.
E= 987.79 6 %IG=72.0 6 PER 100 DECAYS.(Compare with 72.0 14)
E= 934.6 5 %IG=0.025 3 PER 100 DECAYS.