-Ray Emission ProbabilitiesEdgardo Browne

Decay Data Evaluation Project Workshop

May 12 – 14, 2008Bucharest, 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 -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 = E + ER,

where

ER = E2/2 MRc2 is the nuclear recoil energy

Eis the photon energy (in MeV)

MR ~ A is the mass of the daughter nucleus

MR c2 ~ 931.5 x A

• Transition Intensity

IT = I (1 + ),

where

Iis the photon intensity,

is the total conversion coefficient (theoretical interpolated value)

• Relative and Absolute Intensities

• Relative intensities (relative to the intensity of the strongest 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.”)

1993Al15, 1994En02 2000He14 FittedE(keV) E(keV) E(keV)Unevaluated Evaluated  2173.334 (18) 2173.319 (15)

2173.319 (15)

2189.631 (9) 2189.616 (6) 2189.616 (6)2213.19 (11) 2213.181 (9) 2213.181 (9)2265.86 (24)   2265.84 (24)2292.188 (13)  

2292.171 (13)

2341.691 (11)  2341.673 (11)

2393.153 (10) 2393.129 (7) 2393.129 (7)2422.544 (9) 2422.525 (7) 2422.525 (7)2433.826 (18)  

2433.807 (18)

2467.99 (7)   2467.97 (7)2492.44 (3)   2492.42 (3)2537.11 (5)   2537.09 (5)2588.573 (13)  

2588.553 (13)

2631.46 (9)   2631.44 (9)2698.94 (5)   2698.92 (5)2713.75 (5)   2713.73 (5)2751.852 (6) 2751.835 (5) 2751.835 (5)2780.12 (18) 2780.095 (16)

2780.095 (16)

2785.7 (3)   2785.7 (3)2802.8 (5)   2802.8 (5)2843.153 (16)  

2843.130 (16)

66Ga -ray energies

Combining evaluated and unevaluated energies

66Ga Relative -Ray Intensities

Absolute -Ray Emission Probabilities

Ice(1039)/I+(gs) = 2.08 (10)x10-4 (experimental, 1960Sc06)

I+(gs)/Ii+ = 0.8697 (experimental, 1960Sc06)

Ice(1039,E2)/I(1039) = 2.69 (8)x10-4 (Theory, 1978Ro22)

Therefore

I(1039)/ Ii+ = 2.08 (10)x10-4 x 0.8697/ 2.69 (8)x10-4 =0.67(4)

Also Ii+/ Ii = 1.265 (from decay scheme and theoretical Ii+/Ii).

Since Ii+ + Ii = 100%, then Ii+ = 55.8 (24)%, and

I(1039) = 0.67 (4) x 55.8 (24) = 37 (3)%

233Pa - decay

I(312) = 38.6 (5) % (experimental value, Gehrke et al.)

I(+ce) (gs) = 102 (2) %

- 5-12%

What went wrong?

E(keV) T(exp.) T(theo. M1)

300 0.83 (2) 1.04

312 0.79 (2) 0.96

340 0.61 (2) 0.75

Answer: Nuclear penetration effects

Using X rays to normalize a decay scheme

231U -ray spectrum

I(25)=100 (6)

I(84)=50 (3)

IKX=390 (14) EC(K)/EC(Total) = 0.59

K = 0.972

BK=115.6 keV, thus most K-x rays originate from vacancies producedby the electron-capture process.

Total vacancies = IKX EC(Total) / K EC(K) = 680 (33)

Normalization factor N = 100 / 680 (33) = 0.147 (7)

I(25)=100 (6) x 0.147 (7) = 15 (1)%

I(84)=50 (3) x 0.147 (7) = 7.5 (6)%

192Ir and electron capture decay

E(keV) I I206 4.01 (6) 0.305 (9) 5.23 (8)489 0.527 (9)0.0242 (7) 0.540 (9) = 5.77 (8)316 100.0 (5)0.085 (3) 108.5 (6)468 57.76 (20) 0.0294 (9) 58.43 (20)612 6.365 (25) 0.0155 (5) 6.464 (25) = 114.9 (6)

The normalization factor is:

N = 100 / [I(489) (1+489) + I(206) (1+206) + I(316) (1+316) + I(612) (1+612)]

= 100 / 120.7 (7) = 0.828 (5)

N = 0.828 (5)

The electron capture and decay branchings are:

= 100 [I(489) (1+489) + I(206) (1+206)] /120.7 (7) =

100 / [1 + (I(316) (1+316) + I(612) (1+612)/(I(489) (1+489) + I(206) (1+206)) =

100 / [1 + 114.9 (6)/5.77 (8)] = 100 / 20.9 (3) = 4.78 (7)%

= 100 – EC = 100 – 4.78 (7) = 95.22 (7)%

= 95.22 (7)%

= 4.78 (7)%

125Sb Decay Scheme

It takes about a year for the intensity of the 109-keV ray to be in equilibrium (within 1%) with the other rays. The intensityof the 35-keV ray is also affected by the 58-year half-life ofthe 144-keV 125mTc isomer.

Decay Scheme Normalization

• [ I (1 + i) (gs and 144-keV level)] N =100%

• N = 0.2955 (24)

• The equilibrium correction for I(109) is

[T1/2(125Sb) – T1/2(125mTe)/ T1/2(125Sb) ]= 0.943.

- feeding to the 144-keV 125mTe isomer

• I-=[I(109)(1+109) x 0.943 – I(176) (1+176) –

I(380)(1+380) – I(497)(1+497)] N

• I-= 13.4%

Absolute -Ray Intensities Deduced from Decay Scheme

Decay Branching Ratios

Assuming EC(gs) = -(gs) = 0%

-ray transition intensity balance

The corresponding normalization factor is

N = 100 / [ Ii(out) + Ii(gs) – Ii(in)] =

100 / [ Ii(out) – Ii(in)] + Ii(gs), but

[ Ii(out) – Ii(in)] = 0, therefore

N = 100 / Ii(gs)

Ii(out)

Ii(in)

Ii(gs) 0

Ii

Uncertainties of Absolute -Ray Emission Probabilities Deduced from Decay Scheme

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 dI2

2+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!!

SeeNucl. Instr. and Meth. In Phys. Res. A249, 461 (1986)

for general mathematical formulae.

240Am EC Decay to 240Pu

E2 E2 (<1% M1)

988 889

99 – E2

43 – E20+

2+

4+

3+

0

142

43

1031

Pu240

240 Am

3- 50.8 h 0

6561 y

240Am Gamma Rays

1972Ah07 1971LeZO 1972PoZS Recommended ValuesE(keV) I(rel) E(keV) I(rel) keV) I(rel) E(keV) I(rel) I(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)

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) 508.2 (10) 0.073 508.0 (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 0.035 (8) 697.8† 0.035 (8)‡ 0.035 (8)888.7 (1) 25.1 (9) 888.83 (5) 25.1 (4) 888.91 (5) 25 888.85 (5)@ 25.1 (4)• 24.7 (5)916.2 (3) 0.10 (1) 916.1 (2) 0.087 (6) 917.1 (2) 0.07 916.5 (3@) 0.090 (6)• 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) 0.007 (3) 938.2 (10) 0.0054 938.0 (5)& 0.007 (3)‡ 0.007 (3)959.4 (3) 0.005 (1) 959.1 (5) 0.037 (4) 960.2 (2) 0.022 959.9 (3)@ 0.039 (4)• 0.038 (5)987.7 (1) 73.3 (25) 987.79 (6) 73.2 (10) 987.84 (6) 73.2 987.80 (4)@ 73.2 (10)• 72.2 (6)1033.4 (5) 0.011 (2) 1033.5 (3) 0.010 (1) 1034 (1) 0.0095 1033.5 (2)@ 0.010 (1)• 0.0099 (10)1036.3 (4) 0.017 (3) 1036.0 (3) 0.015 (2) 1037 (1) 0.015 1036.2 (2)@ 0.016 (2)• 0.0157 (20)

1089.8 (10) 0.0031 (6) 1091.5 (10) 0.0029 1090.7 (8)& 0.0031 (6)‡ 0.0031 (6)

Normalization Procedures

1. Assumes (43) < 1%, (142) < 1%, and T(GS, 43, 142) > 98% (= 99 + 1%)

I(988) = 72.4 + 0.9 %

2. Assumes just (43) < 1%, and T(GS, 43) > 99% (= 99.5 + 0.5%)

I(988) = 72.0 + 0.6 % Recommended value I(988) = 72.2 + 0.6 %

Program GABS

INPUT: ENSDF Data Set

OUTPUT: Absolute -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.