Default isomeric branching ratios

Branching ratios to isomeric states are used in burnup calculation for the production of long-lived meta-stable nuclides, such as ^241mAm or ^148mPm. The data is not available in ACE format cross section libraries and must therefore be obtained elsewhere. Serpent provides three options for defining the branching ratios:

1. Use of default constant ratios (see table below)
2. Use of user-defined constant ratios (see the set isobra option)
3. Use of energy-dependent ratios read from ENDF format files (see the set bralib option)

User-defined constant ratios override the default values, energy-dependent data overrides constant ratios.

Default data

The default constant branching ratios from update 2.1.27 on are listed below. The values are calculated from energy-dependent branching ratios in the JEFF-3.1 activation file in PWR flux spectrum. The last two columns refer to ground-state and isomeric-state fractions, respectively.

Nuclide	ZAI	MT	Frac. (g)	Frac. (m)
Na-23	110230	102	0.23200	0.76800
Cl-37	170370	102	0.88090	0.11910
Sc-45	210450	102	0.55600	0.44400
Co-59	270590	102	0.44400	0.55600
Ge-72	320720	102	0.50120	0.49880
Ge-74	320740	102	0.66600	0.33400
Ge-76	320760	102	0.40050	0.59950
Se-76	340760	102	0.74090	0.25910
Se-78	340780	102	0.11780	0.88220
Se-80	340800	102	0.84540	0.15460
Se-82	340820	102	0.14020	0.85980
Br-79	350790	102	0.76870	0.23130
Br-81	350810	102	0.09140	0.90860
Kr-78	360780	102	0.97040	0.02960
Kr-80	360800	102	0.60310	0.39690
Kr-82	360820	102	0.33300	0.66700
Kr-84	360840	102	0.18390	0.81610
Rb-85	370850	102	0.87910	0.12090
Sr-84	380840	102	0.25300	0.74700
Sr-86	380860	102	0.19880	0.80120
Y-89	390890	102	0.99790	0.00210
Y-90	390900	102	0.74960	0.25040
Nb-93	410930	102	0.31010	0.68990
Nb-94	410940	102	0.96100	0.03900
Mo-92	420920	102	0.99780	0.00220
Rh-103	451030	102	0.92400	0.07600
Rh-105	451050	102	0.90400	0.09600
Pd-106	461060	102	0.95270	0.04730
Pd-108	461080	102	0.97790	0.02210
Pd-110	461100	102	0.85000	0.15000
Ag-107	471070	102	0.98980	0.01020
Ag-109	471090	102	0.95400	0.04600
Cd-110	481100	102	0.99450	0.00550
Cd-112	481120	102	0.86850	0.13150
Cd-114	481140	102	0.88120	0.11880
Cd-116	481160	102	0.66600	0.33400
In-113	491130	102	0.41910	0.58090
Sn-112	501120	102	0.72530	0.27470
Sn-116	501160	102	0.95680	0.04320
Sn-118	501180	102	0.97940	0.02060
Sn-120	501200	102	0.98750	0.01250
Sn-122	501220	102	0.01120	0.98880
Sn-124	501240	102	0.03750	0.96250
Sn-126	501260	102	0.30180	0.69820
Sb-121	511210	102	0.93690	0.06310
Te-120	521200	102	0.88710	0.11290
Te-122	521220	102	0.64480	0.35520
Te-124	521240	102	0.99120	0.00880
Te-126	521260	102	0.86890	0.13110
Te-128	521280	102	0.92450	0.07550
Te-130	521300	102	0.85590	0.14410
Te-132	521320	102	0.85170	0.14830
I-129	531290	102	0.41300	0.58700
I-131	531310	102	0.98390	0.01610
Xe-124	541240	102	0.83000	0.17000
Xe-126	541260	102	0.86910	0.13090
Xe-128	541280	102	0.89230	0.10770
Xe-130	541300	102	0.91640	0.08360
Xe-132	541320	102	0.88670	0.11330
Xe-133	541330	102	0.96000	0.04000
Xe-134	541340	102	0.98530	0.01470
Cs-133	551330	102	0.90700	0.09300
Cs-134	551340	102	0.99600	0.00400
Cs-135	551350	102	0.98400	0.01600
Cs-137	551370	102	0.90210	0.09790
Ba-130	561300	102	0.88710	0.11290
Ba-132	561320	102	0.91750	0.08250
Ba-134	561340	102	0.92630	0.07370
Ba-135	561350	102	0.99780	0.00220
Ba-136	561360	102	0.97310	0.02690
Ce-136	581360	102	0.86620	0.13380
Ce-138	581380	102	0.97870	0.02130
Pr-141	591410	102	0.65190	0.34810
Pr-143	591430	102	0.31000	0.69000
Pm-147	611470	102	0.53300	0.46700
Eu-153	631530	102	0.98400	0.01600
Dy-164	661640	102	0.37000	0.63000
Ho-165	671650	102	0.94900	0.05100
Er-166	681660	102	0.25030	0.74970
Lu-175	711750	102	0.33310	0.66690
Lu-176	711760	102	0.99900	0.00100
Hf-179	721790	102	0.99100	0.00900
W-182	741820	102	0.86990	0.13010
W-184	741840	102	0.99830	0.00170
Re-185	751850	102	0.99900	0.00100
Re-187	751870	102	0.97290	0.02710
Au-197	791970	102	0.99900	0.00100
Hg-196	801960	102	0.96600	0.03400
Hg-198	801980	102	0.99180	0.00820
Pb-206	822060	102	0.97830	0.02170
Bi-209	832090	102	0.67910	0.32090
Pa-233	912330	102	0.48710	0.51290
U-234	922340	102	0.50000	0.50000
Np-235	932350	102	0.40000	0.60000
Np-239	932390	102	0.35730	0.64270
Pu-236	942360	102	0.50010	0.49990
Am-241	952410	102	0.91900	0.08100
Am-243	952430	102	0.06260	0.93740
Bk-247	972470	102	0.40000	0.60000
Es-253	992530	102	0.03200	0.96800
Es-255	992550	102	0.98400	0.01600

Calculating branching ratios from energy-dependent data

Calculating branching ratios from energy-dependent data is relatively easy using standard detectors. For example, the capture fractions of ²⁴¹Am to ground and metastable state of ²⁴²Am can be obtained with detector input:

% --- Detector material:

mat Am241 1.0 95241.09c 1.0

% --- Detector: (reaction rates using spectrum in material "fuel")

det 1
dm fuel
dr 102 Am241 dr 102g  Am241 dr 102m  Am241

Branching ratios to ground and metastable states can then be obtained by dividing the results in the 2nd and 3rd detector bin with the result of the first bin. The ground state fraction can then be used as the input for the set isobra card.

For a complete example, see:

• Serpent input file and post-processing script
• Energy-dependent branching data from JEFF-3.1 activation file: File:JEFF-3.1 activation file.tgz.