Energy-Balance Tests for ENDF/B-VII

Robert E. MacFarlane
Los Alamos National Laboratory

Nuclear heating can be defined using the energy-balance method; that is, the energy released by charged-particles and the recoil nucleus from a nuclear reaction is given by E + Q - E-bar-neutron - E-bar-gamma. However, not all nuclear data evaluations have perfect energy balance, and in those cases, this formula can give strange results. For example, if the E-bar-gamma value is too large, the energy release can be negative. In a large enough system, this negative value will be cancelled out by the excess energy deposited by the over-large gamma field, and energy will be perfectly conserved. For a system small with respect to photon mean-free-paths, one could see cooling instead of heating! Of course, if E-bar-gamma were too small, it would be possible to get an absurdly high value of the energy-balance heating.
The HEATR module of the NJOY Nuclear Data Processing System can be used to study these energy-balance problems. In addition to computing the heating, it computes some kinematic limits that should bracket the energy-balance heating. If the computed heating falls outside this range, there are problems with the evaluation that could be fixed. The code prepares graphs showing the computed heating and its kinematic limits, and it also prepares graphs showing the photon energy production with its kinematic limits. The graphs are given using both log and linear scales to highlight the low-energy and high-energy regimes.
We have gone through these graphs and prepared qualitative summaries of whether the energy balance is good, fair, or poor for each evaluation from ENDF/B-VII. Some comments on the graphs are sometimes given in the summary also.
It should be noted that the heating for the heavier targets is small with respect to E+Q; thus, we are computing it as a differece between large numbers. Fairly small percentage errors in the photon energy can often lead to large percent errors in the computed heating. These kinds of small errors are inevitable when using model codes to prepare the evaluation because of things like binning and the choice of grids. Evaluators should really adjust their results to smooth out these problems, but this hasn't always been done. Therefore, we use a more relaxed definition of "good" for the heavier targets.
More information of the kinematic checks done by HEATR can be found in the NJOY manual, and the printed outputs from the NJOY runs contain lots of additional information that can be used to help find the sources of the energy-balance problems demonstrated by these graphs.

Click on the desired isotope links to view the energy-balance testing graphs.

H-1 Good.

H-2 Good.

H-3 No gammas.

He-3 No gammas.

He-4 No gammas.

Li-6 Good.

Li-7 Good.

Be-9 No gammas.

Be-9 Good heating. Some small deviations in photon production above 1 MeV.

B-10 Good.

B-11 Good below 11 MeV, fair above.

C-nat Good.

N-14 Good.

N-15 Good.

O-16 Good.

O-17 No gammas.

F-19 Good.

Na-22 No gammas.

Na-23 Good to 4 MeV. Fair to 10 MeV. Poor above 10 MeV.

Mg-24 Good.

Mg-25 Good.

Mg-26 Some modest problems between 8 and 14 MeV. For MT=91 between 8.3 and 9 MeV, MF=3 uses int=3 and MF=12 uses int=2, resulting in a sharp peak in the heating. From 9 to 20 MeV, the problems seem to come from MT=91.

Al-27 Good.

Si-28 Good.

Si-29 Good.

Si-30 Good.

P-31 Good below 2 MeV. Poor from 2 to 20 MeV. Good above 20 MeV.

S-32 Good.

S-33 Good, except for a glitch between 4 and 5 MeV caused by using int=3 in MF3/MT91 and int=2 in MF12/MT91.

S-34 Good below 5 MeV. Fair from 5 to MeV. Good above 10 MeV. The glitch between 5 and 6 MeV comes from using int=3 in MF3/MT91 and int=2 in MF12/MT91.

S-36 Good below 5 MeV. Poor above 5 MeV. The big problem between 5 and 9 MeV comes from MT=91.

Cl-35 Good.

Cl-37 Good.

Ar-36 No gammas.

Ar-38 No gammas.

Ar-40 No gammas.

K-39 Good, except for a feature between 4 and 5 MeV coming from using int=3 in MF=3 and int=2 in MF=12 for MT=91.

K-40 Good.

K-41 Good, except fair between 1 and 10 MeV.

Ca-40 Good.

Ca-42 Good, except fair between 2 and 20 MeV.

Ca-43 Good, except fair between 2 and 20 MeV.

Ca-44 Good, except fair between 2 and 20 MeV.

Ca-46 Good, except fair between 2 and 20 MeV.

Ti-46 Good below 3 MeV. Poor above 3 MeV.

Ti-47 Bad between 3 and 12 MeV, good elsewhere.

Ti-48 Fair between 5 and 14 MeV, OK elsewhere.

Ti-49 Fair from 3 to 8 MeV, OK elsewhere.

Ti-50 Poor from 4.5 to 10 MeV, and from 1 to 15 MeV.

V-nat Poor from 10 to 17 MeV. Fair from 4 to 10 MeV.

Cr-50 Good.

Cr-52 Good.

Cr-53 Good.

Cr-54 Good.

Mn-55 Good.

Fe-54 Good.

Fe-56 Good.

Fe-57 Good.

Fe-58 Good.

Co-58 No gammas.

Co-58m No gammas.

Co-59 Fair from 3 to 5 MeV, OK elsewhere.

Ni-58 Good.

Ni-60 Good.

Ni-61 Good.

Ni-62 Good.

Ni-64 Good.

Cu-63 Good.

Cu-65 Good.

Zn-nat No gammas.

Ga-69 No gammas.

Ga-71 No gammas.

Ge-70 Good.

Ge-72 Good.

Ge-73 Fair for 4 to 20 MeV.

Ge-74 Good.

Ge-76 Good.

As-74 Fair above 2 MeV, OK below.

As-75 Good.

Se-74 No gammas.

Se-76 No gammas.

Se-77 No gammas.

Se-78 No gammas.

Se-79 No gammas.

Se-80 No gammas.

Se-82 No gammas.

Br-79 No gammas.

Br-81 No gammas.

Kr-78 No gammas.

Kr-80 No gammas.

Kr-82 No gammas.

Kr-83 No gammas.

Kr-84 No gammas.

Kr-85 Good to 9 MeV, fair above.

Kr-86 No gammas.

Rb-85 No gammas.

Rb-86 Good to 2 MeV, fair above.

Rb-87 Good to 2 MeV, fair above.

Sr-84 Good.

Sr-86 No gammas.

Sr-87 No gammas.

Sr-88 No gammas.

Sr-89 No gammas.

Sr-90 No gammas.

Y-89 Good to 12 MeV, fair above.

Y-90 Good.

Y-91 No gammas.

Zr-90 Good.

Zr-91 Poor above 2 MeV.

Zr-92 Poor above 3 MeV.

Zr-93 No gammas.

Zr-94 Poor above 3 MeV.

Zr-95 No gammas.

Zr-96 Poor above 3 MeV.

Nb-93 Good below 800 keV, fair to 20 MeV. Negative kermas.

Nb-94 No gammas.

Nb-95 No gammas.

Mo-92 Poor above 500 keV. Negative kermas.

Mo-94 Poor above 500 keV. Negative kermas.

Mo-95 Good.

Mo-96 Poor abov 500 keV. Negative kermas.

Mo-97 Poor abov 500 keV. Negative kermas.

Mo-98 Poor abov 500 keV. Negative kermas.

Mo-99 No gammas.

Mo-100 No gammas.

Tc-99 Good.

Ru-96 No gammas.

Ru-98 No gammas.

Ru-99 No gammas.

Ru-100 No gammas.

Ru-101 Good to 8 MeV, fair above.

Ru-102 No gammas.

Ru-103 No gammas.

Ru-104 No gammas.

Ru-105 No gammas.

Ru-106 No gammas.

Rh-103 Good.

Rh-105 No gammas.

Pd-102 Good.

Pd-104 Good.

Pd-105 Good.

Pd-106 Good.

Pd-107 No gammas.

Pd-108 Good.

Pd-110 Good.

Ag-107 Good.

Ag-109 Good.

Ag-110m No gammas.

Ag-111 Good.

Cd-106 Good to 2.5 MeV, fair above.

Cd-108 No gammas.

Cd-110 No gammas.

Cd-111 Poor above 1.5 MeV.

Cd-112 No gammas.

Cd-113 No gammas.

Cd-114 No gammas.

Cd-115m Poor from .5 to 10 MeV. Negative kermas.

Cd-116 No gammas.

In-113 No gammas.

In-115 No gammas.

Sn-112 No gammas.

Sn-113 Good.

Sn-114 No gammas.

Sn-115 No gammas.

Sn-116 No gammas.

Sn-117 No gammas.

Sn-118 No gammas.

Sn-119 No gammas.

Sn-120 No gammas.

Sn-122 No gammas.

Sn-123 No gammas.

Sn-124 No gammas.

Sn-125 Good, except for a big, sharp glitch at 6 MeV. Negative kermas. Comes from a bad photon yield (1.565e6!) at the threshold in MF=6/MT=16.

Sn-126 No gammas.

Sb-121 No gammas.

Sb-123 No gammas.

Sb-124 No gammas.

Sb-125 No gammas.

Sb-126 Good.

Te-120 No gammas.

Te-122 No gammas.

Te-123 No gammas.

Te-124 No gammas.

Te-125 No gammas.

Te-126 No gammas.

Te-127m No gammas.

Te-128 No gammas.

Te-129m No gammas.

Te-130 No gammas.

Te-132 Good, except for a sharp glitch at 16 MeV. Negative kermas. The sharp problem in the heating is due to faulty angular distributions in MF=6, MT=91 at 16 MeV.

I-127 Good.

I-129 No gammas.

I-130 Good. Could use a little improvement at 6 MeV.

I-131 No gammas.

I-135 No gammas.

Xe-123 No gammas.

Xe-124 No gammas.

Xe-126 No gammas.

Xe-128 No gammas.

Xe-129 No gammas.

Xe-130 No gammas.

Xe-131 Good to 8 MeV, poor above.