**56-Ba-137 Review**

By V.G. Pronyaev, NDS, IAEA

22 March 2004

**General Comment:**

Taking into account that the accuracy of nuclear data for fission
products is most important in neutron transport and nuclear
transmutation calculations, the following priority to the quality of the
data can be given when we compare different evaluations:

1.  Most important energy region is a region of spectrum with maximum
    neutron fluxes in thermal and fast fission reactors, namely around
    0.0253 eV and below 5 MeV.

2.  Most important cross sections in order of reducing of their
    importance are integral cross sections: capture, total, elastic,
    inelastic with excitation of levels and other threshold cross
    sections; differential cross sections: secondary neutron spectrum
    from inelastic scattering and elastic scattering differential cross
    sections, gamma production cross section and spectra.

Abbreviations: B-6 -- ENDF/B-VI, J-3 -- JENDL-3, F-2 -- JEF-2, B-2 --
BROND-2, C-3 -- CENDL-3,

CS -- cross section, RRR -- resolved resonance region, URR -- unresolved
resonance region SOM -- spherical optical model, SM -- statistical
model, reaction mechanism, PEQ -- pre-equilibrium decay model, reaction
mechanism.

##### 

##### **Files**

ENDF/B-VI -- old and obsolete ENDF/B-V evaluation was revised in the RRR
by R.Q. Wright (1988). 9 MLBW s-resonances are given in the RRR for E~n~
10^-5^ to 1.95 keV (as in S.F. Mughabghab, 1981). No unresolved
resonance region is given. Results of optical and statistical model
calculations without account of contribution of the pre-equilibrium and
direct processes are given for energy above 1.95 keV.

JEF-2 file: identical to old and obsolete ENDF/B-V evaluation without
revision made by R.Q. Wright in 1988. 5 MLBW s-resonances and 3
p-resonance in the RRR for E~n~ 10^-5^ to 1.95 keV. No URR is given. For
energy above 1.95 keV F-2 is the same as B-6.

JENDL-3.2 -- 1990 JNDC FPND working group evaluation. The resolved
resonances (49 positive and 1 negative MLBW s-resonances and 63
p-resonances) are given for En up to 11.885 keV. In the energy range
below 3 keV parameters are based on experimental data, for higher
energies many artificial levels were generated with STAT code by
assuming average resonance parameters D=380 eV, S~0~=0.57E-4,
S~1~=0.45E-4. URR region with contribution of s-, p- and d- waves covers
energy range from 11.885 keV to 100 keV. Average resonance parameters
and strength functions for s- and p-waves were taken from S.F.
Mughabghab, 1981, and d-wave from SOM calculations, and adjusted to
experimental data on capture and total CS. For energy above 100 keV the
results of optical, statistical and pre-equilibrium decay reaction
models were used in the evaluation. Direct-semi-direct nuclear reaction
mechanisms were accounted in capture cross section evaluation. 8
discrete levels to 2.2071 MeV excitation energy were included in the
statistical model calculations of inelastic scattering. No direct
excitation was accounted.

CENDL-3 evaluation in the RRR and URR is taken from JENDL-3.2 library
with (wrong) modification of parameters of first resonance in the RRR.
Results of OM and SM calculations with account of contribution of PEQ
and DR (for inelastic scattering) mechanisms. 2 discrete levels to 0.662
MeV excitation energy were included in the statistical model
calculations of inelastic scattering. MF=4 and MF=5 files used for
energy-angular distributions with excitation of continuum of the states.

###### Thermal and resonance region

Table below shows the thermal cross section values (barns at 0.0253 eV),
resonance integral RI (barns) and position and width of negative
resonance for all libraries. JEF-2 as old and obsolete evaluation in the
RRR was not included in the comparison.

+------------+-----------+-----------+--------------------------------+
| Cross      | ENDF/B-VI | JENDL-3.2 | Experiment, if relevant and    |
| section ,  |           |           | exists                         |
|            |           | =CENDL-3  |                                |
| parameter  |           |           | Comments                       |
|            |           |           |                                |
|            |           |           | Partial conclusions            |
+------------+-----------+-----------+--------------------------------+
| E~min~,    | 1.0E-5    | 1.0E-5    |                                |
| RRR, eV    |           |           |                                |
+------------+-----------+-----------+--------------------------------+
| E~max~,    | 1.9475    | 11.885    |                                |
| RRR, keV   |           |           |                                |
+------------+-----------+-----------+--------------------------------+
| N~res~     | 9         | 50        | Ratio of numbers of p- to      |
|            | s-r       | s-r       | s-resonances in RRR J-3 is     |
|            | esonances | esonances | about 1; it should be 3. J-3   |
|            |           |           | positions and widths for some  |
|            | (1        | (1        | resonances were assigned by    |
|            | negative) | negative) | Kikuchi random-statistically   |
|            |           |           | basing on average parameters.  |
|            |           | 63        | This is the best way to        |
|            |           | p-r       | account for missed resonances. |
|            |           | esonances |                                |
+------------+-----------+-----------+--------------------------------+
| Total cs,  | 11.14     | 9.0       | 5.2 b for \<E\>=1.26 -- 18.8   |
| b          | (therm.)  | 2(therm.) | eV (X4=21992).                 |
|            |           |           |                                |
|            | \~5.72 at | \~3.6 at  | B-6 is closer to exp data      |
|            | 10 eV     | 10 eV     |                                |
|            |           |           |                                |
|            |           | 5.64(t    |                                |
|            |           | herm)C-3, |                                |
|            |           | 1.95      |                                |
|            |           | (C-3) at  |                                |
|            |           | 10 eV     |                                |
+------------+-----------+-----------+--------------------------------+
| Elastic    | 6.03      | 3.90      | No exp data, probably too low  |
| cs, b      |           |           | in C-3, and too high in B-6    |
|            |           | 1.84(C-3) |                                |
+------------+-----------+-----------+--------------------------------+
| Capture    | 5.11      | 5.12      | 5.1±0.4(S.F.Mughabghab, 1981)  |
| cs, b      |           |           |                                |
|            |           | 3.80      | 3.6±0.2(S.F.Mughabghab, 2003)  |
|            |           | (C-3)     |                                |
|            |           |           | Parameters of fictitious       |
|            |           |           | "positive" resonance in C-3    |
|            |           |           | are adjusted to new thermal    |
|            |           |           | capture CS                     |
+------------+-----------+-----------+--------------------------------+
| RI, b      | 3.92      | 4.75      | 4.3±1.0(S.F.Mughabghab, 2003). |
|            |           |           | No direct exp data. Mughabghab |
|            |           | 1         | evaluation is obtained         |
|            |           | 38.2(C-3) | probably only from known       |
|            |           |           | resonances. J-3 with           |
|            |           |           | assignment of possible missed  |
|            |           |           | resonances is more             |
|            |           |           | reliable(?). First positive    |
|            |           |           | resonance in C-3 is wrong      |
|            |           |           | (non-existent). This leads to  |
|            |           |           | very high RI                   |
+------------+-----------+-----------+--------------------------------+
| R', RRR,   | 6.2184    | 5.15      | Possibly slightly low in J-3   |
| fm         |           |           |                                |
+------------+-----------+-----------+--------------------------------+
| E~r~(-),   | -26.      | -26.      | There is an error in C-3 where |
| eV         |           |           | negative 26 eV resonance was   |
|            |           | No (C-3), | introduced as positive one.    |
|            |           | +26.      |                                |
+------------+-----------+-----------+--------------------------------+
| ~n~(-), eV | 0.081     | 0.080     |                                |
|            |           | (         |                                |
|            |           | positive) |                                |
+------------+-----------+-----------+--------------------------------+
| (-), eV    | 0.083     | 0.084     |                                |
|            |           | (         |                                |
|            |           | positive) |                                |
+------------+-----------+-----------+--------------------------------+
| E~min~,    | \-        | 11.885    |                                |
| URR, keV   |           |           |                                |
+------------+-----------+-----------+--------------------------------+
| E~max~,    | \-        | 100\.     |                                |
| URR, keV   |           |           |                                |
+------------+-----------+-----------+--------------------------------+
| R', URR,   | \-        | 5.729     | Possibly slightly low in J-3,  |
| fm         |           |           | what can lead to slightly low  |
|            |           |           | elastic scattering cross       |
|            |           |           | section.                       |
+------------+-----------+-----------+--------------------------------+
| D~0~, min, | \-        | 205\.     |                                |
| eV         |           |           |                                |
+------------+-----------+-----------+--------------------------------+
| FAST       | 5.25      | 5.38      | J-3, C-3 is close to the       |
| capture,   |           |           | experimental data              |
| mb         |           | 9.1 (C-3) |                                |
+------------+-----------+-----------+--------------------------------+
| Capture,   | \~0.024   | \~0.0539  | 0.0766 (X4=22307, at \<30-40\> |
| b,         |           |           | keV) 0.054±0.010 (X4=30328, at |
| E~n~=37.5  |           |           | \<30-40\> keV), 0.0845±0.0034  |
| keV        |           |           | (X4=220307, 37.5 keV),         |
|            |           |           | 0.0769±0.0029 (X4=22337)       |
+------------+-----------+-----------+--------------------------------+

Large difference in total and elastic scattering cross section in the
thermal energy point and in resonance energy range is due to the
position, neutron width of the negative resonance and potential
scattering radius. The J-3 library gives values in eV region below the
experimental values. B-6 gives better fit in eV region but does not fit
at "cold" neutron point. C-3 with wrong sign of energy of first
resonance gives wrong RI. J-3 resonances in the RRR are s-resonances and
p-resonances with random-statistical assignment of positions and widths
to missed resonances. Due to this the RI in J-3 is higher than in B-6
and in S.F. Mughabghab evaluation, but this looks reasonable(?).

**Fast region**

Table below describes major characteristics of evaluations in the fast
neutron energy region (E~n~ \> 100 keV).

B-6 is very old evaluation in the FAST energy region and cannot compete
with other evaluations. J-3 and C-3 evaluations are rather similar. As
seems the imaginary part of optical potential is slightly low than
needed in C-3 at low energies, what leads to the overestimation of
non-elastic cross section. Non-elastic cross sections for neighboring
nuclei should be considered when OM parameters are adjusted.

Direct reaction mechanism with excitation of collective levels in the
inelastic scattering should be accounted in the evaluations for larger
number of low-lying levels. Energy-angular distributions for secondary
particles should be calculated with SM, PEQ and direct reaction
mechanisms contributions and presented in the file MF=6.

No secondary gamma spectra are given in files of all libraries.

###### Recommendation and conclusion

JENDL-3.2 evaluation with newly adjusted position and width of negative
resonance and R' in the RRR to fit eV and "cold" neutron energy
experimental data can be selected. JENDL-3.2 evaluation in the URR can
be selected. JENDL-3.2 can be recommended for high-energy range after
some improvements.

###### Further possible improvements

To revise parameters of negative resonance in JENDL-3.2 library to fit
new S.F. Mughabghab evaluated thermal capture cross section value. To
revise R' and neutron width of negative resonance in JENDL-3.2 by
adjusting to existing experimental data on total CS in eV region. Use
non-SOM model to account for direct process. Use MF=6 file for
energy-angular distributions of secondary particles with account of SM,
PEQ and direct reaction mechanisms.

+------------+---------+---------+---------+-------------------------+
| Cross      | EN      | JE      | CENDL-3 | Experiment, if relevant |
| section,   | DF/B-VI | NDL-3.2 |         | and exists              |
|            |         |         |         |                         |
| parameter  | =JEF-2  |         |         | Comments                |
|            |         |         |         |                         |
|            |         |         |         | Partial conclusions     |
+------------+---------+---------+---------+-------------------------+
| Begin of   | 1.9475  | 100\.   | 100\.   | The use of OM and SM    |
| OM and SM  |         |         |         | calculations starting   |
| ca         |         |         |         | from 1.9475 keV in B-6  |
| lculations |         |         |         | can be not reliable.    |
|            |         |         |         |                         |
| E~min~,    |         |         |         |                         |
| FAST, keV  |         |         |         |                         |
+------------+---------+---------+---------+-------------------------+
| Total      | \~5.    | \~4.67  | \~4.    | 4.65 b ( \<En\>=0.1 --  |
|            | 57(0.15 | (0.15   | 97(0.15 | 0.2 MeV, X4=22307). B-6 |
|            | MeV)    | MeV)    | MeV)    | is too high.            |
|            |         |         |         |                         |
|            | \~4.    | \~4.    | \~4.65  |                         |
|            | 98(19.5 | 99(19.5 | (19.5   |                         |
|            | MeV)    | MeV)    | MeV)    |                         |
+------------+---------+---------+---------+-------------------------+
| Elastic    | 5.56 b  | \~4.65  | 4.94 b  | 4.8±0.5 b at 0.143 MeV  |
|            | at 0.15 | b at    | at 0.15 | (X4=22033)              |
|            | MeV     | 0.15    | MeV     |                         |
|            |         | MeV     |         | B-6 is too high above   |
|            | \~2.49  |         | 2.175 b | 10 MeV because has no   |
|            | b at 5  | 2.50 b  | at 5    | (n,2n)                  |
|            | MeV     | at 5    | MeV     |                         |
|            |         | MeV     |         |                         |
+------------+---------+---------+---------+-------------------------+
| Capture    | 0.022 b | 0.028 b | 0.028 b | 0.033 b (X4=22307)      |
|            | at 150  | at 150  | at 150  |                         |
|            | keV     | keV     | keV     | 0.028 (X4=30328, at     |
|            |         |         |         | \<100-200\> keV) 0.0422 |
|            |         |         |         | (X4=22307)              |
|            |         |         |         |                         |
|            |         |         |         | B-6 is below            |
|            |         |         |         | experimental data.      |
+------------+---------+---------+---------+-------------------------+
| Discrete   | 8       | 8       | 2       | According latest ENSDF  |
| levels     | levels  | levels  | levels  | 2 levels are missed in  |
| inelastic  | to 1.84 | to 2.04 | to      | B-6 and 6 levels are    |
| scat.      | MeV     | MeV     | 0.662   | missed in J-3.          |
|            |         |         | MeV     |                         |
|            |         |         |         | Contribution of DR in 1 |
|            |         |         |         | low-lying level in C-3. |
+------------+---------+---------+---------+-------------------------+
| Continuum  | E~con   | E~con   | E~cont  | PEQ model contribution  |
| levels     | t~=1.84 | t~=2.12 | ~=0.662 | accounted in J-3, C-3   |
| inelastic  | MeV     | MeV     | MeV     | but not in B-6.         |
| scattering |         |         |         |                         |
+------------+---------+---------+---------+-------------------------+
| Total      | 1.874 b | \~2.0 b | 2.383 b | B-6: total inelastic =  |
| inelastic  | at 5    | at 5    | at 5    | the first neutron       |
| cross      | MeV     | MeV     | MeV     | emission cross section. |
| section    |         |         |         | Average experimental    |
|            | 1.118 b | \~0.317 | \~0.243 | value for non-elastic   |
|            | at 20   | b at 20 | b at 20 | cross section (50 \<Z\< |
|            | MeV     | MeV     | MeV     | 60, 4 \<E~n~\< 6 MeV)   |
|            |         |         |         | is 2.12 b. Probably B-6 |
|            |         |         |         | underestimates and C-3  |
|            |         |         |         | overestimates slightly  |
|            |         |         |         | the inelastic           |
|            |         |         |         | scattering CS at 5 MeV. |
+------------+---------+---------+---------+-------------------------+
| (n,2n)     | absent  | 1.70 b  | 1.732 b | J-3 normalized to       |
|            |         | at 14   | at 14   | systematics at 14 MeV.  |
|            |         | MeV     | MeV     |                         |
+------------+---------+---------+---------+-------------------------+
| (n,p),     |         |         |         | Minor cross sections.   |
| (n,a) and  |         |         |         | J-3, C-3 are more       |
| other      |         |         |         | reliable.               |
+------------+---------+---------+---------+-------------------------+
| Elastic    | is      | SOM+SM  | SOM+SM  |                         |
| scattering | otropic | calcu   | calcu   |                         |
| angular    |         | lations | lations |                         |
| distr.     |         |         |         |                         |
+------------+---------+---------+---------+-------------------------+
| Inelastic  | is      | SM      | SM+PEQ  | MF=4, MT=91 symmetric   |
| scattering | otropic | calc.,  |         | in J-3 in CMS. MF=4,    |
| angular    |         | sy      | +DR     | MT=91 in CENDL-3 has no |
| distr.     |         | mmetric | calc.   | sense, MF=6 should be   |
|            |         | in CMS  |         | used.                   |
+------------+---------+---------+---------+-------------------------+
| Secondary  | Temp    | Prob    | Prob    | B-6 gives wrong spectra |
| neutron    | erature | ability | ability | for E~n~ above (n,2n)   |
| spectra    | prese   | tables  | tables  | threshold.              |
|            | ntation | with SM | with SM |                         |
|            |         | and PEQ | and PEQ |                         |
|            |         | mec     | mec     |                         |
|            |         | hanisms | hanisms |                         |
+------------+---------+---------+---------+-------------------------+

######