**WPEC SG 21: Assessment of Neutron Cross-Section Evaluations for the
Bulk of Fission Products**

**36-Kr-80 Review**

I. Sirakov, INRNE, January 12, 2004

######## **[Files]{.underline}**

***ENDF/B-VI:*** Year of origin 1978, taken from ENDF/B-V, no revisions
since then

***JEF-2:*** Year of origin 1982, data taken from ENDF/B-V, last
revision 1989

***JENDL-3:*** Year of origin 1990, revised (trivially) in 2002 when
transformed to JENDL-3.3

######## **[Thermal and resonance region]{.underline}**

***ENDF/B-VI, JEF-2:*** Resolved resonance region up to 1 keV with
resonance parameters based on BNL-325 (1973) and experimental data of
Block et al (1978); SLBW representation for 4 s-wave resonances at 89.2,
106, 640, and 927 eV and a bound resonance level at -118 eV; scattering
radius 7.47 fm. No unresolved resonance region (Table 1). Computed
resonance integral 68.6 b. ***JEF-2*** changed the flag to the MLBW
representation (1987).

***JENDL-3*:** Resolved resonance region up to 1 keV with resonance
parameters based on BNL-325 (1981); account taken of s-wave; MLBW
representation for three resonances at 106, 451, and 927 eV, and eight
out-of-range (background) resonances. The negative resonance at -120 eV
added to reproduce the thermal capture cross section (Table 2) according
to BNL-325 (1981). Scattering radius 6.6 fm. Unresolved region up to 100
keV; S0 and S2 strength functions calculated with CASTHY; S1 based on
systematics of Mughabghab; radiation width of 230 meV from Mughabghab's
compilation. Level spacing determined to reproduce the capture cross
section from CASTHY; the effective scattering radius of 7.5 fm fitted to
the calculated MT=1 at 100 keV. Computed resonance integral 60.2 b.

**Note on the resonance region** (up to 100 keV for JENDL)**:**

The capture cross section from about hundred eV to several hundred keV
has a predominant contribution to the one-group capture cross section
(1E-5 eV - 20 MeV) over fast-reactor weighting spectrum
(<http://www.nndc.bnl.gov/sg21/nucl/acs/accs.htm>) and accounts for the
one-group values of ***ENDF/B-VI*** (243.8 mb), ***JEF-2*** (243.7 mb)
and ***JENDL-3*** (293.0 mb). The higher value of ***JENDL-3*** is
related to its higher capture cross section from 4 keV to \~1 MeV.

The higher value of the capture resonance integral for
***ENDF/B-VI/JEF-2*** (68.6 b) compared to ***JENDL-3*** (60.2 b) is due
to the stronger capture resonance at 106 eV as well as to the
***ENDF/B-VI*** resonances at 89.2 eV and 640 eV (not available in
***JENDL-3***) which contribute more than the ***JENDL-3*** resonance at
451 eV.

Disadvantage of ***ENDF/B-VI***(***JEF-2***) is the lack of unresolved
resonance region. Moreover, the ***ENDF/B-VI***(***JEF-2***) show a
unreasonable (non-smooth) shape of MT=102 in the energy region 1-50 keV
due to the linear-linear interpolation law applied between rather
distant energy points at 1, 5, 10 and 50 keV.

**Experimental data** -- Thermal capture cross sections of all
evaluations (Table 2) are not very close to the experimental value of
15.6(19) b (Barabanov 1972,
[EXFOR40120](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=40120&DatType=H&RetType=byAccNum&ReDo=N)
002), but fully agree with the recommendation of 11.5(5) b (Mughabghab
2003,
[INDC(NDS)-440](http://www.nndc.bnl.gov/sg21/nucl/indc-nds-440.pdf)).
The resonance integral data of 56.1(28) b by Bradley, 1972
([EXFOR10627](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=10627&DatType=H&RetType=byAccNum&ReDo=N)
003) as well as the RI recommendation of 56.1(56) b (Mughabghab 2003,
[INDC(NDS)-440](http://www.nndc.bnl.gov/sg21/nucl/indc-nds-440.pdf)) are
in better agreement with ***JENDL-3*** value of 60.2 b compared to 68.6
b of ***ENDF/B-VI***(***JEF-2***). Capture cross section data of Walter,
1984
([EXFOR21913](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=21913&DatType=H&RetType=byAccNum&ReDo=N)
006,
[EXFOR22037](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=22037&DatType=H&RetType=byAccNum&ReDo=N)
008), generally agree with all evaluations in the region 2.5 -- 50 keV,
but are only in favor of ***JENDL-3*** above 50 keV.

**Recommendation/Conclusion**: ***JENDL-3*** is recommended up to 100
keV for its better agreement with the recommended thermal capture cross
section (Mughabghab, 2003) and experimental average capture cross
section data between 50 and 100 keV (Walter, 1984). In addition,
***ENDF/B-VI*** and ***JEF-2*** show unreasonable (non-smooth) shapes of
MT=102 between 1 and 50 keV.

######## **[Fast neutron region]{.underline}**

-   Methodology

***ENDF/B-VI, JEF-2:*** Spherical OM code ABACUS for MT=1 and MT=2;
statistical model code CERBERO for MT=4, 51-56, 91, 102, 103, 107;
FASCRO code for MT=16, 104, 105, 106; no preeq corrections; 6 discrete
levels (from 616 keV to 3.4 MeV) adopted for the inelastic scattering.
Legendre coefficients from CHAD code to get anisotropic angular
distribution for MF=4, MT=2 in CM system. Account taken of MT=1, 2, 4,
16, 51-56, 91, 102, 103, 104, 105, 106, 107. ***JEF-2*** also includes
(n,2p) production data (MT=111) from REAC-ECN-4 Library and a corrected
Q-value of 2.356 MeV instead of 0.9685 MeV for MT=107.

***JENDL-3:*** Spherical OM and statistical model code CASTHY for MT=1,
4, 51-79, 91, 102 by taking into account competing reactions MT=16, 22,
28, 103, 104, 105, 106, 107, 111 which were calculated with the preeq
and multi-step evaporation model code PEGASUS. The gamma-ray strength
function (6.99E-4) adjusted at 100 keV to the measured capture cross
section (Walter 1984). Direct and semi-direct capture estimated; 29
discrete levels (from 616.6 keV to 4.393 MeV) adopted for the inelastic
scattering. MT=103 and MT=107 normalized to recommended by Forrest
(1986) values at 14.5 MeV; elastic calculated as (MT1 -- sum of partial
cross sections); Legendre coefficients from CASTHY to get anisotropic
angular distribution for MF=4, MT=2 and MT=51-79 in CM system. MT=1, 2,
4, 16, 22, 28, 51-79, 91, 102, 103, 104, 105, 106, 107, 111.

-   MT=1

***ENDF/B-VI*** and ***JEF-2*** follow the structure of the inelastic
cross section in the region 1.5-6 MeV with a peak at 3.5 MeV. In
addition, MT=1 is not smooth at the inelastic scattering threshold of
624 keV and at 11.5-MeV point of steep descent on the MT=4 curve.

***JENDL-3*** shows a reasonably smooth shape and better agreement with
experimental (EXFOR) data for KrNat(n,tot). The maximum discrepancy
between ***ENDF/B-VI**(**JEF-2**)* and ***JENDL-3*** is 1.35 b at 3.5
MeV.

-   MT=2

***JENDL-3*** and ***ENDF/B-VI**(**JEF-2**)* are close except for the
regions 200-600 keV and 4-15 MeV where ***JENDL-3*** is higher with
maximum discrepancies of 0.5 b and 0.9 b respectively.

-   MT=4

***ENDF/B-VI**(**JEF-2**)* are systematically higher than ***JENDL-3***.
The maximum difference of 1.62 b at 3.5 MeV is the main contributor to
the above mentioned MT1 discrepancy of 1.35 b (MT=2 and MT=102
contribute -0.25 b and -0.02 b respectively). The (n,2n) threshold is
11.7 MeV.

-   MT=16

***JENDL-3*** shows better agreement with the experimental data of
Kondaiah, 1968
([EXFOR11884](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=11884&DatType=H&RetType=byAccNum&ReDo=N)
005) and Bazan, 1989
([EXFOR13184](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=13184&DatType=H&RetType=byAccNum&ReDo=N)
003) in the region 14-14.7 MeV; ***ENDF/B-VI**(**JEF-2**)* are
systematically higher than ***JENDL-3*** with a maximum discrepancy of
270 mb at 20 MeV. The (n,3n) threshold is above 20 MeV. The cross
sections MT=28 and MT=22 of ***JENDL-3*** that jointly give about 320 mb
at 20 MeV, are assumed to be zero in ***ENDF/B-VI**(**JEF-2**)*.

-   MT=102

***JENDL-3*** is in better agreement with the experimental data of
Walter, 1984
([EXFOR21913](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=21913&DatType=H&RetType=byAccNum&ReDo=N)
006,
[EXFOR22037](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=22037&DatType=H&RetType=byAccNum&ReDo=N)
008) available up to 264 keV. ***ENDF/B-VI**(**JEF-2**)* show
systematically lower values compared to ***JENDL-3***.

-   MT=103

In contrast to ***JENDL-3***, ***ENDF/B-VI**(**JEF-2**)* are not
consistent with the experimental data of 55(9) mb for the
80Kr(n,p)80Br-m reaction at 14.4 MeV
([EXFOR11884](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=11884&DatType=H&RetType=byAccNum&ReDo=N)
004, Kondaiah 1968). Their values of 24 mb are significantly below these
data.

-   MT=107

From systematics \[1\] - \[2\], it follows that (n,) cross sections for
different isotopes of a given element become smaller as the isotope mass
A increases. Comparison between 80Kr(n,) evaluations and experimental
data for 86Kr(n,)83Se-g reaction at 14.4 MeV
([EXFOR11884](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=11884&DatType=H&RetType=byAccNum&ReDo=N)
010, Kondaiah 1968) shows that only ***JENDL-3*** could be reasonable
since the ***ENDF/B-VI**(**JEF-2**)* values at 14.4 MeV are below the
experimental data.

**Recommendation/Conclusion**: ***JENDL-3*** recommended in the fast
energy region 100 keV - 20 MeV. ***JENDL-3*** is in better agreement
with the experimental data (MT=16, 102). ***ENDF/B-VI*** and ***JEF-2***
do not seem reasonable for MT=1, 103, 107.

\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--

**[Table 1]{.underline}.** Summary for Resolved and Unresolved Resonance
Region: Kr-80

+---------+---+---------+-------+----+-------------------------------+
| Library | Y | First   | RRR   | U  | Remarks                       |
|         | e | Authors |       | RR |                               |
|         | a |         |       |    |                               |
|         | r |         |       |    |                               |
+---------+---+---------+-------+----+-------------------------------+
| EN      | 1 | A.      | 1     | \- | RR parameters based on        |
| DF/B-VI | 9 | Prince  | keV\  |    | BNL-325 (1973) and            |
|         | 7 | (BNL)   | \     |    | experimental data of Block et |
|         | 8 |         | SLBW  |    | al (1978); Four s-wave        |
|         |   |         |       |    | resonances at 89.2, 106, 640, |
|         |   |         |       |    | and 927 eV, and a bound       |
|         |   |         |       |    | resonance level at -118 eV;   |
|         |   |         |       |    | scattering radius 7.47 fm.    |
|         |   |         |       |    | Computed resonance integral   |
|         |   |         |       |    | 68.6 b.                       |
+---------+---+---------+-------+----+-------------------------------+
| JEF-2   | 1 | Sci     | 1     | \- | RR parameters taken from      |
|         | 9 | entific | keV\  |    | ENDF/B-V. Flag changed to     |
|         | 8 |         | \     |    | MLBW.                         |
|         | 2 | Co-ord  | MLBW  |    |                               |
|         |   | ination |       |    |                               |
|         |   |         |       |    |                               |
|         |   | Group   |       |    |                               |
+---------+---+---------+-------+----+-------------------------------+
| JENDL-3 | 1 | JNDC FP | 1     | 1  | RR parameters based on        |
|         | 9 | Nuclear | keV\  | 00 | BNL-325 (1981); account taken |
|         | 9 | Data    | \     | k  | of s-wave; Three resonances   |
|         | 0 | Working | MLBW  | eV | at 106, 451, and 927 eV and   |
|         |   | Group   |       |    | eight out-of-range            |
|         |   |         |       |    | (background) resonances; The  |
|         |   |         |       |    | bound resonance level at -120 |
|         |   |         |       |    | eV added to reproduce the     |
|         |   |         |       |    | thermal capture cross section |
|         |   |         |       |    | (Table 2) according to        |
|         |   |         |       |    | BNL-325 (1981). Scattering    |
|         |   |         |       |    | radius 6.6 fm.                |
|         |   |         |       |    |                               |
|         |   |         |       |    | URR: S0 and S2 strength       |
|         |   |         |       |    | functions calculated with     |
|         |   |         |       |    | CASTHY; S1 based on           |
|         |   |         |       |    | systematics of Mughabghab;    |
|         |   |         |       |    | radiation width of 230 meV    |
|         |   |         |       |    | from Mughabghab's             |
|         |   |         |       |    | compilation. Level spacing    |
|         |   |         |       |    | determined to reproduce the   |
|         |   |         |       |    | capture cross section from    |
|         |   |         |       |    | CASTHY; the effective         |
|         |   |         |       |    | scattering radius of 7.5 fm   |
|         |   |         |       |    | fitted to the calculated MT=1 |
|         |   |         |       |    | at 100 keV.                   |
|         |   |         |       |    |                               |
|         |   |         |       |    | Computed resonance integral   |
|         |   |         |       |    | 60.2 b.                       |
+---------+---+---------+-------+----+-------------------------------+

**[Table 2]{.underline}.** Thermal Cross Sections for Kr-80

+--------------------------------+------------+-------------+---------+
| Library / Experiment           | Total      | Capture     | Elastic |
+--------------------------------+------------+-------------+---------+
| ENDF/B-VI                      | 21.298 b   | 11.739 b    | 9.559 b |
+--------------------------------+------------+-------------+---------+
| JEF-2                          | 20.676 b   | 11.739 b    | 8.936 b |
+--------------------------------+------------+-------------+---------+
| JENDL-3                        | 18.840 b   | 11.503 b    | 7.337 b |
+--------------------------------+------------+-------------+---------+
| Barabanov et al (1972)         |            | 15.6(19) b  |         |
|                                |            |             |         |
| ([EXFOR40120                   |            |             |         |
| ](http://www.nndc.bnl.gov/htbi |            |             |         |
| n/csisrs.cgi?AccNum=40120&DatT |            |             |         |
| ype=H&RetType=byAccNum&ReDo=N) |            |             |         |
| 002)                           |            |             |         |
+--------------------------------+------------+-------------+---------+
| BNL-325 (1973)                 |            | 14.0(15) b  |         |
+--------------------------------+------------+-------------+---------+
| BNL-325 (1981)                 |            | 11.5(5) b   |         |
+--------------------------------+------------+-------------+---------+
| S.F.Mughabghab,                |            | 11.5(5) b   |         |
| [INDC(ND                       |            |             |         |
| S)-424](http://www-nds.iaea.or |            |             |         |
| .at/reports/indc-nds-424.pdf), |            |             |         |
| p.73 (2001)                    |            |             |         |
+--------------------------------+------------+-------------+---------+
| S.F.Mughabghab,                |            | 11.5(5) b   |         |
| [INDC(ND                       |            |             |         |
| S)-440,](http://www.nndc.bnl.g |            |             |         |
| ov/sg21/nucl/indc-nds-440.pdf) |            |             |         |
| p.11 (2003)                    |            |             |         |
+--------------------------------+------------+-------------+---------+

**References:**

**1.** J.Csikai et al., Fusion Engineering and Design **37**, 65 (1997).

**2.** A.Majdeddin et al., INDC(HUN)-031, Distr. L, IAEA (1997).