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

**36-Kr-84 Review**

I. Sirakov, INRNE, February 12, 2003

######## **[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 1984, taken from JENDL-2, last revisions
1990, 2002

***CENDL-3:*** Year of origin 1999, last revision 2001

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

***ENDF/B-VI:*** Resolved resonance parameters up to 2.0 keV based on
BNL-325 (1973); SLBW representation for the 3 s-wave resonances at 519,
580, and 1625 eV; scattering radius 7.47 fm. No unresolved resonance
region (Table 1). Computed resonance integral 3.49 b.

***JEF-2:*** Resolved resonance parameters up to 2.0 keV; MLBW
representation for the 3 s-wave resonances at 519, 580, and 1625 eV;
scattering radius 7.47 fm. No unresolved resonance region. Computed
resonance integral 3.49 b.

***JENDL-3*:** Resolved resonance region up to 2.48 keV; MLBW
representation; Parameters of the two s-wave resonances (519, 580 eV)
adopted from BNL-325 (1981) as levels of certain isotopic assignment; a
negative resonance added at --150 eV to reproduce the thermal capture
cross section (Table 2). Scattering radius 7.03 fm; Unresolved region up
to 100 keV; S0, S1 and S2 strength functions calculated with CASTHY;
Level spacing determined to reproduce the capture cross section from
CASTHY; the scattering radius fitted to the calculated MT=1 at 100 keV.
Computed resonance integral 2.42 b.

***CENDL-3:*** Resonance parameters taken from JENDL-3 except the
average radiative widths at 100keV, which decrease to 145 meV compared
to JENDL-3 values of 200 meV. Computed resonance integral 2.39 b.

**Note on the resonance region**: The capture cross section in the
interval \~ 100 eV -- 100 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>).
The resonance of the uncertain isotopic assignment at 1625 eV, available
in ***ENDF/B-VI*** (***JEF-2***) but not in ***JENDL-3***
(***CENDL-3***) evaluations, accounts for the difference in the above
one-group capture cross sections of 6.4087E-2 (6.4066E-2) b and
4.9940E-2 (4.7514E-2) b respectively. No EXFOR data on measured
resonance integrals. All evaluations agree with the EXFOR capture cross
section data (Alsen 1980, Hensley 1984) because of the large
experimental uncertainties and do not contradict the isomeric production
cross section data for capture at 25 keV (Thirumala Rao 1972,
[EXFOR30501](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=30501&DatType=H&RetType=byAccNum&ReDo=N)
002).

**Recommendation/Conclusion**: ***JENDL-3*** (***CENDL-3***) recommended
in the resonance region up to 100 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, 51-63, 91, 102, 103, 107;
MT=16, 104, 105 from FASCRO code; no preeq corrections; 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, 51-63, 91,
102, 103, 104, 105, 106, 107. ***JEF-2*** also includes MT=111 from
REAC-ECN-4 Library.

***JENDL-3:*** Spherical OM and statistical model code CASTHY for MT=1,
4, 51-91, 102 by taking into account competing reactions MT=16, 17, 103,
107, etc, which were calculated with the preeq and multi-step
evaporation model code PEGASUS. The gamma-ray strength function adjusted
to measured capture cross section at 30 keV. Direct and semi-direct
capture estimated; 16 levels up to 3.72 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 in CM system. MT=1, 2, 4, 16, 17,
22, 28, 51-66, 91, 102, 103, 104, 105, 106, 107.

***CENDL-3:*** Spherical OM and unified preeq-statistical model code
SUNF; 13 levels up to 3.04 MeV adopted for the inelastic scattering;
DWBA code DWUCK4 to calculate the direct inelastic scattering
contribution. Legendre coefficients obtained to present anisotropic
angular distribution for MF=4, MT=2 in CM system. MT=1, 2, 4, 16, 17,
22, 28, 51-63, 91, 102, 103, 104, 105, 106, 107.

-   MT=1

***ENDF/B-VI, JEF-2:*** Unrealistic shape of the total cross section
that follows the structure of the inelastic cross section in the region
of several MeV.

***JENDL-3*** and ***CENDL-3*** are reasonable as can be seen from
comparison of the evaluated files for 84Kr(n,tot) with experimental
(EXFOR) data for KrNat(n,tot). Natural Kr has an average mass number
(\~83.9) close to the mass number of 84Kr.

-   MT=2

***JENDL-3*** and ***CENDL-3*** are close up to 8 MeV. The peak at 11
MeV is not reasonable in ***JENDL-3***. It appears since the sharp slope
of the (n,inl)-decrease starts at 10 MeV while the (n,2n)-rise starts at
10.7 MeV. ***CENDL-3*** is about 0.4-0.5 b lower than ***JENDL-3***
above 11 MeV. This difference is 'compensated' in MT=1 by higher
***CENDL-3*** values for (n,n') about 11 MeV, and for (n,2n) above 13
MeV.

-   MT=4

***ENDF/B-VI, JEF-2:*** Show rather peaked shape at \~4 MeV and a rise
at 20 MeV.

***JENDL-3, CENDL-3:*** Show reasonable shape. ***CENDL-3*** is about
0.4-0.5 b higher than ***JENDL-3*** about 11 MeV.

-   MT=16

All evaluations show reasonable shape. ***CENDL-3*** is about 0.4-0.5 b
higher than ***JENDL-3*** above 13 MeV.

-   MT=102

***ENDF/B-VI, JEF-2:*** Do not take account of the direct (semi-direct)
capture, and are too low at high energies.

-   MT=103

***ENDF/B-VI, JEF-2*** are not consistent with the experimental
([EXFOR11884](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=11884&DatType=H&RetType=byAccNum&ReDo=N)
008) data for 84Kr(n,p)84Br-g at 14.4 MeV (Kondaiah, 1968).

-   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 84Kr(n,) evaluations and experimental
data for 86Kr(n,)83Se-g reaction
([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*** is reasonable. In
addition, the quantitative systematics \[2\] for the 84Kr(n,) cross
section gives the prediction of 3.96(-.93,+1.20) mb at 14.7(2) MeV,
which agrees very well with the ***JENDL-*3** value of 3.7 mb. The
prediction of \[3\] is 4.85(-.71,+.83) mb, and is also in favor of
***JENDL-*3**.

**Recommendation/Conclusion**: ***JENDL-3*** and ***CENDL-3***
recommended in fast energy region 100 keV - 20 MeV; ***CENDL-3*** seems
favorable for MT=2, but is not reasonable for MT=107.

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

**[Table 1]{.underline}.** Summary for Resolved and Unresolved Resonance
Region: Kr-84

+---------+---+---------+-------+----+-------------------------------+
| Library | Y | First   | RRR   | U  | Remarks                       |
|         | e | Authors |       | RR |                               |
|         | a |         |       |    |                               |
|         | r |         |       |    |                               |
+---------+---+---------+-------+----+-------------------------------+
| EN      | 1 | A.      | 2     | \- | RR parameters based on data   |
| DF/B-VI | 9 | Prince  | keV\  |    | from BNL-325 (1973); 3 s-wave |
|         | 7 | (BNL)   | \     |    | resonances at 519, 580, and   |
|         | 8 |         | SLBW  |    | 1625 eV; scattering radius    |
|         |   |         |       |    | 7.47 fm. Computed resonance   |
|         |   |         |       |    | integral 3.49 b.              |
+---------+---+---------+-------+----+-------------------------------+
| JEF-2   | 1 | Sci     | 2     | \- | RR parameters taken from      |
|         | 9 | entific | keV\  |    | ENDF/B-V. Flag changed to     |
|         | 8 |         | \     |    | MLBW. Computed resonance      |
|         | 2 | Co-ord  | MLBW  |    | integral 3.49 b.              |
|         |   | ination |       |    |                               |
|         |   |         |       |    |                               |
|         |   | Group   |       |    |                               |
+---------+---+---------+-------+----+-------------------------------+
| JENDL-3 | 1 | JNDC FP | 2.48  | 1  | RR parameters of the two      |
|         | 9 | Nuclear | keV\  | 00 | s-wave resonances (519, 580   |
|         | 9 | Data    | \     | k  | eV) adopted from BNL-325      |
|         | 0 | Working | MLBW  | eV | (1981) as levels of certain   |
|         |   | Group   |       |    | isotopic assignment; a        |
|         |   |         |       |    | negative resonance added at   |
|         |   |         |       |    | --150 eV to reproduce the     |
|         |   |         |       |    | thermal capture cross         |
|         |   |         |       |    | section.                      |
|         |   |         |       |    |                               |
|         |   |         |       |    | scattering radius 7.03 fm;    |
|         |   |         |       |    |                               |
|         |   |         |       |    | URR: S0, S1 and S2 strength   |
|         |   |         |       |    | functions calculated with     |
|         |   |         |       |    | CASTHY; Level spacing         |
|         |   |         |       |    | determined to reproduce the   |
|         |   |         |       |    | capture cross section from    |
|         |   |         |       |    | CASTHY; the scattering radius |
|         |   |         |       |    | fitted to the calculated MT=1 |
|         |   |         |       |    | at 100 keV. Computed          |
|         |   |         |       |    | resonance integral 2.42 b.    |
+---------+---+---------+-------+----+-------------------------------+
| CENDL-3 | 1 | Ch      | 2.48  | 1  | Resonance parameters taken    |
|         | 9 | ong-Hai | keV\  | 00 | from JENDL-3 except the       |
|         | 9 | Cai     | \     | k  | average radiative widths at   |
|         | 9 | (NKU),\ | MLBW  | eV | 100 keV**,** which decreased  |
|         |   | Yo      |       |    | by \~30% below JENDL-3        |
|         |   | u-Xiang |       |    | values. Computed resonance    |
|         |   | Zhuang  |       |    | integral 2.39 b.              |
|         |   | (CNDC)  |       |    |                               |
+---------+---+---------+-------+----+-------------------------------+

**[Table 2]{.underline}.** Thermal Cross Sections for Kr-84

+--------------------------------+------------+------------+----------+
| Library / Experiment           | Total      | Capture    | Elastic  |
+--------------------------------+------------+------------+----------+
| ENDF/B-VI                      | 6.8318 b   | 82.9 mb    | 6.7489 b |
+--------------------------------+------------+------------+----------+
| JEF-2                          | 6.8336 b   | 82.9 mb    | 6.7507 b |
+--------------------------------+------------+------------+----------+
| JENDL-3                        | 6.3071 b   | 110.0 mb   | 6.1971 b |
+--------------------------------+------------+------------+----------+
| CENDL-3                        | 6.3071 b   | 110.0 mb   | 6.1971 b |
+--------------------------------+------------+------------+----------+
| BNL-325 (1981)                 |            | 110(15) mb |          |
+--------------------------------+------------+------------+----------+
| S.F.Mughabghab, INDC(NDS)-     |            | 111(15) mb |          |
|                                |            |            |          |
| 424, p.69 (2001)               |            |            |          |
+--------------------------------+------------+------------+----------+

**References:**

**1.** R.Doczi et al., INDC(HUN)-032, Distr. L, IAEA (1997).

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

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