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

**36-Kr-82 Review**

I. Sirakov, INRNE, January 6, 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 100 eV with
resonance parameters based on BNL-325 (1973); SLBW representation for
one s-wave resonance at 39.8 eV (GN=88.3 meV, GG=236 meV) and a bound
resonance level at -42.83 eV; scattering radius 7.47 fm. No unresolved
resonance region (Table 1). Computed resonance integral 183.56 b.
***JEF-2*** changed the flag to the MLBW representation.

***JENDL-3*:** Resolved resonance region up to 400 eV with resonance
parameters mostly adopted from BNL-325 (1981); account taken of s-wave;
MLBW representation for one resonance at 39.63 eV (GN=124 meV, GG=227
meV) and five out-of-range (background) resonances at -160 eV, 646 eV,
657 eV, 1605 eV and 1659 eV; the negative resonance at -160 eV added to
reproduce the thermal capture cross section (Table 2) according to
BNL-325 (1981). Scattering radius 7.3 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 7.39 fm fitted
to the calculated MT=1 at 100 keV. Computed resonance integral 228 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*** (90.8 mb), ***JEF-2*** (90.8 mb) and
***JENDL-3*** (102 mb). The higher value of ***JENDL-3*** is mainly due
to its higher capture cross section from 40 keV to \~1 MeV.

The higher value of the capture resonance integral for ***JENDL-3***
(228 b), compared to ***ENDF/B-VI*** (184 b), is fully due to its
stronger resonance at \~40 eV, which matters now because of the higher
weight of integrating (1/E) in the low energy range. Since the
difference of the widths is relatively small, the ratio of the resonance
maxima (10559 b / 8783 b = 1.2) approximately equals the ratio of the
resonance integrals (228 b / 184 b = 1.2).

Disadvantage of ***ENDF/B-VI***(***JEF-2***) is the lack of unresolved
resonance region, in addition to the low upper limit (100 eV) for the
resolved resonance region. Moreover, the ***ENDF/B-VI***(***JEF-2***)
show unreasonable (non-smooth) shapes of MT=1, 2 and 102 in the energy
region 1-50 keV due to the linear-linear interpolation law applied
between rather distant energy points at 1, 10 and 50 keV.

**Experimental data** -- The rather scattered capture cross section data
of Walter, 1984
([EXFOR21913](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=21913&DatType=H&RetType=byAccNum&ReDo=N)
008) are in general agreement with all evaluations in the region 2.5 --
100 keV. The recent recommendations of Mughabghab, 2003
([INDC(NDS)-440](http://www.nndc.bnl.gov/sg21/nucl/indc-nds-440.pdf)),
however, for a thermal capture cross section of 19.0(40) b as well as
for a resonance capture integral of 130(13) b infer substantial
overestimation in ***JENDL-3*** (=28 b at E=25.3 meV, and RI=228 b) as
well as in ***ENDF/B-VI***(***JEF-2***) ( =30.17 b at E=25.3 meV, and
RI=184 b).

**Recommendation/Conclusion**: ***JENDL-3*** can only be recommended in
its URR (0.4-100 keV) where the agreement with the experimental data of
Walter (1984) is present and, unlike ***ENDF/B-VI***(***JEF-2***),
reasonable shapes of MT=1, 2 and 102 are shown.

No recommendation can be made for the resolved resonance region (below
400 eV) since the ***JENDL-3*** thermal capture cross section of 28 b
and resonance capture integral of 228 b seem to be too high according to
the recent recommendations of Mughabghab, 2003
([INDC(NDS)-440](http://www.nndc.bnl.gov/sg21/nucl/indc-nds-440.pdf)).
They may need correction toward the recommended values of 19(4) b and
130(13) b, respectively, through the resonance parameters of the bound
and first positive resonance level. Similar is the case with the
***ENDF/B-VI***(***JEF-2***) evaluation in the RRR up to 100 eV.

######## **[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, 51-59, 91, 102, 103, 107;
FASCRO code for MT=16, 104, 105, 106; no preeq corrections; 9 discrete
levels (from 777 keV to 2.92 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, 51-59, 91, 102, 103, 104, 105, 106, 107. ***JEF-2*** also includes
(n,2p) production data (MT=111) from REAC-ECN-4 Library.

***JENDL-3:*** Spherical OM and statistical model code CASTHY for MT=1,
4, 51-64, 91, 102 by taking into account competing reactions MT=16, 17,
22, 28, 103, 104, 105, 107, etc, which were calculated with the preeq
and multi-step evaporation model code PEGASUS. The gamma-ray strength
function (1.69E-4) adjusted at 100 keV to the measured capture cross
section (Walter 1984). Direct and semi-direct capture estimated; 14
discrete levels (from 776 to 2.92 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=51-64 in CM system. MT=1, 2,
4, 16, 17, 22, 28, 51-64, 91, 102, 103, 104, 105, 107.

-   MT=1

All evaluations seem to be in general agreement with the experimental
(EXFOR) data for KrNat(n,tot), available from 100 keV to 20 MeV.

***ENDF/B-VI**(**JEF-2**)* follow the structure of the inelastic cross
section in the region 1.5-6.5 MeV with peaks at 3.5, 4.5, and 5.5 MeV.
In addition, MT=1 is not smooth at the energy of the 787-keV inelastic
threshold, at other level excitation energies, and at 11-MeV point of a
steep slope on the MT=4 curve.

***JENDL-3*** shows a reasonably smooth shape. The maximum discrepancy
between ***ENDF/B-VI**(**JEF-2**)* and ***JENDL-3*** is 0.5 b at both
3.5 and 4.5 MeV.

-   MT=2

***JENDL-3*** and ***ENDF/B-VI**(**JEF-2**)* are close up to 4 MeV.
Their largest discrepancy of 0.7 b at 11 MeV is almost compensated in
MT=1 by the MT=4 contribution of -0.6 b difference.

The small peak at 11.1 MeV is not reasonable on the ***JENDL-3*** curve.
It appears since the steep slope of the (n,inl)-decrease starts at 10
MeV until the (n,2n)-rise starts at 11.1 MeV.

-   MT=4

***ENDF/B-VI*** and ***JEF-2*** are systematically higher than
***JENDL-3***. The maximum difference of 0.65 b at 4.5 MeV is the main
contributor to the above mentioned MT1 discrepancy of 0.5 b (MT2
contributes -0.15 b). The small drawback of ***JENDL-3***, that affects
MT4 and MT2, was described above (see MT=2). The (n,2n) threshold is
11.1 MeV.

-   MT=16

All evaluations show reasonable shape and do not contradict the
experimental data for Kr-86(n,2n)Kr-85-m at 14.4 MeV (Kondaiah 1968,
[EXFOR11884](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=11884&DatType=H&RetType=byAccNum&ReDo=N)
009). ***ENDF/B-VI**(**JEF-2**)* are systematically higher than
***JENDL-3*** with a maximum discrepancy of 150 mb at 20 MeV. The (n,3n)
threshold is at 19.1 MeV. The cross sections MT=28 and MT=22 of
***JENDL-3*** that jointly give about 40 mb at 20 MeV, are assumed to be
zero in ***ENDF/B-VI**(**JEF-2**)*, similarly to MT=17.

-   MT=102

***ENDF/B-VI, JEF-2:*** Do not take account of the direct (semi-direct)
capture, and are too low at high energies. The descent that starts at
600 keV is not reasonable on ***ENDF/B-VI**(**JEF-2**)* curve, since it
is supposed to start at the inelastic scattering threshold of 786 keV
(see ***JENDL-3*** curve). The above deficiency appears because there is
no calculated point at (or close below) the inelastic threshold and the
interpolation is made between the 'neighboring' points at 600 and 800
keV.

***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)
008) available up to 244 keV.

-   MT=103

Unlike ***ENDF/B-VI**(**JEF-2**)*, ***JENDL-3*** agrees with the
experimental data of Kondaiah, 1968
([EXFOR11884](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=11884&DatType=H&RetType=byAccNum&ReDo=N)
007) at 14.4 MeV and shows a reasonable shape.

-   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 82Kr(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*** could be reasonable.
In addition to the low values presented (lower than the above
experimental data), ***ENDF/B-VI*** and ***JEF-2*** do not show a
reasonable shape.

**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=102, 103). ***ENDF/B-VI*** and
***JEF-2*** do not seem reasonable for MT=1, 102, 103, 107.

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

**[Table 1]{.underline}.** Summary for Resolved and Unresolved Resonance
Region: Kr-82

+---------+---+---------+-------+----+-------------------------------+
| Library | Y | First   | RRR   | U  | Remarks                       |
|         | e | Authors |       | RR |                               |
|         | a |         |       |    |                               |
|         | r |         |       |    |                               |
+---------+---+---------+-------+----+-------------------------------+
| EN      | 1 | A.      | 100   | \- | RR parameters based on        |
| DF/B-VI | 9 | Prince  | eV\   |    | BNL-325 (1973); one s-wave    |
|         | 7 | (BNL)   | \     |    | resonance at 39.8 eV (GN=88.3 |
|         | 8 |         | SLBW  |    | meV, GG=236 meV) and a bound  |
|         |   |         |       |    | resonance level at -42.83 eV; |
|         |   |         |       |    | scattering radius 7.47 fm.    |
|         |   |         |       |    |                               |
|         |   |         |       |    | Computed resonance integral   |
|         |   |         |       |    | 183.56 b.                     |
+---------+---+---------+-------+----+-------------------------------+
| JEF-2   | 1 | Sci     | 100   | \- | RR parameters taken from      |
|         | 9 | entific | eV\   |    | ENDF/B-V. Flag changed to     |
|         | 8 |         | \     |    | MLBW.                         |
|         | 2 | Co-ord  | MLBW  |    |                               |
|         |   | ination |       |    |                               |
|         |   |         |       |    |                               |
|         |   | Group   |       |    |                               |
+---------+---+---------+-------+----+-------------------------------+
| JENDL-3 | 1 | JNDC FP | 400   | 1  | RR parameters based mainly on |
|         | 9 | Nuclear | eV\   | 00 | BNL-325 (1981); account taken |
|         | 9 | Data    | \     | k  | of s-wave; One resonance at   |
|         | 0 | Working | MLBW  | eV | 39.63 eV (GN=124 meV, GG=227  |
|         |   | Group   |       |    | meV) and five out-of-range    |
|         |   |         |       |    | (background) resonances; the  |
|         |   |         |       |    | negative resonance at -160 eV |
|         |   |         |       |    | added to reproduce the        |
|         |   |         |       |    | thermal capture cross section |
|         |   |         |       |    | (Table 2) according to        |
|         |   |         |       |    | BNL-325 (1981). Scattering    |
|         |   |         |       |    | radius 7.3 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 scattering radius |
|         |   |         |       |    | fitted to the calculated MT=1 |
|         |   |         |       |    | at 100 keV.                   |
|         |   |         |       |    |                               |
|         |   |         |       |    | Computed resonance integral   |
|         |   |         |       |    | 228 b.                        |
+---------+---+---------+-------+----+-------------------------------+

**[Table 2]{.underline}.** Thermal Cross Sections for Kr-82

  ---------------------------------------------------------------------- ------------- -------------- ----------
  Library / Experiment                                                   Total         Capture        Elastic

  ENDF/B-VI                                                              40.38 b       30.17 b        10.21 b

  JEF-2                                                                  39.95 b       30.18 b        9.77 b

  JENDL-3                                                                46.59 b       28.01 b        18.58 b

  BNL-325 (1973)                                                                       45(15) b       

  BNL-325 (1981)                                                                       28(20) b       

  S.F.Mughabghab,                                                                      22.4(43) b     
  [INDC(NDS)-424](http://www-nds.iaea.or.at/reports/indc-nds-424.pdf),                                
  p.73 (2001)                                                                                         

  S.F.Mughabghab,                                                                      19.0(40) b     
  [INDC(NDS)-440,](http://www.nndc.bnl.gov/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).