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

**36-Kr-78 Review**

I. Sirakov, INRNE, January 16, 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 865 eV with
resonance parameters based on BNL-325 (1973) and experimental data of
Block et al (1978); SLBW representation for three s-wave resonances at
108.4, 450.9, and 640 eV and a bound resonance level at -120 eV;
scattering radius 7.47 fm. No unresolved resonance region (Table 1).
Computed resonance integral 23.67 b. ***JEF-2*** changed the flag to the
MLBW representation (1987).

***JENDL-3*:** Resolved resonance region up to 800 eV with resonance
parameters based on BNL-325 (1981); MLBW representation for 3 s-wave
resonances at 108.4, 450.9, and 640 eV, and bound resonance level at
-122 eV. The negative resonance 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 7.56 fm fitted to the calculated MT=1 at 100 keV.
Computed resonance integral 25.8 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*** (272.5 mb), ***JEF-2*** (272.4 mb)
and ***JENDL-3*** (351.9 mb). The higher value of ***JENDL-3*** is due
to its higher capture cross section from 0.8 to 2 keV and from 10 keV to
\~1 MeV.

The close values for the capture resonance integrals of ***JENDL-3***
(25.8 b) and ***ENDF/B-VI/JEF-2*** (23.67 b) are due to the identical
positive resonances. The difference is mainly due to the ***JENDL-3***
higher capture cross section in the regions 0.5-50 eV and 0.8 to 2 keV.
Disadvantage of ***ENDF/B-VI***(***JEF-2***) is the lack of unresolved
resonance region. Moreover, the ***ENDF/B-VI***(***JEF-2***) show
unreasonable (non-smooth) shapes of MT=1 and MT=2 in the energy region
1.5-50 keV, as well as of MT=102 in the region 4-50 keV.

**Experimental data** -- The resonance integral data of 20(1) b by
Maguire, 1978
([EXFOR10796](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=10796&DatType=H&RetType=byAccNum&ReDo=N)
007) as well as the recent recommendation for the resonance capture
integral of 19.5(20) b by Mughabghab, 2003
([INDC(NDS)-440](http://www.nndc.bnl.gov/sg21/nucl/indc-nds-440.pdf))
give preference to the ***ENDF/B-VI***(***JEF-2***) value of 23.67 b
compared to the 25.8 b of ***JENDL-3***, in spite of the not very good
agreement.

***ENDF/B-VI***(***JEF-2***) thermal capture cross sections of 4.85 b
(Table 2) fully agree with the recent recommendation of 4.73(68) b by
Mughabghab, 2003
([INDC(NDS)-440](http://www.nndc.bnl.gov/sg21/nucl/indc-nds-440.pdf)),
until ***JENDL-3*** value of 6.2(9) b only agrees with BNL-325 (1981)
and with the previous Mughabghab's (2001) recommendation
([INDC(NDS)-424](http://www-nds.iaea.or.at/reports/indc-nds-424.pdf)).

Capture cross section data of Walter, 1984
([EXFOR21913](http://www.nndc.bnl.gov/htbin/csisrs.cgi?AccNum=21913&DatType=H&RetType=byAccNum&ReDo=N)
004), available from 10 to 244 keV, generally agree with all evaluations
in the region 10 -- 40 keV, but are only in favor of ***JENDL-3*** above
40 keV.

**Recommendation/Conclusion**: ***ENDF/B-VI***(***JEF-2***) is
recommended in the resolved resonance region up to 865 eV. ***JENDL-3***
is recommended in its unresolved resonance region from 865 eV to 100
keV.

The above recommendation has the advantage of 1) adopting the
***ENDF/B-VI/JEF-2*** thermal capture cross section of 4.85 b; 2)
getting a RI value less than the ***JENDL-3*** value; 3) retaining the
***JENDL-3*** unresolved resonance region and the better agreement
between ***JENDL-3*** and the capture cross section data (Walter-1984)
above 40 keV; and 4) avoiding the unreasonable shapes of
***ENDF/B-VI***(***JEF-2***) in MT=1,2 (1-50 keV) and MT=102 (4-50 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, 51-53, 91, 102, 103, 107;
FASCRO code for MT=16, 104, 105, 106; no preeq corrections; 3 discrete
levels (from 455 keV to 1.98 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, 51-53, 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, 51-79, 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 (10.3E-4) adjusted at 100 keV to the measured capture cross
section (Walter 1984). Direct and semi-direct capture estimated; 29
discrete levels (from 455 keV to 2.99 MeV) adopted for the inelastic
scattering. MT=16 normalized to measured by Kondaiah (1968), and MT=103
and MT=107 and 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**(**JEF-2**)* follow the structure of the inelastic cross
section in the region 1.5-6 MeV with a peak at 4 MeV. In addition, MT=1
is not smooth at the energy of the 461-keV inelastic threshold.

***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 1.1 b at 4 MeV.

-   MT=2

The evaluations show reasonably smooth shapes, being close except at
high energies, where ***JENDL-3*** is 0.7 b higher than
***ENDF/B-VI**(**JEF-2**)* in the whole region 10-20 MeV. There is no
discrepancy between the evaluations at 4 MeV.

-   MT=4

***ENDF/B-VI**(**JEF-2**)* are systematically higher than ***JENDL-3***.
The maximum difference of 1.0 b at 4 MeV is the main contributor to the
above mentioned MT1 discrepancy of 1.1 b (MT=102 and MT=103 contribute
50 mb and 60 mb respectively). The (n,2n) threshold is 12.1 MeV.

-   MT=16

All evaluations are close up to 18 MeV and in 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)
002) at 14.4 MeV. The (n,3n) threshold is above 20 MeV.

-   MT=28

Besides (n,n) (MT=22), ***ENDF/B-VI**(**JEF-2**)* does not take account
of (n,np) (MT=28) and assumes it to be zero. According to ***JENDL-3***,
however, MT=28 is higher than MT=16 with values larger than 0.5 b at
energies above 16 MeV. The MT=22 is about 0.11 b at 20 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. The sharp descent that starts
at 400 keV is not reasonable on the ***ENDF/B-VI**(**JEF-2**)* curve,
since it is supposed to start at the inelastic scattering threshold of
460 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 400
and 500 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)
004) available up to 244 keV.

-   MT=103

The quantitative systematics \[1\] for the 78Kr(n,p) cross section gives
the prediction of 97.5 (-8.5,+9.0) mb at 14.7(2) MeV, which is close to
the ***JENDL-*3** value of 120 mb and too far from
***ENDF/B-VI**(**JEF-2**)* value of 240 mb.

-   MT=107

The quantitative systematics \[2\] for the 78Kr(n,) cross section gives
the prediction of 40.0 (-6.3,+7.3) mb at 14.7(2) MeV which agrees very
well with the ***JENDL-*3** value of 37.5 mb in contrast to
***ENDF/B-VI**(**JEF-2**)* value of 18.5 mb. The systematics \[3\] is
also in favor of ***JENDL-*3** with the prediction of 42.7 (-4.0,+4.4)
mb. In addition, ***ENDF/B-VI*** and ***JEF-2*** do not show a
reasonable trend above 10 MeV.

**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) and seems reasonable for all cross
sections. ***ENDF/B-VI*** and ***JEF-2*** do not seem reasonable for
MT=1, 102, 103, 107 and do not take account of MT=28.

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

**[Table 1]{.underline}.** Summary for Resolved and Unresolved Resonance
Region: Kr-78

+---------+---+---------+-------+----+-------------------------------+
| Library | Y | First   | RRR   | U  | Remarks                       |
|         | e | Authors |       | RR |                               |
|         | a |         |       |    |                               |
|         | r |         |       |    |                               |
+---------+---+---------+-------+----+-------------------------------+
| EN      | 1 | A.      | 865   | \- | RR parameters based on        |
| DF/B-VI | 9 | Prince  | eV\   |    | BNL-325 (1973) and and        |
|         | 7 | (BNL)   | \     |    | experimental data of Block et |
|         | 8 |         | SLBW  |    | al (1978); Three s-wave       |
|         |   |         |       |    | resonances at 108.4, 450.9,   |
|         |   |         |       |    | and 640 eV, and a bound       |
|         |   |         |       |    | resonance level at -120 eV;   |
|         |   |         |       |    | scattering radius 7.47 fm.    |
|         |   |         |       |    | Computed resonance integral   |
|         |   |         |       |    | 23.67 b.                      |
+---------+---+---------+-------+----+-------------------------------+
| JEF-2   | 1 | Sci     | 865   | \- | 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 | 800   | 1  | RR parameters based on        |
|         | 9 | Nuclear | eV\   | 00 | BNL-325 (1981); account taken |
|         | 9 | Data    | \     | k  | of s-wave; Three resonances   |
|         | 0 | Working | MLBW  | eV | at 108.4, 450.9, and 640 eV,  |
|         |   | Group   |       |    | and a bound resonance level   |
|         |   |         |       |    | at -122 eV. The negative      |
|         |   |         |       |    | resonance 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 7.56 fm  |
|         |   |         |       |    | fitted to the calculated MT=1 |
|         |   |         |       |    | at 100 keV.                   |
|         |   |         |       |    |                               |
|         |   |         |       |    | Computed resonance integral   |
|         |   |         |       |    | 25.8 b.                       |
+---------+---+---------+-------+----+-------------------------------+

**[Table 2]{.underline}.** Thermal Cross Sections for Kr-78

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

  ENDF/B-VI                                                              13.71 b       4.85 b         8.87 b

  JEF-2                                                                  13.61 b       4.85 b         8.77 b

  JENDL-3                                                                14.08 b       6.20 b         7.88 b

  BNL-325 (1981)                                                                       6.2(9) b       

  S.F.Mughabghab,                                                                      6.2(9) b       
  [INDC(NDS)-424](http://www-nds.iaea.or.at/reports/indc-nds-424.pdf),                                
  p.73 (2001)                                                                                         

  S.F.Mughabghab,                                                                      4.73(68) b     
  [INDC(NDS)-440,](http://www.nndc.bnl.gov/sg21/nucl/indc-nds-440.pdf)                                
  p.11 (2003)                                                                                         
  ---------------------------------------------------------------------- ------------- -------------- ----------

**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).