WPEC SG21: Assessment of Neutron Cross-Section Evaluations for the Bulk
of Fission Products

> **48-Cd-110 Review**

Mike Herman, BNL, April 10, 2003

#### General

**Properties**

Stable nucleus, natural abundance 12.49%, fission yield substantial.

**EXFOR data**

Total by Dukarevich (1967) and Musaelyan (1990), elastic by Popov (1985)
and angular distributions by Musaelyan (1990), (n,2n) single point at
14.4 MeV by Lu (1970), capture data at thermal energy by Goldhaber
(1947) and by Del Musgrove (1978) and by Stroud (1971), (n,p) two points
around 14 MeV by Yu-Wen Yu (1967) and by Popelnik (1887), other reaction
channels not measured.

**Evaluations**

-   **ENDF/B-VI** resonance region: year of origin 1991, author R.Q.
    Wright,(ORNL); fast energy region: year of origin 1993, authors J.
    McCabe, A.B. Smith and J. W. Meadows; last revision 1996

-   **JEF-2** year of origin 1974, authors R.E. Schenter and F.
    Schmittroth, data taken from ENDF/B-V, last revision 1989

-   **BROND-2** none

-   **JENDL-3.2** year of origin 1990, last revision 1993

-   **CENDL-3** none

# Thermal and resonance region

*** ***

#### ENDF/B-VI

-   RR range from 1.0E-5 eV to 7.1758 keV. The MLBW formalism used with
    the highest energy resonance at 9860 eV. The RR parameters taken
    from S.F. Mughabghab et al (1981) and from table 3 of Musgrove et al
    (1978)). There are 55 s-wave and 48 p-wave resonances including 11
    s-wave resonances above 7175.8 eV. The bound level at -110 eV has a
    gamma-n0 of 304.44 meV and accounts for about 92 percent of the
    thermal capture cross section. The calculated capture resonance
    integral is 42 barns. The total cross section at thermal is 29.24
    barns.

-   UR range from 7.1758 to 100 keV based on the average capture cross
    sections from Musgrove et al., (Harwell Conf. on Neutron Physics and
    Nucl. Data, table V, page 449. (1978)) with original values
    multiplied by a factor of 0.9833.

**JEF-2**

-   RR parameters taken from BNL-325 (June 1973). No more information
    provided.

#### JENDL-3.2 

-   RR (MLBW formula) up to 7 keV. Resonance parameters taken from
    JENDL-2, and slightly modified. JENDL-2, evaluation was based on
    experimental data of Liou et al. (1974) and Musgrove et al (1978)
    The average radiation width for s-wave levels was assumed to be 0.1
    eV below 3.130 keV and 0.071 eV, and for p-wave 0.084 eV above 3.1
    keV. A negative resonance was added in order to reproduce thermal
    capture and total cross sections given by Mughabghab et al. (1981).
    For JENDL-3.2 the parameters of the negative resonance were adjusted
    to decrease elastic scattering cross section below 1 keV - needed to
    improve total cross section on natural Cd around 10 eV.

-   UR region: 7 keV - 100 keV. s0 and s1 neutron strength functions
    based on Mughabghab et al (1981), while s2 calculated with optical
    model code CASTHY. The observed level spacing adjusted to reproduce
    capture cross section calculated with CASTHY. The effective
    scattering radius obtained from fitting the total cross section at
    100 keV. The radiation widths based on the compilation of Mughabghab
    et al (1981).

**Recommendation/Conclusion**

ENDF/B-VI and JENDL-3.2 total cross sections are almost identical in the
resonance region, while JEF-3 is consistently lower between resonances.
The same is also true for the elastic cross sections down to 0.0038 eV.
For lower energies there strong discrepancies between the three
evaluations (up to factor of 4 for total and more than an order of
magnitude for elastic) with ENDF being the highest and JEF the lowest.

All three evaluations agree for the capture cross section below 1 eV and
reproduce Mughabghab recommendation at thermal energy (11 mb) rather
than the Goldhaber measurement from 1947. In the resonance region JEF
background is by an order of magnitude higher than in the remaining two
evaluations, which also reveal a more detailed structure at the end of
the resonance range. JEF resonances tend to be shifted with respect to
those of the ENDF and JENDL -- a feature observed also in total and
elastic.

Both ENDF/B-VI and JENDL-3.2 can be recommended. These evaluations are
based on the same set of experimental data but provide different
results. There is no clear experimental evidence in favor of any of the
two, although JENDL is much closer to a single measurement of the
elastic cross section at thermal energy (see Table 2). Slight preference
can be given to the ENDF/B-VI as a more recent one.

# Fast neutron region

#### ENDF/B-VI methodology

-   The direct reaction contribution to inelastic scattering calculated
    assuming a one-phonon vibrational model using coupled-channels code
    ANLECIS.

-   Weisskopf model used for inelastic scattering to continuum and for
    the radiative capture (code ABAREX). Width fluctuations within the
    frame of the Moldauer approach.

-   Preequilibrium effects in the inelastic scattering approximated by
    Weisskopf calculations with increased nuclear temperature

-   (n,2n), (n,p), and (n,alpha) and other minor channels reactions
    calculated with code GNASH

-   Non-isotropic angular distributions for elastic only.

#### JEF-2 methodology

-   Fragmentary information on evaluation methodology available.

-   Inelastic (MT=91) evaporation spectrum parameters (LF=9) obtained
    using NCAP code. No other spectra provided.

-   All angular distributions assumed isotropic.

#### JENDL-3 methodology

-   Methodology fairly up-to date, all important effects taken into
    account.

-   Spherical optical and statistical model calculation performed with
    CASTHY including preequilibrium effects.

-   OMP\'s for neutron determined to reproduce total cross sections
    measured on natural Cd by Foster and Glasgow (1971).

-   DWBA calculations for the two (2+ and 3-) collective levels.

-   Direct and semi-direct mechanisms considered in the calculations of
    the capture cross sections. Gamma-ray strength function (4.65e-04)
    adjusted to reproduce capture cross section of 245 mb at 30 keV as
    measured by Musgrove et al. (1978)

-   Calculated (n,2n), (n,p) and (n,alpha) cross sections normalized to
    the experimental values

-   Angular distributions of secondary neutrons assumed isotropic except
    for the two collective levels calculated within DWBA.

Comparison of ENDF/B-VI, JEF-2, and JENDL-3

-   MT=1. Evaluations differ, ENDF is the closest to the experimental
    data.

-   MT=2. . The JEF-2 shape is different from the ENDF and JENDL and
    fits experimental data better. On the other hand, independent
    calculations with EMPIRE-II code support ENDF and JENDL shape.

-   MT=4. . No experimental data for comparison. JEF shape is
    unrealistic, while those of ENDF and JENDL are reasonable.
    Preequilibrium component appears to be stronger in the JENDL
    evaluation.

-   MT=16. ENDF and JENDL evaluations close to a single point of Lu
    (JENDL within experimental uncertainty). ENDF is considerably higher
    than JENDL above 13 MeV, most likely to the lower preequilibrium
    contribution. Independent EMPIRE-II calculations (including MSD and
    MSC mechanisms) support ENDF.

-   MT=102. ENDF/B-VI and JENDL-3.2 reasonably close to experimental
    data and superior to JEF-2.

-   MT=103. Two contradicting experimental points around 14 MeV
    available. JENDL and JEF follow the higher one by Yu Wen-Yu (1967),
    while ENDF reproduces the more recent and more accurate measurement
    of Popelnik (1985). Also, independent EMPIRE-II calculations support
    ENDF.

-   MT=107. No experimental data available. JENDL and JEF agree up to 16
    MeV while ENDF is by a factor of 2 lower.

# Recommendation/Conclusion

JENDL-3 uses fairly up-to date physics, which, in the fast energy
region, is superior to the approach used in the ENDF/B-VI evaluation.
However, the latter one compares nicely to the EMPIRE-II calculations
that use advanced theoretical modeling. In addition, the ENDF/B-VI
evaluation is more recent. Both JENDL-3.2 and ENDF/B-VI are recommended.

[Table 1.]{.underline} Summary for Resolved and Unresolved Resonance
Region for 48-Cd-110

+------+---+--------------+-----+---+---------------------------------+
| Lib  | Y | First        | RRR | # | Remarks                         |
| rary | e | Authors      |     |   |                                 |
|      | a |              |     | U |                                 |
|      | r |              |     | R |                                 |
|      |   |              |     | R |                                 |
+------+---+--------------+-----+---+---------------------------------+
| E    | 1 | J. McCabe,   | 7.1 | 1 | > RR parameters taken from S.F. |
| NDF/ | 9 | A. B. Smith  | 758 | 0 | > Mughabghab et al (1981) and   |
| B-VI | 9 |              | keV | 0 | > from table 3 of Musgrove et   |
|      | 6 |              |     | k | > al (1978))                    |
|      |   |              | M   | e |                                 |
|      |   |              | LBW | V |                                 |
+------+---+--------------+-----+---+---------------------------------+
| J    | 1 | R.E.         | 7.1 |   | RR parameters taken from        |
| EF-2 | 9 | Schenter and | 758 |   | BNL-325 (1973)                  |
|      | 8 | F.           | k   |   |                                 |
|      | 9 | Schmittroth  | eV\ |   |                                 |
|      |   |              | \   |   |                                 |
|      |   |              | M   |   |                                 |
|      |   |              | LBW |   |                                 |
+------+---+--------------+-----+---+---------------------------------+
| J    | 1 | FP NUCLEAR   | 7   | 1 | RR parameters taken from        |
| ENDL | 9 | DATA W.G.    | k   | 0 | JENDL-3.2 except of those for   |
| -3.2 | 9 |              | eV\ | 0 | s-wave resonance at 5.853 keV   |
|      | 3 |              | \   | k | (GN = 7.531 eV and GG = 2.12    |
|      |   |              | M   | e | eV, rather than GN=15.31 eV and |
|      |   |              | LBW | V | GG=0.262 eV adopted by          |
|      |   |              |     |   | JENDL-3.2).                     |
+------+---+--------------+-----+---+---------------------------------+

[Table 2.]{.underline} Thermal Cross Sections for Cd-110

+--------------------------------------+---------+-----------+--------+
| File/ Experiment/Evaluation          | # Total | # Capture | # E    |
|                                      |         |           | lastic |
+--------------------------------------+---------+-----------+--------+
| ENDF/B-VI                            | 29.329  | 11.0124 b | 1      |
|                                      | b       |           | 8.3166 |
|                                      |         |           | b      |
+--------------------------------------+---------+-----------+--------+
| JEF-2                                | 14.3719 | 11.1053 b | 3      |
|                                      | b       |           | .26637 |
|                                      |         |           | b      |
+--------------------------------------+---------+-----------+--------+
| JENDL-3.2                            | 16.9585 | 11.0572 b | 5      |
|                                      | b       |           | .90128 |
|                                      |         |           | b      |
+--------------------------------------+---------+-----------+--------+
| Goldhaber (1947)                     |         | 0.200(2)  |        |
|                                      |         | b         |        |
+--------------------------------------+---------+-----------+--------+
| Vertebnyj (1970)                     |         |           | 4.3(2) |
|                                      |         |           | b      |
+--------------------------------------+---------+-----------+--------+
| BNL-325 (1981)                       |         | 11(1) b   |        |
+--------------------------------------+---------+-----------+--------+
| S.F.Mughabghab, INDC(NDS)-424,       |         | 11(1) b   |        |
| (2001)                               |         |           |        |
+--------------------------------------+---------+-----------+--------+