RESONANCE EVALUATION OF 239PU IN THE RESONANCE REGION UP TO 4 KEV

Resolved resonance evaluation of the Pu cross section in the energy range up 4 keV has been carried out with the SAMMY computer code. Existing resolved resonance evaluation such as ENDF/B-VIII.0 and JENDL4 data libraries for Pu is limited to 2.5 keV whereas above this energy the unresolved resonance methodology is used. High resolution transmission and fission data taken at the Oak Ridge Electron Linear Accelerator (ORELA) permitted extending the resonance region up to 4 keV. The thermal and average fission cross section values calculated with the resonance parameters derived in the evaluation fall close to that indicated in the suggested IAEA fission standards.


INTRODUCTION
An R-matrix resonance evaluation of the 239 Pu cross section was carried out at the Institut de Radioprotection et de Sûreté Nucléaire (IRSN) in support of criticality safety applications. The reduced Rmatrix formalism, also known as the Reich-Moore methodology, of the SAMMY code together with several experimental data was used in the evaluation. Recent capture data measurement performed at the Los Alamos Neutron Science Center (LANSCE) with the Detector for Advanced Neutron Capture Measurements (DANCE) was included in the evaluation. Transmission data from ORELA measured at the nitrogen liquid temperature and flight path of 80 meters and fission cross section measured at a flight path of 86 meters helped extending the energy resonance region up to 4 keV. Issues with the unresolved resonance representation of the 239 Pu cross sections above 2.5 keV motivated the study of the feasibility of applying a resolved resonance representation from 2.5 keV to 4 keV.

239 Pu RESONANCE EVALUATION IN THE ENERGY RANGE OF 10 -5 EV TO 4 KEV
A resolved resonance range (RR) evaluation of the 239 Pu cross section was carried using the multilevel SAMMY R-matrix code. [1] The resonance evaluation in most of the existing nuclear data library is limited to the energy range from thermal to 2.5 keV with an unresolved resonance range (URR) representation above 2.5 keV. An apparent issue with reproducing the average cross section in the URR exists in the energy range 2.2 keV to 4 keV. Hence, a study of the feasibility of applying a resolved resonance representation from 2.5 keV to 4 keV was carried out. The URR representation of 239 Pu in existing data library above 2.5 keV is founded solely on statistical sampling on the basis of the average resonance parameters. While the URR evaluation were carefully done cluster of resonances in the energy range 2.5 keV to 4 keV precluded reproducing the average cross section based solely on the average resonance parameters.

External Energy Levels Determination
The long-range interferences in the R-matrix formalism play a major role in fitting fissile isotopes. Interference in the scattering and fission channels may lead to dubious interpretation of the resonance parameters. For fissile isotopes the latter is very pronounced while the former plays an important role as well. In the present evaluation the first step consisted of finding pseudo resonances below 10 -5 eV, also known as the energy bound levels, and above 4 keV which are the resonances that mock up the resonance above 4 keV. Five negative resonances and three energy levels above 4 keV were found that describe well the interference effect in the energy range 0 to 4 keV. The eight external energy levels are listed in Table I in which for each the resonance energy Er, gamma width Γγ, neutron width Γn, two fission widths Γf1 and Γf2 and the spin and parity J π are shown. Negative signs associated with the fission partial widths Γf1 and Γf2 reflect the sign of the reduced amplitude width γf1 and γf2. It follows a convention established in the ENDF resonance parameters representation. The last column in Table I1 lists the resonance total angular momentum and parity. The ground state spin of the 239 Pu is 0 + which leads, for s-wave (l=0), to two resonance total angular momentum, namely 0 + and 1 + . Penetrability for higher angular momentum (l>0) shows negligible contribution to the cross section below 4 keV. The effect of the external level is shown in Fig. 1 which corresponds to the scattering cross section in the energy range 10 -5 eV to 4 keV without the presence of resonances in this energy range. In the plateau around the energy of 2 keV the scattering cross-section due to the external energy values is about 11.10 barns corresponding to a scattering radius of 9.40 fm. It is interesting to note that the analysis of high-resolution transmission data led to an effective scattering radius of 9.41 fm. The number of resonances that fitted the experimental data in the energy range 0 to 4 keV is 1572.

239 Pu Resonance Parameter Evaluation
The experimental database used in the present evaluation is listed in Table II. The two sets of data that permitted extending the energy region up to 4 keV were the high-resolution transmission data of Harvey et al. [2] and the fission data of Weston et al. [3] Note that the only experimental total cross section data in the low energy range is that of Bollinger et al. [4] It should be noted that the most recent capture data of Mosby et al. [5] is listed in Table II and that there are no experimental capture data in the energy region above 1 keV suitable for resonance region analysis and evaluation. Sequential analysis of this data with the SAMMY code were performed until a reasonable representation of the data was achieved. The data of Gwin et al. indicated in Table II correspond to two sets of simultaneous capture and fission measurements [6,7] and one set of fission measurement. [8] These data covers the thermal energy region (0.0253 eV). Harvey et al. transmission data (total cross section) with different thicknesses were of paramount importance in the determination of effective scattering radius.

Results of the Fitting of the Experimental Data
The analysis and evaluation of the experimental data displayed in Table II were done up to 4 keV. As usual in the evaluation process, the first step consisted of verifying the consistency on the experimental data. Since the energy range of the experimental data is diverse, the SAMMY fitting of the data was performed by fitting the experimental data with common energy ranges. For instance, in the energy region 100 eV to 1000 eV the transmission data of Harvey (0.07471 atoms/barn) [2], the Weston fission data [3], and Mosby capture data [5] were used most of the time. It should be noted that aside from the Mosby data, there are no other capture data that could, reliably, be used in the energy range above 100 eV. An example of the SAMMY fit of the experimental data of Harvey transmission data [2], Weston fission cross section data [3], and Mosby capture cross section data [5] is displayed in Fig. 2.

Figure. 2. SAMMY fit of the Harvey transmission data (bottom), Weston fission cross section data (middle) and Mosby capture cross section data (top).
It should be said that in this energy region the percentage difference between the average fission cross section of Weston [3] and that calculated with the present resonance evaluation is of ~2 %. The thermal fission, capture and scattering cross sections (0.0253 eV) are displayed in Table III. Shown also in Table III are three values corresponding to ENDF/B-VIII.0 and the values listed at the Atlas of Neutron Resonances (ANR). [10] The standard fission recommended cross section is 752.371 ± 2.182 barns.
[11] The uncertainty in the results of this work were calculated based on data covariance generated along with the evaluation.

BENCHMARK RESULTS (TEX EXPERIMENTS)
Benchmark calculations using the resolved resonance evaluation presented in this work were carried out to understand the impact of the new evaluation in benchmark calculations. The 239 Table II V. The experimental benchmark keff is listed in column four and uncertainties given in column five. The energy average lethargy of neutrons causing fission (EALF) is listed in column six. The following column lists the results of calculations using ENDF/B-VIII.0. The last column corresponds to the results using the 239 Pu resonance evaluation developed in this work. Table V suggests that the keff results for EALF less than 4 keV have been improved in comparison to ENDF/B-VIII.0 results. This also indicates that extending the resonance range up to 4 keV, into the unresolved energy range, improves the benchmark keff estimation. All the benchmark calculations were done with MCNP with 10 pcm standard deviation that is ± 0.0001.

CONCLUSIONS
Reassessment and evaluation of the 239 Pu resonance parameters were done at IRSN with the SAMMY code in the energy range 0 to 4 keV. High-resolution transmission data were important in the resonance determination in the energy above 2.5 keV till 4 keV. Issues with the unresolved resonance representation of the 239 Pu cross section motivated the evaluation. New capture measurements done at the LANCE were included in the evaluation. Benchmark calculations were done based on the recent TEX experiments and the results indicate that the new evaluation provides an improvement in the benchmark calculation, mainly for case 3 and 5. However, further investigation in the evaluation above 4 keV is needed.