Theoretical calculation and evaluation of neutron inducedreactions on Pu isotopes

The nuclear data on n+Pu reactions for the incident energy up to 200 MeV are consistently calculated and evaluated in order to meet the design requirements of Generation-IV reactors and accelerator driven systems. The optical model, the distorted wave Born approximation theory, the Hauser-Feshbach theory, the fission model, the evaporation model, the exciton model and the intranuclear cascade model are used in the calculation, and new experimental data are taken into account. Our data are compared with experimental data and the evaluated data from JENDL-4/HE and TENDL. In addition, the variation tendency of reaction cross sections related to the target mass numbers is obtained, which is very important for the prediction of nuclear data on neutron-actinides reactions because the experimental data are lacking.


Introduction
Recent decades, Generation-IV reactors and accelerator driven systems (ADS) are under study to reduce the nuclear accident probability and minimize the production of nuclear waste. Pu isotopes are important fuel or radioactive waste, accurate nuclear data of neutron-induced reactions on Pu isotopes below 200 MeV are needed to reduce uncertainties in the design and operation of these facilities.
At present, there are two nuclear data libraries including n+Pu reaction data up to 200 MeV. One is JENDL-4/HE library [1]. In this library, JENDL-4.0 is adopted at incident energies E n ≤20 MeV (the evaluation finished in 2009), and JENDL-HE2007 is adopted for 20 ≤ E n ≤ 200 MeV, this evaluation was finished in 2001. The other is TENDL [2], which is the calculated results by TALYS code with default parameters. After the evaluation of these, some new experimental data were measured and some discrepancies with previous experimental data were observed. Therefore, the purpose of this paper is to obtain new nuclear data for n+ 239,240,242,244 Pu reactions below 200 MeV.
In Sect. 2, the theoretical models are introduced briefly, and in Sect. 3 the calculated results are provided. Finally, a summary is given in Sect. 4.

Theoretical model
The theoretical models are outlined briefly here, the detail can be found in Refs. [3,4]. The optical model is applied to obtain the total, nonelastic, elastic cross sections * e-mail: guo_hairui@iapcm.ac.cn * * e-mail: hanyl@ciae.ac.cn and elastic scattering angular distributions, transmission coefficients and inverse cross sections. Our global phenomenological Woods-Saxon type optical potentials for nucleon [5], deuteron [6], triton [7], helium [8] and alpha [9] at incident energies up to 200 MeV are used. The distorted wave Born approximation theory is applied to calculate the direct inelastic scattering cross sections and angular distributions. The Hauser-Feshbach model with width fluctuation correction and evaporation model are used to analyze the particle emissions from the equilibrium decay processes for the incident energy below and above 20 MeV, respectively. The angular-momentum dependent exciton model is applied to calculate the particle emissions from the pre-equilibrium process, and the improved Iwamoto-Harada pick-up model is included in the exciton model for the calculation of light composite particle emissions. The intranuclear cascade emissions of one to four nucleons are considered and calculated with the empirical formula [10]. Fission is considered as a compondnucleus decay channel. The Bohr-Wheeler theory and the Madland-Nix formula are used to calculate the fission rate and fission spectra, respectively.
The nuclear theoretical model code, UNF [11], is used for the incident energy below 20 MeV. The double differential cross sections are calculated with the linear momentum dependent exciton state density model. The recoil effects are taken into account strictly, so the energy balance is held in every channels. MEND code [12] is used for 20≤ E n ≤200 MeV, and the double differential cross sections of emitted particles are given by using the Kalbach systematics.

Results and analysis
All cross sections, angular distributions, energy-angle distributions of neutron, proton, deuteron, triton, helium-3 and alpha emissions, number of neutrons per fission, and prompt fission neutron spectra are calculated. Some of the results are shown in the following figures.
The calculated total cross section of n+ 239 Pu reaction is compared with experimental data [13][14][15][16] and evaluated data from JENDL-4/HE and TENDL in Fig. 1. The present result reproduces the experimental data rather well and differs slightly from those in JENDL-4/HE and TENDL. It should be mentioned that all resonance cross sections in this work are taken from JENDL-4.0. The fission cross section for n+ 239 Pu reaction is given in Fig. 2. The calculated result is in good agreement with the experimental data [17][18][19]. It can be seen that the data from TENDL are larger than the experimental data for 40≤ E n ≤120 MeV. The fission cross section for n+ 240 Pu reaction is given in Fig. 3. The calculated result is in good agreement with the recent experimental data [20,21]. It can be seen that the present result is a little larger than the data from JENDL-4/HE below 20 MeV where the present result fits the recent experimental data from Refs. [20,21] better, while the data from JENDL-4/HE fit the experimental data from Refs. [22,23] better. The (n, γ) reaction cross section for n+ 242 Pu reaction is given in Fig. 4. The present result reproduces the new experimental data from Ref. [24] well, while the data from JENDL-4/HE pass through the old experimental data from Ref. [25]. The new experimental data measured at LAN-SCE are about 3 times lower than the old ones. Therefore, more investigation into the experimental data is needed.
The fission cross section for n+ 242 Pu reaction is given in Fig. 5. The present result is in good agreement with the recent experimental data from Ref. [20] over the entire energy region, while the data from JENDL-4/HE is consistent with the experimental data from Ref. [23]. TENDL does not reproduce the experimental data at high energies.
The fission cross section for n+ 244 Pu reaction is given in Fig. 6. The calculated result is in good agreement with  the experimental data [23]. There is no evaluated data for this reaction in JENDL-4/HE.
The variation tendency of reaction cross sections related to the target mass numbers is very important for the prediction of nuclear data on neutron-actinides reactions. The trend of fission cross sections for n+ 240,242,244 Pu reactions are shown in Fig. 7. The fission cross sections decrease as the mass number increases.

Summary
The nuclear data on n+ 239,240,242,244 Pu reactions are obtained in the incident energy region below 200 MeV. Some new experimental data are taken into consideration. The present results are in good agreement with the experimental data generally, and reproduce them better than the evaluated data from JENDL-4/HE and TENDL for some reaction channels. The present results have been transformed into ENDF-B formatted data files for application.