Nuclear Data Evaluation of 55 Mn by the EMPIRE code with Emphasis on the Capture Cross Section

Transcription

1 International Conference Nuccllearr Enerrgy fforr New Eurrope 2009 Bled / Slovenia / September ABSTRACT Nuclear Data Evaluation of 55 Mn by the EMPIRE code with Emphasis on the Capture Cross Section Alberto Milocco, Andrej Trkov Jožef Stefan Institute Jamova cesta 39, SI-1000 Ljubljana, Slovenia Alberto.Milocco@ijs.si, Andrej.Trkov@ijs.si Roberto Capote Noy International Atomic Energy Agency P.O. Box 100, Wagramer Strasse 5 A-1400 Vienna, Austria R.CapoteNoy@iaea.org Manganese is one of the constituents of alloys for structural components and a dosimetry material. Its nuclear data evaluation is indispensable for design of nuclear devices. This work is a first attempt to calculate the 55 Mn cross sections with the code EMPIRE. This system allows a consistent calculation of the nuclear data up to 150 MeV. The sensitivity studies on the input parameters from RIPL-2 are presented. The results are compared with the ENDF/B-VII evaluation for 55 Mn. Further improvements are necessary for the new evaluation, arguably concerning the non elastic reaction channels. 1 INTRODUCTION Manganese is one of the constituents of alloys for structural components and a dosimetry material. Its nuclear data evaluation is indispensable for design of nuclear devices. Much emphasis is currently placed on its use for fusion reactor neutronics. The current ENDF/B-VII evaluation for 55 Mn dates back to 1988 [1], besides minor revisions that are more recent. A new evaluation is needed for inclusion in the FENDL-3 nuclear data library. This paper is a first attempt to calculate the 55 Mn cross sections with the code EMPIRE [2]. Major attention is paid to the capture cross section, which is known as a critical point in any evaluation and is important for dosimetry applications. The cross sections are calculated up to 150 MeV because nuclear data are needed at high energies for fusion applications. The covariance data are not yet considered. EMPIRE is a complex system including various nuclear models. A consistent selection of them is required, as illustrated in Section 2. They represent the physics core in present evaluation, which features the whole set of cross sections from first principles. The IAEA coordinated project RIPL-2 produced an almost complete and up to date database for the EMPIRE input parameters [3]. The sensitivity studies on these parameters are presented in Section 3. They concern the RIPL catalogue for the optical model potential, the number of discrete levels of the nuclei involved in the excusive cross sections, the choice of the gamma strength functions and the use of the tuning parameters to fit the measured capture cross section

2 821.2 In Section 4, the plots are presented with the comparison between the major results from the EMPIRE calculations, the ENDF/B-VII library and the experimental data. In the case of (n,2n) and (n,g), also the IRDF-2002 evaluations are used for comparison. The experimental data are retrieved from the EXFOR database [4]. The graphical visualisation of the calculated cross sections and comparison with the EXFOR experimental data is achieved with the EMPIRE system or the ENDVER code [5]. The conclusions of the work and the future activities are drawn in the Section 5. 2 COMPUTATIONAL METHOD The generality and flexibility of the EMPIRE code requires prior choices of the physics modules. The optical model for the direct reactions is implemented in the ECIS06 code [6], which is built into the EMPIRE system. The ECIS module can deal with spherical nuclei or deformed ones, such as 55 Mn. The effect of the nuclear deformations can be taken into account with the Distorted Wave Born Approximation (DWBA) or the Coupled Channel (CC) method. The choice for the 55 Mn case consists of calculating the total, elastic, absorption, direct inelastic cross sections and the transmission coefficients within the CC model (DIRECT=2 option in EMPIRE terminology). Four low lying discrete/collective levels are coupled. The other discrete levels and the continuum are treated within the DWBA formalism. The calculated absorption cross section is available for the pre equilibrium emission. A major feature of EMPIRE is a set of five pre equilibrium models. The generalised exciton model PCROSS is selected to calculate the pre equilibrium component above ~10 MeV. If the absorbed neutron is not involved in the pre equilibrium processes, then the system reaches statistical equilibrium and the neutron is passed to the compound nucleus. The statistical model is the advanced implementation of the Hauser Feshbach theory. It takes into account the width fluctuation corrections below some energy, as in the Hoffmann, Richert, Tepel and Weidenmueller (HTRW) model. The γ emission involves E1, E2 and M1 transitions. The Giant Multipole Resonance model known as Brink Axel hypothesis is used. The calculations are not normalised to the experimental γ width at the neutron binding energy (a default in the EMPIRE), which is a common practise in many cross section evaluations. The approach keeps the consistency among the calculations in the GDR energy region by calculating the γ width from the giant resonance parameters. This choice enhanced the sensitivity in the parametric studies. Different approaches are available for the level densities. The one specific to the EMPIRE is chosen. It consists of the super fluid model below the critical excitation energy and the Fermi gas model above. The EMPIRE specific level densities, in addition to explicit treatment of the collective effects and their dumping, also include the effects of dynamic deformation, which is induced by the rotation at high spin (as an extension of the Fermi gas model). The approach is recommended for high energy nucleon induced reactions. In the low energy range, the EMPIRE calculations provide the average value of the cross sections. The resonances can be subsequently evaluated by retrieving the resonance parameters from the EMPIRE library. The resonances thus obtained overwrite the average cross sections in the resonance range. 3 RIPL-2 PARAMETERS DETERMINATION The following subsections describe the physical issues, which are directed to the RIPL- 2 parameters. The issues concerning the EXFOR data are not addressed in depth and no adjustments of the experimental data (such as re normalisations) have been performed.

3 Optical model The optical model parameters for any nucleus and ejectile can easily be invoked by assigning the RIPL-2 catalogue number of the OMP. The present computations have been performed with the rotational dispersive CC neutron OMP for Mn by R.Capote, E.Soukhovitski, J.M.Quesada, S.Chiba (catalogue number 1484, unpublished). RIPL-2 library gives the possibility to choose also a global spherical OMP by A. J. Koning, J. P. Delaroche (catalogue number 2405 [7]). In this case the flag for the direct reaction option has to be changed to DIRECT=0. Figure 1 shows the comparison between the total cross section as calculated with both optical models. The most recent experimental data are also plotted (Abfalterer, 2001). The agreement of the rotational dispersive CC OMP with these measurements is excellent, meaning that they could be used to fit the OMP parameters. The RIPL-2 parameters for OMP 2405 are dated A more recent release of the optical model parameters by Koning would agree with Abfalterer measurements much better [8], but is not yet available in RIPL-2. RIPL 1484 RIPL ABFALTERER Figure1: Comparison between total cross sections as calculated with rotational dispersive CC neutron OMP and global spherical OMP 3.2 Level density The consistency of the level density model parameterisation with the experimental discrete levels can be checked in the EMPIRE by plotting the cumulative number of levels for each nucleus. Graphical representation helps to identify the level at which the cumulative plot starts to bend because the discrete levels, which are not detected experimentally, are missing from the spectrum and the high energy end of the cumulative plot is too low. The levels lying above this point should be excluded from consideration. This is done by changing the Nmax entry in the file with the discrete levels. Three example of level density fit are shown in Figures 2, 3 and 4 for 56 Mn. The choice of the Nmax parameter largely affects the capture cross section, as shown in Figure 5. Systematics predictions indicate that missing levels occur mainly in odd-odd nuclei, as in this case. The fitting with only 5 discrete levels is not very reliable because the level density models do not pretend to describe the first low lying levels. Thus, the Nmax parameter for 56 Mn is set to 17 discrete levels. The number of discrete levels for the 55 Mn is increased up to the limit that the total inelastic cross section does not present an unphysical dip at about 3 MeV, which occurs with greater Nmax. The magnitude of the (n,p) (n,α) cross sections are largely affected by the number of discrete levels in the 55 Cr and 52 V nuclei. In such cases, the Nmax is chosen after comparison with the calculated cross sections.

4 821.4 Table I reports the Nmax setting for any nucleus involved in the exclusive spectra. In EMPIRE it is possible to modify the level density a parameter for each nucleus to refine the fit. The a parameter is changed up to the limit of its experimental uncertainty for the 56 Mn, 55 Cr, 52 V, 51 V and 51 Ti level densities. The effect on the calculated cross sections is not found to be very important. Figure 2: Cumulative plot with Nmax=40 Figure 3: Cumulative plot with Nmax=17 Figure 4: Cumulative plot with Nmax=5 Figure 5:Effect of Nmax on (n,γ) cross section Table1: Nmax choice for the nuclei involved in the exclusive spectra 56 Mn 55 Mn 54 Mn 53 Mn nucleus Nmax nucleus 50 V 52 Ti 51 Ti 50 Ti 50 Sc 49 Sc 48 Sc 47 Sc 48 Ca Nmax Gamma strength function 55 Cr The EMPIRE offers in RIPL-2 a series of E1 γ ray strength functions. Altogether, six different shapes of the γ ray strength function can be selected. Depending on the formalism chosen, the shape changes especially at the low γ emission energies. Figure 6 shows the effect of three representations of the γ ray strength functions on the capture cross section. EGLO is the Enhanced Generalised Lorentzian and is the default in the EMPIRE. MLO1 is the Modified Lorentzian, version 1. GFL is the Generalised Fermi Liquid Model. Actually, the MLO1 is the recommended γ ray strength function because of it general use with different nuclei. The choice of the γ ray strength function influences also the gamma 54 Cr 53 Cr 53 V 52 V 51 V 47 Ca

5 821.5 emission spectra, as can be seen in Figure 7 at 125 degrees with 4 MeV incident neutron. The MLO1 is preferable also in this case. Figure 6:Effect of GSF on (n,g) cross section Figure 7: Effect of GSF on γ spectrum 3.4 Collective levels The default collective levels are those included in the RIPL 1484 OMP. The collective levels are increased to 28 after editing the local file with collective levels ( lev.col). The extra levels include the specific deformation at their energy up to 6 MeV. The effect of the extra levels can be observed in the total inelastic cross section above 12 MeV (Figure 8). The decrease in the inelastic cross section after inclusion of more collective levels corresponds to an increase in the (n,2n) cross section (Figure 8). The inclusion of 28 collective levels modifies the 14.1 MeV neutron emission spectra at 15 degrees around ~11 MeV. The discrepancy with experimental data remains from 12 MeV to 14 MeV. 25-Mn-55(N,INL) (N,2N), SIG 28 C. LEV. INL 4 C. LEV. INL 28 C. LEV. (N,2N) 4 C. LEV. (N,2N) EXP. DATA Figure 8: Effect of more collective levels on the inelastic and (n,2n) cross sections Figure 9: Effect of more collective levels on the neutron emission spectrum 3.5 Tuning The γ transmission coefficients for a specific nucleus can be modified to fit the capture cross section. The magnitude of the capture cross section is definitively lower then for other channel, so there is some freedom in artificially changing it. The tuning of the pre equilibrium component is done by setting the TUNEPE card to 2. The tuning of the compound component is done locally at energies from 3 to 14 MeV. The global TUNE card is left as described in Section 2. The effect of the new tuning is to fit the capture channel with Menlove data between 3 and 16 MeV (Figure 10).

6 821.6 Figure 10: (n, γ) fit with the tuning 4 RESULTS OF THE EVALUATION AND COMPARISONS For the proper comparison with other evaluations and with the experimental data, the resonance parameters from Leal evaluation [9] are used to reconstruct the resonance region. Around 1 MeV, the EMPIRE calculations of the total and elastic cross sections do not present the resolution of the ENDF/B-VII nuclear data since the latter were obtained by fitting measurements in this energy range (Figures 11 12). The EMPIRE evaluation extends up to 150 MeV, whereas the ENDF/B-VII arrives at 20 MeV. The EMPIRE evaluation of the total inelastic cross section differs from the ENDF/B-VII one to a significant extent below 10 MeV (Figure 13). The EMPIRE (n,2n) evaluation is compared also with the IRDF-2002 evaluation by Zolotarev, which is the state of the art for this reaction. The EMPIRE (n,2n) cross section is underestimated from 15 to 25 MeV by about 10% (Figure 14). The capture cross sections from EMPIRE and ENDF/B-VII are quite consistent in the compound contribution up to ~10 MeV. At higher energies, where the pre equilibrium component becomes increasingly important, the EMPIRE evaluation is higher then the ENDF/B-VII one (Figure 15). The ENDF/B-VII evaluation of the capture cross section has been adopted for the IRDF-2002 dosimetry file. The EMPIRE evaluation of the (n,p) cross section is higher at the maximum then the ENDF/B-VII evaluation and the same holds for the (n,α) cross section (Figures 16-17). The 14.1 MeV neutron emission spectra at 30 degrees with EMPIRE evaluation is not satisfactory because of the discrepancy with the experimental data around 12 MeV and below 1 MeV. Figure 11:Total cross section Figure 12:Elastic cross section

7 821.7 Figure 13: Total inelastic cross section Figure 14: (n,2n) cross section Figure 15: Capture cross section Figure 16: (n,p) cross section Figure 17: (n,α) cross section Figure 18. Neutron emission spectrum 5 CONCLUSIONS Existing 55 Mn evaluations only extend up to 20 MeV and show deficiencies in the resonance region, therefore a re-evaluation was attempted. The new nuclear data evaluation with the EMPIRE system is not yet satisfactory. A revision of some physical assumptions is required, especially for pre-equilibrium mechanisms, and/or further refinement of the RIPL-2 input parameters. Future activities would involve the validation with integral experiments and the calculation of the covariances.

8 821.8 REFERENCES [1] K. Shibata, "Calculation of Neutron-Induced Reaction Cross Section of Manganese-55", JNST, 26[10], 1989, pp [2] M. Herman et al., "EMPIRE: Nuclear Reaction Model Code System for data evaluation", Nuclear Data Sheets 108, 2007, pp [3] T.Belgya et al., "Handbook for calculations of nuclear reaction data: Reference Input Parameter Library II", IAEA-TECDOC-1506, Vienna, Austria [4] [5] A. Trkov, "ENDVER: the ENDF File Verification Support Package", IAEA-NDS-77, Vienna, Austria [6] J. Raynal, ECIS-06, Coupled Channel, Statistical Model, Schroedinger and Dirac Equation, Dispersion Relation, NEA-0850, NEA DB layouts Code Collection [7] A. J. Koning, J. P. Delaroche, "Local and Global Nucleon Optical Models from 1 KeV to 200 MeV", Nuclear Physics A 713, 2003, pp [8] M. Avrigeanu et al., "Fast-Neutron Induced Pre-equilibrium Reactions on 55Mn and 63,65Cu at Energies up to 40 MeV", Nuclear Physics A, 806, 2008, pp [9] L. Leal, Personal communication, October 2008