TALYS: Comprehensive Nuclear Reaction Modeling

Transcription

1 : Comprehensive Nuclear Reaction Modeling A.J. Koning Λ, S. Hilaire and M.C. Duijvestijn Λ Λ Nuclear Research and Consultancy Group NRG, P.O. Box 25, NL-1755 ZG Petten, The Netherlands Commissariat à l Energie Atomique, DAM/DIF/DPTA, Boîte Postale 12, 9168 Bruyères-le-Châtel, France Abstract. is a nuclear-reaction program which simulates nuclear reactions that involve neutrons, gamma-rays, protons, deuterons, tritons, helions, and alpha-particles, in the 1 kev - 2 MeV energy range. A suite of nuclear-reaction models has been implemented into a single code system, enabling us to evaluate basically all nuclear reactions beyond the resonance range. An overview is given of the main nuclear models used, such as newly developed optical models, various compound nucleus, fission, gamma-ray strength, level density, and pre-equilibrium models, all driven by a comprehensive database of nuclear-structure parameters. The predictive power of the code is demonstrated by comparing calculated results with a very diverse set of experimental observables. Our aim is to show that represents a robust computational approach that covers the whole path from fundamental nuclear-reaction models to the creation of complete data libraries for nuclear applications. INTRODUCTION With the advent of fast computers, software that simulates nuclear reactions is able to play an increasingly important role in nuclear data. It is possible to provide an exact computational scheme for sophisticated nuclear models, not only new ones but also those that have been lying on the shelf for decades, and only now become amenable for numerical implementation. Largescale comparisons with measurements are within reach. is a nuclear reaction program created at NRG Petten, the Netherlands, and CEA Bruyères-le-Châtel, France. The idea to make was born in 1998, when we decided to implement our combined knowledge of nuclear reactions into one single software package. The objective is to provide a complete and accurate simulation of nuclear reactions in the 1 kev - 2 MeV energy range, through an optimal combination of reliable nuclear models, flexibility, and user-friendliness. There are two main purposes of, which are strongly connected. First, it is a nuclear physics tool that can be used for the analysis of nuclear-reaction experiments. The interplay between experiment and theory gives us insight in the fundamental interaction between particles and nuclei, and precise measurements enable us to constrain our models and their parameters. In return, when the resulting nuclear models are believed to have sufficient predictive power, the prediction can even give an indication of the reliability of measurements. The many examples of presented in this paper and in various other contributions to this conference confirm that our software project would be nowhere without the existing experimental database. After the nuclear physics stage comes the second function of, namely as a nuclear data tool: After fine-tuning the adjustable parameters of the various reaction models using available experimental data, can generate nuclear data for all open reaction channels, interpolating between and extrapolating beyond experimental data, on a user-defined energy and angle grid beyond the resonance region. The associated nucleardata libraries that can be constructed provide essential information for existing and new nuclear technologies. Important applications that rely directly on the output of nuclear-reaction simulation software like are conventional and innovative power reactors (GEN- IV), accelerator-driven systems, and transmutation of radioactive waste, fusion reactors, homeland security, medical-isotope production, and radiotherapy, oil-well logging, geophysics, and astrophysics. NUCLEAR MODELS Figure 1 shows the nuclear models implemented in. Nuclear Structure and Model Parameters All nuclear models make use of structure and model parameters. There is an automatic reference to parameters as masses, resonances, etc.; see the lower left box of Fig. 1. With a few exceptions, our database is based on the Reference Input Parameter Library [1]. 1154

2 Loops possible over: Direct reaction: Preequilibrium: Output: * Incident energies * Spherical OM * Exciton model *File output * DWBA 2 component * Natural isotopes * Rotational CC * p h LD phenom. defined by surface effects keywords * Vibrational CC Optical Model: * Kalbach systematics * Giant resonances *Dedicated * Phenomenology angular distribution * Weak coupling files with Input: local / global cluster emission spectra,... * Keywords, eg: * γ ray emission projectile n element fe mass 56 energy 14. Nucl. Structure: * Abundancies * Discrete levels * Deformations * Masses * Level density par. * Resonance par. * Fission barrier par. * Thermal XS * Microscopic LD * Prescission shapes Compound: * Width fluctuations Moldauer GOE triple integr. HRTW * Hauser Feshbach * Fission competition isotopic yields * γ ray emission * GC+ Ignatyuk Multiple emission: * Exciton (any order) * Hauser Feshbach * Fission competition isotopic yields * γ ray cascade * All flux depleted * Exclusive channels * Recoils ENDF: * transport libs * activation libs FIGURE 1. Optical Model and Direct Reaction Model Flowchart of. Compound Nucleus Model We use the coupled-channel code ECIS-97 [2] as a subroutine for all optical model and direct reaction calculations. It is the only module in that is not written from scratch but adopted from outside. ECIS- 97 delivers the basic observables such as the elastic angular distribution, the reaction, and the total cross sections. Moreover it yields the transmission coefficients for compound-nucleus calculations and all cross sections and angular distributions for discrete states. The default optical-model potentials (OMP) used in are the local and global parameterisations for neutrons and protons of [3]. For nuclides outside the scope of this OMP, i.e., strongly deformed nuclides, we allow input of potentials on an individual basis. With this, coupledchannel calculations for various types of deformation (symmetric-rotational, harmonic-vibrational, vibrationrotational, and asymmetric-rotational) can be automatically performed. For near-spherical nuclides, direct reactions are calculated with DWBA, and inelastic scattering off odd-a nuclei is described by the weak-coupling model. For deuteron, triton, Helium-3, and alpha OMPs, we use a folding approach applied on the aforementioned OMPs. The term compound nucleus reaction is commonly used for two different processes: (i) capture of the projectile in the target nucleus to form a compound nucleus, which subsequently emits a particle or gamma; (ii) multiple emission from the chain of excited residual nuclides following the binary reaction. Both are included in. At low incident energy (i) plays an important role. It differs from (ii) at two important points: (a) the presence of width-fluctuation corrections and (b) nonisotropic, though still symmetric, angular distributions. It is calculated with the Hauser-Feshbach formalism including width fluctuation corrections (WFC). The WFC factor accounts for the correlations that exist between the incident and outgoing waves. From a qualitative point of view, these correlations enhance the elastic channel and accordingly decrease the other open channels. In general, the WFC factor may be calculated using three different expressions, which have all been implemented in : The HRTW model, the Moldauer model, and the model using the Gaussian Orthogonal Ensemble (GOE). A comparison between the three models is given in [4], where the Moldauer model is confirmed as the best default choice. All WFC models are generalized to include continuum particle emission, gamma-ray competition, and fission. Gamma-ray coefficients are modeled with 1155

3 Kopecky-Uhl s generalized Lorentzian and the appropriate giant-dipole resonance parameters. Besides cross sections, compound angular distributions are calculated using Blatt-Biedenharn coupling factors, again within a full Hauser-Feshbach expression with WFC. For multiple emission, the whole reaction chain is followed by depleting each [nucleus-excitation energyspin-parity] bin with particle, gamma, or fission decay until all channels are closed. In the process, all particle and residual production cross sections are accumulated to their final values. Non-equidistant energy grids in this decay scheme ensure enoughprecisioninthecompoundevaporation peaks. Level Densities We use several models for the level density in, which range from phenomenological analytical expressions to tabulated level densities derived from microscopic calculations. So far, the most robust approach seems to be a Fermi gas model at high energies, with shell- and energy-dependent level-density parameter a, and a constant-temperature model, fitted to the known discrete states, at low energy. For non-fissile nuclides, we generally use an effective level-density model, i.e., all collective enhancements are included in the level-density parameter a. For fissile nuclides, we account for an explicit rotational and vibrational enhancement as well as their appropriate damping at high energies. More precise details on the various forms for the level density can be found in the manual and in [5]. Fission For fission, the default model used in is based on the Hill-Wheeler expression for the transmission coefficient for one, two, or three barriers. If the excitation energy of the compound nucleus is lower than the barrier heights, fission-transmission coefficients display a resonant structure that is due to the presence of nuclear excited levels in the second well of the potential-energy surface. These so-called class II states modify the fission transmission coefficients. The total fission transmission coefficient for a compound nucleus is then obtained by summing the individual Hill-Wheeler terms over all head band transition states and, for the continuum, integrating it using the aforementioned fission level densities. Multichance fission for all residual nuclides is included. A novel feature for any general nuclear model code is the ability to predict fission yields. This is done with the multi-modal random neck rupture model and the scission point model, as described in more detail in [5]. Pre-Equilibrium Model For energies above a few MeV, pre-equilibrium reactions play an important role. For nucleon reactions, we have implemented a two-component exciton model with a new form for the internal transition rates based on the OMP of [3], which yields an improved description of pre-equilibrium processes over the whole energy range [6]. Another feature necessary to cover a large energy range is the generalization of multiple pre-equilibrium processes up to any order of particle emission. This is accomplished by keeping track of all successive particlehole excitations of either proton or neutron type; see [6] for the mathematical outline. On top of the contribution of the single-particle exciton model, which yields essentially structureless emission spectra, we add a contribution from giant resonances, computed with a macroscopic, phenomenological model, accounting for the energy-weighted sum rule. Pre-equilibrium photon emission is taken into account with the model of Akkermans and Gruppelaar [7]. For pre-equilibrium reactions involving deuterons up to alpha particles, a (too-low) contribution is automatically calculated within the exciton-model reaction equations. However, for nuclear reactions involving projectiles and ejectiles with different particle numbers, mechanisms like stripping, pick-up, and knock-out play an important role and these direct-like reactions need to be added incoherently. Kalbach [8] developed a phenomenological contribution for these mechanisms, which we have included in, resulting in a much better prediction of complex-particle cross sections as compared to many older reaction codes. However, the (very) phenomenological nature of the model still provides a challenge to construct a more physical approach for these reactions in the future. Finally, pre-equilibrium angular distributions are predicted by Kalbach s systematics. From a physical point of view, the quantum-mechanical multi-step approach is preferable, although it is difficult to find justification (from applications) for angular precision that goes beyond that of the systematics. Including our existing multi-step direct software is nevertheless left as future work. THE CODE The present version of is written in Fortran77, and so far has been successfully compiled with various f77 and f9/f95 compilers. We have aimed at a setup that is as modular as Fortran77 allows it to be, using programming procedures that are consistent throughout the whole code. In total, there are about 25 subroutines adding up to a total of more than 4 lines, plus the 1156

4 2 lines of the ECIS-97 subroutine. The code is rather flexible in its use. Indeed, a complete set of cross sections can already be obtained with minimal effort, through a four-line input file of the type given in Fig. 1, which produces the best blind answers can currently give. Generally, a user wants to be more specific on the choice of nuclear models, their parameters, and degree of output. For this, more than 15 different keywords are available that can be specified to e.g., fit experimental data. The code has been thoroughly tested on a formal level, through random input files (probing every corner of the code). Full dripline-todripline calculations (including the production of ENDF- 6 data files) for all types of projectiles up to 2 MeV, have been performed to validate the code computationally and to test the continuity (smoothness) of the results. WHAT CAN WE DO WITH? The main aim of is to provide a complete set of answers for a nuclear reaction, for all open channels and associated cross sections, spectra, and/or angular distributions. It depends on the current status of nuclearreaction theory, and our ability to model that theory, whether these answers are generated by more or less sophisticated physical methods or by simpler phenomenological approaches. The following data can be calculated: Total, elastic, and reaction cross sections, Non-elastic cross sections per discrete state, Elastic and non-elastic angular distributions, Exclusive reaction channels ((n,2n), (n,np), etc.), Exclusive double-differential spectra, Exclusive isomeric-production cross sections, Discrete and continuum gamma-ray production cross sections, Extrapolation of non-threshold cross sections down to the thermal energy range [9], Total particle-productioncross sections, e.g., (n,xn), Single- and double-differential particle spectra, Residual production cross sections (+ isomers), Recoils, Fission cross sections and fission yields. Figures 2 and 3 give an impression of the variety of nuclear reactions that can be simulated. The shown curves are obtained from blind calculations (e.g., residual production, energy spectra), after minor fitting (e.g., capture, (n; α), inelastic), and after significant parameter adjustments (e.g., fission cross section). A complete ENDF-6 data file, above the resonance range, up to 2 MeV can be computed in about 4 minutes (2-MeV file) up to 4 hours (2-MeV file) on a 1- GHz PC. Various new evaluations for the JEFF-3 library have been produced [1] through fitting, using model parameters, of the experimental data. With default input files, is also suitable for mass production of nuclear data and has been used to generate data for largescale activation libraries such as EAF [11], but also for more fundamental purposes such as astrophysics [12]. CONCLUSIONS The development of has followed the first completeness, then quality principle. This merely means that, in our quest for completeness, we try to divide our effort equally among all nuclear-reaction types. We think that, with the exception of a few fission items (neutron spectrum, evaporating fragments), the code is indeed complete. Quality is obviously a different and subjective issue, and it is certain that future enhancements in various theoretical models are needed to bring our computed results even closer to measurements. REFERENCES 1. Reference Input Parameter Library, 2. J. Raynal, Notes on ECIS94, CEA Saclay Report No. CEA-N-2772, (1994). 3. A.J. Koning and J.P. Delaroche, Nucl. Phys. A713, 231 (23). 4. S. Hilaire, Ch. Lagrange and A.J. Koning, Ann. Phys. 36, 29 (23). 5. M.C. Duijvestijn and A.J. Koning, Fission yield predictions with, this conference. 6. A.J. Koning and M.C. Duijvestijn, A global preequilibrium analysis from 7 to 2 MeV based on the optical model potential, Nucl. Phys. A, in press. 7. J.M. Akkermans and H. Gruppelaar, Phys. Lett. 157B, 95 (1985). 8. C. Kalbach, Pre-equilibrium reactions with complex particle channels, this conference. 9. Collaboration with JUKO Research (J. Kopecky). 1. A.J. Koning, M.C. Duijvestijn, S.C. van der Marck, R. Klein Meulekamp, and A. Hogenbirk, New nuclear data evaluations for Ca, Sc, Fe, Ge, Pb, and Bi isotopes, this conference. 11. R.A. Forrest, European Activation File EAF-25, this conference. 12. E. Khan, S. Goriely, D. Allard, E. Parizot, T. Suomijarvi, A.J. Koning, S. Hilaire, and M.C. Duijvestijn, Impact of the giant dipole resonance on the photodisintegration of ultrahigh energy cosmic rays, submitted to AstroParticle Journal. 1157

5 Cu(n,n) 63 Cu (a) n + 93 Nb: Total cross section (b) dσ/dω (mb/sr) Cross section (mb/sr) Θ c.m. (deg) n + 93 Nb at 1 kev Hauser Feshbach Moldauer HRTW GOE Elastic angular distribution (c) Energy (MeV) Pu 239(n,f) ENDF/B VI JEFF 3. (d) Angle (deg) Ge(n,γ) (e) Exp ENDF/B VI Pb(n,n 1 ) J Π = 3, E x = 2.61 MeV (f) Towle and Gilboy (1963) Almen Ramstroem (1975) ENDF/B VI.8 ENDF/B VI.8 mod 2 1e 2 1e 1 1e+ 1e+1 E (MeV) Energy (MeV) FIGURE 2. vs. experimental data: (a) n + 63 Cu elastic angular distributions, (b) n + 93 Nb total cross section, (c) different width fluctuation correction models compared for 1 kev n + 93 Nb, (d) n Pu total fission cross section, (e) 74 Ge (n;γ) cross section, (f) 28 Pb inelastic cross section for first discrete level. 1158

6 2 27 Pb(n,2nγ) Level 1 > Level : E γ =.8 MeV Vonach et al. (1994) (a) MeV n+ 238 U Pre neutron emission mass yield curve (b) 15 1 cross section (mb) 1 Yield [%] Vives et al (2) Energy (MeV) 4 Ca(n,α) A 2 MeV n + 28 Si: recoil spectrum 4 ENDF/B VI.8 (c) 15 Exact approach Average energy approximation (d) 3 2 Cross section (mb/mev) dσ/de [mb/mev] (p,xp): 62 MeV 27 Al 54 Fe 56 Fe 6 Ni 89 Y 12 Sn 197 Au nat Pb 29 Bi (e) Recoil energy of 24 Mg (MeV) p + nat Fe 56 Co 55 Co 54 Mn (f) Mn E out [MeV] Incident energy (MeV) FIGURE 3. vs. experimental data: (a) exclusive gamma-ray production for 27 Pb(n,2n), (b) fission mass yield curve for 5.5 MeV n U, (c) 4 Ca(n;α) cross section, (d) two different recoil models for 2 MeV n + 28 Si, (e) 62 MeV (p,xp) spectra for various targets, (f) p + nat Fe residual production cross sections. 1159