1 INTRODUCTION

A report issued by an international study group on the transmutation of nuclear waste using accelerator driven systems has highlighted the need for specific sets of nuclear data [1]. These authorative requirements include fission product yields at intermediate incident neutron energy up to 150 MeV. Prior to 1996, only four types of evaluated fission yield datasets existed, namely for spontaneous fission, and for fission-induced by thermal and fast spectrum, and by ‘high energy’ (14 – 15 MeV) neutrons. A new type of evaluation for energy-dependent neutron-induced fission yields is required in order to derive the data recommended for the proposed transmutation of nuclear waste. Such evaluations would have to be based on systematics and theoretical model calculations. Unlike fission cross sections, where nuclear models are successfully used for the calculation of unmeasured cross sections, such models or theories exist only for low-energy fission yields. Hence, an IAEA project was established to consider and address this situation, although the participants were entering a completely new field of research for which progress and outcome were unpredictable.

The emphasis of the work has been concerned with the development of adequate systematics and models for the calculation of energy-dependent fission yields up to 150-MeV incident neutron energy. Several problems need to be solved, such as the correct choice of model parameters and multiplicity distributions of emitted neutrons, and the effect of multi-chance fission. Models and systematics have been tested for lower-energy yields, but failed to reproduce recent experimental data (particularly at higher energies) and parameters had to be modified. Other models have been developed from the analysis of experimental data in order to derive systematic dependencies, and were adapted in the course of the studies to predict fission product yields. Discussions formed a fruitful basis for improvements to the models, and a benchmark exercise revealed the true worth and predictive capabilities of the systematics and theoretical models developed during the course of the study. Necessary improvements and the direction of future studies were also noted and revealed during the course of the work. The objectives, tasks, achievements, conclusions and recommendations are summarized at the beginning of the resulting IAEA technical report. Participants have also provided detailed accounts of their interrelated work.

An IAEA Coordinated Research Project (CRP) on fission product yield data was initiated in 1997, with the primary aim of developing systematics and nuclear models to assist in the evaluation of energy-dependent fission yields for incident neutron energies up to 150 MeV. A multinational team with the appropriate expertise participated in this work programme. New concepts for both systematics and theoretical models were developed. Various predictions of the fission-product mass distributions were compared in a benchmark exercise that gave remarkably good results below 50 MeV. Reasons were formulated for the discrepancies at higher energies and some failures of the model predictions, pointing the way towards future investigations and fission yield evaluations. 

All the work can be found in the technical report.

The primary objectives of the CRP were to study all the problems involved in the development of nuclear models and systematics, and to derive a method for fission-yield evaluation as a function of incident neutron energy. This CRP entered an entirely new field of research, as usable models and systematics do not exist over such an energy range, and the outcome of the work was deemed to be unpredictable. While the goals of the CRP were  limited to the development of appropriate nuclear models and systematics for the prediction of fission yields as tools for the evaluation of energy-dependent fission yields up to 150 MeV, no recommended fission yield data were derived.

3. MODELLING OF FISSION FRAGMENT MASS DISTRIBUTION

Fission is a slow process on a nuclear time scale, involving deformation of the whole nucleus, and is always a compound process. A captured low-energy neutron leads directly to an equilibrated compound system (first-chance fission). At sufficiently high incident neutron energies (E_n) of a few MeV, the emission of a pre-equilibrium neutron becomes possible (second-chance fission) at an approximately 100-fold faster timescale than fission. Still higher E_n can lead to the emission of two (third-chance fission) or more (multi-chance fission) pre-equilibrium neutrons before fission. This behaviour is also applicable to other projectiles, except that there is always a threshold for fission. At such high energies, a ‘composite nucleus’ (target nucleus plus projectile) is formed that emits fast particles, and gradually loses excitation energy and memory of the incident particle by many nucleon-nucleon interactions before reaching an equilibrated compound stage of the reaction, where fission may occur (multi-chance or emissive fission). Thus, the fissioning nucleus has a mass lower than the composite nucleus by the number of pre-equilibrium particles emitted. Fission occurs when the saddle point deformation of the nucleus is reached. On the descent from saddle to scission, neutrons may be emitted and reduce the excitation energy. The highly-excited primary fission fragments are de-excited by the emission of prompt neutrons resulting in secondary fission fragments, followed by prompt rays to form the primary fission products. The latter are generally neutron rich and reach stability by the emission of delayed neutrons and/or by radioactive β^- decay. We distinguish between the ‘pre-neutron-emission mass distribution’ of primary fission fragments and the ‘post-neutron-emission mass distribution’ of secondary fission fragments. Mass distributions from low-energy neutron-induced actinide fission are predominantly asymmetric, and such an effect is reflected by the light and heavy mass peaks corresponding to complementary fission fragments. These mass distributions have successfully been represented by five Gaussians, accounting for the observed fine structure in the asymmetric peak regions, whereas seven Gaussians gave a better fit for spontaneous fission, and less than five Gaussians were adequate for the pre-actinides and higher actinides where increased symmetric fission is observed [2]. 

Brosa et al. [3] have developed a model that relates the above representations of fission fragment mass distributions to different fission modes (corresponding to separate fission channels) through which an excited nucleus in the actinide region can undergo fission: a symmetric ‘Superlong’ (SL) mode and two asymmetric modes ‘Standard 1’ (ST-1) and ‘Standard 2’ (ST-2). The SL mode corresponds to the symmetric peak; both the ST-1 and ST-2 modes correspond to two Gaussians, each mode being composed of a light and heavy mass peak in asymmetric fission. ST-1 and ST-2 are responsible for the observed fine structure in the asymmetric peaks. The positions of the asymmetric mass peaks are determined by shell effects: ST-1 contribution to the heavy mass peak at about A = 134 is attributed to the formation of spherical heavy fragments close to Z = 50 and N = 82; that of ST-2 at about A = 142 is identified with the deformed shell closure at N ≅ 88. As a consequence, these positions have been observed to be stable with respect to the change in mass of the fissioning nuclide, as also confirmed by the Brosa model that predicts a change of the mean heavy fragment mass for ST-2 from 142 in ²³⁸U to 140 in ²²⁶U fission. Thus, only the position of the light mass peak shifts with a change of the mass of the fissioning nuclide. 

The symmetric fission contribution has been observed to increase for lower mass actinides (e.g., ²³²Th), and is the only fission mode for pre-actinides (A ≤ 227). A similar trend can be observed for the higher actinides, with only symmetric fission for A ≥ 257. This systematic behaviour is correctly predicted by the Brosa model [3]. However, whereas the symmetric fission of pre-actinides and the smaller symmetric fission contribution in the case of actinides are due to the SL mode, there is a super-short mode responsible for the symmetric fission of the heavy actinides. The preferred fission mode also changes with increasing excitation energy due to the disappearance of shell effects, so that fission mechanisms are described solely by the liquid drop model: first the ST-1 contribution disappears, followed by ST-2, to leave only the SL mode and a symmetric mass distribution.

The development of systematics is based on experimental data, and represents an empirical approach to understanding the fission process. Measured fission yield distributions are fitted by suitable functions. Mass distributions are normally (but not necessarily) represented by a model consisting of Gaussians as described above. Model parameters are obtained for different composite nuclides and excitation energies, and the functional dependencies of these parameters on the masses and charges of the composite nuclides and on the excitation energies are generally derived through least-squares analyses. The systematics can be restricted to neutron-induced fission of a certain target nuclide or include different target nuclides and projectiles to derive global systematics. 

Emissive fission contributions to the total reaction cross section for a given target-projectile combination are calculated in the theoretical approach to obtain the fissioning nuclides contributing to the observed mass distribution. Fission fragment mass distributions are then derived with the aid of a suitable nuclear model that calculates the formation of given pairs of complementary fission fragments from the probabilities for the different fission modes and the neck rupture. This approach does not use any fitting procedure. Only the model parameters are adjusted by comparing the predictions with measured yield distributions, and can be used to calculate mass distributions from any target-projectile combination.

4. DATA ANALYSES

Available experimental data for energy-dependent neutron-induced fission yields are insufficient for the development of systematics, whereas the theoretical model approach is not affected. One possibility would be to extend the studies to yield data from photon- and light charged-particle-induced fission. Detailed studies are required to quantify the differences between neutron-induced and other fission reactions, and assess the feasibility of their combined use in systematics. Measurements can also be recommended that are important for the development of systematics and theoretical models. Clearly, for the development of systematics and for the intercomparison of model predictions, the proposed studies cannot be restricted to minor actinides. Models and systematics have to be extensively applicable, and as many data as possible need to be used in their development. However, fairly complete and up-to-date collections of experimental data (bibliographies and data compilations) exist only for neutron-induced fission yields. Measurement methods can be sub-divided into basically two types: 

(1) Physical measurements, in which prompt fission fragments are recorded simultaneously and directly to be identified by their mass and charge and/or kinetic energy - this method covers practically the complete range of the mass distribution. 

(2) Measurements of the characteristic radiation from fission-product decay (mass spectrometry is not possible at higher neutron energies because of the extremely small amounts of fission products available). 

The second method can only be applied to specific fission products, and the mass range covered is incomplete. On the other hand, the results of radiation studies are more accurate, and enable the determination of fine structure in mass distributions and charge dispersions in mass chains. 

`Provisional masses’ are determined in physical measurements that lie between the pre- and post-neutron-emission mass distribution. The raw data have to be corrected for neutron emission by fragments to obtain pre- or post-neutron-emission mass distributions. This correction is a rather complicated procedure that depends on the experimental arrangements and requires assumptions concerning the neutron multiplicity distribution as a function of fragment mass (for the incident neutron energy range under consideration, there are practically no experimental or evaluated data). Furthermore, each recorded mass has a Gaussian distribution due to the nature of the experimental set-up. Formulae to correct for this incomplete mass resolution have been proposed and used in data analyses, but there is no evidence that a certain correction method is reliable and universally applicable. Finally, in the analysis of raw data, measurers often assume that mass distributions are symmetric in shape (complementary fission fragments), and the point of symmetry is determined from the composite nucleus mass and nu-bar, which is incorrect because of multi-chance fission. 

4.1 Multi-Chance Fission

Fissioning nuclei differ from the original composite nuclei in emissive fission. Thus, several problems have to be taken into account and addressed. 

(a) Formation of the compound nucleus. 

The formation process of the compound nucleus prior to disintegration has been established to be unimportant. Therefore, the mass distribution from a given fissioning nuclide at a given excitation energy is expected to be independent of the original target and projectile. However, global systematics of fission-product mass distributions are developed as a function of the composite nuclei resulting from different target-projectile combinations. Studies are required to determine the possible differences in the pre-equilibrium particle emission characteristics for different target-projectile combinations leading to the same composite nuclei.

(b) Shape of the mass distribution.

Effects due to multi-chance fission that influence the final observed mass distribution can be subdivided into three main categories:

(1) change of fission mode contribution; 
(2) change of mass peak position and point of mass symmetry;
(3) change in neutron emission by fragments. 

4.2 Development of Systematics and Models

Existing systematics and models for mass and charge distributions were only designed and valid for low-energy fission up to 14 MeV. Therefore, studies were undertaken to assess the applicability and adaptability of these techniques to intermediate energy fission, and determine whether new models and systematics need to be developed. These investigations entered a new field of research, and the outcome and degree of success were unpredictable. 

Measurements of charge distributions are even far more scarce in the intermediate energy range than those of mass distributions or cumulative fission yields. Furthermore, charge distribution data derived by measurers from their experimental results depend on assumptions made about the charge distribution functions and absolute mass yield data. Thus, the decision was taken to solve the problem of reliable mass distribution predictions first (required for correction of measured data and derivation of charge distribution functions), before investigating the feasibility of modelling charge distributions as functions of the fissioning nuclide and excitation energy. 

5 OUTPUTS 

5.1 Data Files 

A bibliographic database of experimental yield data from neutron-, photon- and light charged-particle-induced fission has been assembled. The data are published in this final report, and also as a computer file in the Appendix of a CD-ROM to enable direct access to the desired references.  

Experimental yield data from neutron- and light charged-particle-induced fission have been collected and compiled in different data files. All of these fission yield data have been converted to the well‑known EXFOR format, and have been incorporated into the EXFOR database [4]. The associated CD‑ROM also includes these experimental data to allow rapid computer searches. 

Sets of reference fission yields have been assembled through an evaluation effort. These fission yields have been derived with higher accuracy than those recommended for complete yield sets in evaluated data files through careful evaluation of individual reference fission products. Full use was also made of correlations and covariance information by means of analysis and correction of the experimental data and assessment of uncertainties. No final overall adjustment has been applied to these fission-yield data, as normally done for complete yield sets to comply with physical constraints, a procedure that reduces the overall uncertainty of complete yield sets but increases the uncertainty of individual yields. Reference fission-yield sets are presented as two individual papers in the final technical report; one paper contains the data for U-235T, U-235F and U-235H, and for U-238F and U-238H, and the other paper is devoted to the spontaneous fission of  ²⁵²Cf. 

5.2 Dedicated studies  

Several dedicated studies were performed by more than one participant, and the individual results are presented in the various contributions to the final report. 

5.2.1 Measurements 

Several measurements (initiated by Duijvestijn, Ethvignot, Goverdovskii and Zhdanov) were performed to support the investigations of the CRP. The results have been used for the development of systematics, derivation of model parameters, and to check the validity of the fission-yield predictions. 

5.2.2 Differences between neutron-induced and other fission reactions 

Studies have been performed to determine the validity of using both neutron- and non-neutron-induced fission yields in systematics. However, not all functional dependencies, values for model parameters and numerical results can be used (e.g., transfer of angular momentum). 

5.2.3 Multi-chance fission contributions  

A theoretical study of the fission mechanisms and the emissive fission contributions to the total fission cross section was undertaken in order to obtain the contributions of the fissioning nuclides to the total fission-yield distributions. Fission cross sections for neutron- and proton-induced reactions have been analysed and compared with different model calculations to obtain the best descriptions. The Statistical Model was found to be the most adequate for this purpose. Also, the emissive fission contribution to the observed fission cross section is dependent on target fissility and fission probability for high excitation energies. A method of partitioning the observed neutron-induced fission cross section into emissive and non-emissive fission has been validated for all neutron energies up to 200 MeV on Th, U, Np and Pu target nuclides. Emissive fission contributions (also for symmetric and asymmetric fission) have been calculated for several target nuclides. 

5.2.4 Systematics derived from experimental data 

The systematic behaviour of the energy dependence of the experimental fission yields was studied for several fissioning nuclides. 

5.2.5 Phenomenological models for the fission-yield distributions derived from experimental data 

Two new phenomenological models were developed for the analysis of experimental yield distributions from neutron-, proton- and alpha-particle-induced fission. Detailed studies of the dependencies of model parameters on target nuclide, projectile and incident-particle energy have revealed regularities in their behaviour that can be used for systematics. 

5.2.6 Theoretical prediction of fission yields at intermediate incident-particle energies  

A new theoretical approach has been developed to predict fission yields at intermediate energies and solve the problems of emissive fission as well as the changing fission characteristics with excitation energy. This approach is based on the Brosa model for the calculation of fission yield distributions, coupled to a nuclear reaction code for the calculation of fission cross sections and emissive fission contributions. 

5.2.7 Progress towards computer programs for evaluations 

Models and systematics have been developed that can in principle be used for an evaluation of energy-dependent fission yields. However, the results of the benchmark exercise are not conclusive enough to recommend one analytical method, and the same is true for the computer programs. 

5.3 Models and systematics 

(a) Fission-yield systematics and covariance study of U-238 (Liu Tingjin)
(b) Five Gaussian systematics for fission-product mass yields (Katakura)
(c) Systematics of fission-product yields (Wahl)
(d) Phenomenological model for fragment mass and charge distribution in actinide nuclei fission (Kibkalo et al.)
(e) Modal approach to the description of fragment mass yields (Zhdanov et al.)
(f) Fission yields from nucleaon-induced reactions at intermediate energies (Duijvestijn and Koning) 

All of this material can be found in the technical report.

6 CONCLUSIONS 

Accuracy requirements for fission yields in waste transmutation studies are ill-defined. We assume that only fission yields ≥ 2% are important, and should be known to about 25% relative accuracy, amounting to roughly 1.5% absolute yield uncertainty for peak fission yields of 6-7%. At low energies for ²³⁸U where agreement is better, the discrepancies among calculations are 2.5% in many cases. Clearly for some of the nuclides included in the benchmark exercise, the agreement is worse, even without detailed analyses. Therefore, the target of 25% relative accuracy for the important fission yields can not be met to date. Furthermore, since the comparisons of experiments are also inconclusive, we are not in a position to recommend with confidence any of the models or computer programs for use in applied calculations. 

Models for fission-yield predictions at intermediate energies have been developed for the first time, and contributions to mass distributions due to different fission modes and emissive fission have been calculated. These models have the potential to give reliable predictions after additional improvements involving detailed analyses of their contents, parameters, results and reasons for discrepancies. Proposals for further developments and improvements should be based on more reliable quantitative theoretical predictions of the influence of multi-chance fission and shapes of the mass distribution and associated components. The inclusion of higher energies above 100 MeV in such studies is equally important, as the present limit of 150 MeV has only been set as the first step in the evaluation of nuclear data for transmutation. 

REFERENCES  

[1] KONING, A.J., FUKAHORI, T., HASEGAWA, A., International Evaluation Cooperation: Intermediate Energy Data, NEA/WPEC-13, ECN-RX-98-014, 13 (1998).

[2] WAHL, A.C., IAEA final report of a coordinated research project on “Compilation and evaluation of fissions yield nuclear data”, IAEA-TECDOC-1168, Vienna (2000) ISSN 1011-4289, 45-75.

[3] BROSA, U., et al., Nuclear scission, Phys. Rep. 197 (1990) 167-262. 

[4] McLANE, V., EXFOR basics, a short guide to the nuclear reaction data exchange format BNL-NCS-63380, IAEA-NDS-206 (2000).  see also: iaea-nds-0206