Spallation reaction study for ﬁssion products in nuclear waste: Cross section measurements for 137 Cs, 90 Sr and 107 Pd on proton and deuteron

. Spallation reactions for the long-lived ﬁssion products 137 Cs, 90 Sr and 107 Pd have been studied for the purpose of nuclear waste transmutation. The cross sections on the proton- and deuteron-induced spallation were obtained in inverse kinematics at the RIKEN Radioactive Isotope Beam Factory. Both the target and energy dependences of cross sections have been investigated systematically. and the cross-section differences between the proton and deuteron are found to be larger for lighter fragments. The experimental data are compared with the SPACS semi-empirical parameterization and the PHITS calculations including both the intra-nuclear cascade and evaporation processes.


Introduction
The role of nuclear power has been emphasized since the middle of the twentieth century. The nuclear safety and security are, however, matters of concern to the entire world. One of the major issues is the management on the radioactive waste in the spent nuclear fuel produced from the nuclear power plant.
In recent years, a research and development has been performed using the partitioning and transmutation technology for the reduction of the high-level radioactive waste (HLW) [1] and for the resource recycling from the spent nuclear fuel [2]. Long-lived fission products (LLFPs) and minor actinides (MA) are two main components in HLW. The transmutation for MA has been widely discussed in a concept of using the accelerator-driven system. The study for the LLFP transmutation is limited.
The transmutation on the LLFP nuclei 137 Cs, 90 Sr and 107 Pd have received much attention. 137 Cs and 90 Sr a e-mail: wanghe@ribf.riken.jp have large weight fractions (40%) in LLFP and they are known to as the heat generator in high-level radioactive waste [1]. Due to their relatively short half lives of 30 years [3], 137 Cs and 90 Sr have large radiotoxicities. Indeed, the radiotoxicities in these two LLFP nuclei are predominant (more than 90%) in the first 100 years after the reprocessing of spent fuel. The palladium metal is one of useful materials in HLW but it has a radioactive isotope 107 Pd, which is a long-lived fission product with a half-life of 6.5 × 10 6 years [3]. In considering a possible mechanism for the reduction in the radioactivities of 137 Cs, 90 Sr and 107 Pd, the related nuclear reaction data are very scarce. Thermal neutron capture reactions were once investigated for these three LLFP nuclei [4][5][6].
In the present work, the spallation reactions have been performed for 137 Cs, 90 Sr and 107 Pd in the aspect of nuclear waste transmutation for LLFP. The inverse reaction technique was adopted in the present work: the LLFP beams were used and proton/deuteron-induced reactions were conducted by using proton and deuteron targets. The technique allows us to avoid the difficulties associated with using a highly radioactive target, to identify the reaction products unambiguously, and to study systematically the target dependence of reactions. The present reaction study enables us to provide high-quality data for a possible solution to the LLFP transmutation.

Experiment
The experiment was performed at the RIKEN Radioactive Isotope Beam Factory, operated by RIKEN Nishina Center and the Center for Nuclear Study, University of Tokyo. The secondary beams were produced by in-flight fission of a 238 U beam at 345 MeV/nucleon incident on a 1-mm-thick beryllium target located at the object point of the BigRIPS separator [7]. Several BigRIPS settings were applied to optimize the transmission of 137 Cs, 90 Sr and 107 Pd, respectively. The particle identification for the secondary beams was made event-by-event by measuring the time of flight (TOF), the magnetic rigidity (Bρ), and the energy loss ( E) as described in Refs. [8,9] with similar experimental setups. The beam energies were both 185 MeV/nucleon for 137 Cs and 90 Sr in front of the secondary targets. For 107 Pd, the data were taken at both 196 and 118 MeV/nucleon. To induce the secondary reactions, three types of targets were used. They were CH 2 , CD 2 [10] and natural carbon. The target thicknesses are summarized in Table 1. In addition, data were taken by using the target holder with no target-material inserted (empty-target), in order to measure the background contribution.
The reaction residues were collected and analyzed by the ZeroDegree spectrometer [7]. In order to cover a broad range of fragments, several different magnetic rigidity (Bρ) settings were applied: −9%, −6%, −3%, 0%, and +3% relative to the Bρ value of the beam. Thus, a sufficient overlap was obtained for neighboring settings. The particle identification was made again using the TOF-Bρ-E method in a similar way to BigRIPS. In addition, the mass number A was deduced from the TOF information and a total kinetic energy (TKE) measurement using a LaBr 3 (Ce) scintillator placed at the final focus of the ZeroDegree spectrometer for the identification of different charge states. An example of the particle identification for reaction products detected by the ZeroDegree spectrometer is shown in Fig. 1 for the 137 Cs secondary beam on the carbon target. It is noted that the fully-stripped ions are contaminated by the lighter fragments with hydrogen-like (Q = Z − 1) charge states. In Fig. 1(b), a two-dimensional plot of A versus A/Q is shown and the plot was obtained by selecting the events within Z = 55 ± 0.5, as indicated by the horizontal dashed lines in Fig. 1(a). Using this technique, the fully-stripped ions were unambiguously distinguished from the other charge states.

Results
The isotopic distributions of cross sections for the different elements produced by the 137 Cs and 90 Sr beams on proton and deuteron are displayed in Figs. 2 and 3, respectively. The proton-and deuteron-induced cross sections (σ p and σ d ) were deduced from the measurements using the CH 2 and CD 2 targets, respectively, after subtracting the contributions from carbon (using data from the C target run) and beam-line materials (using data from the emptytarget run). The data analysis for 107 Pd is ongoing. Figures 2(a) and 3(a) correspond to the charge-pickup reactions. In this channel, the σ p values are larger than the σ d ones. It was also found that σ p is larger than σ d for the charge-pickup reaction channel of 136 Xe [12] at a high reaction energy. Isotopes close to the projectile in mass, such as Cs and Xe (Sr and Rb) in the 137 Cs ( 90 Sr) case, are mainly produced from the so-called "peripheral" reactions, where neutron evaporation dominates [14]. For these isotopes, as displayed in Panels (b) and (c) in Figs. 2 and 3, both σ p and σ d keep an almost constant value over a wide range of mass numbers and then slightly decrease for the neutron-deficient side. For other elements, the isotopic distributions show bell shapes as displayed in Panels (d)-(f) in Figs. 2 and 3. It was suggested that the position of the maximum is determined by the competition between the evaporation of protons and neutrons [11]. In addition, it is found that σ d becomes larger than σ p in these channels and their difference increases towards the neutron-deficient side for the lighter products. As the light-mass products are probably produced by a central collision, this difference between σ d and σ p might be related to the energy deposited. In the central collision, the cross sections depend on the energy deposited. At the same reaction energy, more energy can be deposited in the deuteron-induced reaction than that for proton because the deuteron has two nucleons. Thus, the production cross section on deuteron is larger than those on proton for the light products.
The spallation reaction is known to proceed through a two stage processes: the first stage is dominated by the nucleon-nucleon collisions, and followed by the de-excitation of pre-fragments. These two stages are commonly described by intra-nuclear cascade model and an evaporation model, respectively. For a quantitative understanding of the isotopic distribution, a theoretical calculation including these two processes was performed using the particle and heavy ion transport code system (PHITS) [15]. In the PHITS calculation, the cascade and evaporation processes were simulated by using the Intranuclear Cascade model of Liège (INCL4.6) [17] and the generalized evaporation model (GEM) [18], respectively.
The PHITS calculations reproduce the experimental systematic trends well as shown in both Figs. 2 and 3. PHITS overestimates the cross sections on the neutronrich sides for some low-Z products, such as I, Te and Sb, as shown in Fig. 2(d)-(f). In addition, the odd-even staggering effect is overestimated by PHITS.
The experimental data were also compared to the SPACS semi-empirical parameterization [16], which has been recently developed to suit proton-and neutroninduced spallation reactions. The SPACS results are in a reasonable agreement with the isotopic distribution for the proton-induced cross sections. An underestimation is found for the Cs and Sr isotopic chains, as shown in Panel The total spallation cross sections on proton and deuteron are important to evaluate the potential of spallation reaction for the LLFP transmutation. The cross sections for the proton and deuteron were determined to be 1110(17) mb and 1300(15) mb for 137 Cs, and 785(10) mb and 998(10) mb for 90 Sr [13] by integrating the isotopic distributions in Figs. 2 and 3, respectively. These total spallation cross sections are larger than their thermal neutron-capture cross sections of 270 mb [4] and 10 mb [5]. The large total cross sections indicates that the spallation reaction could be a promising mechanism for the transmutation of 137 Cs and 90 Sr.
The number of radioactive nuclei with long halflives created in the spallation reaction is important to evaluate the reduction of radiotoxicities after the reaction. Among the reaction products, the long-lived isotopes 135 Cs and 79 Se are the main components of radioactivity following the spallation of 137 Cs and 90 Sr, respectively. Their production cross sections on proton are around 64 mb and 1 mb, respectively. Since the total spallation cross sections for both 137 Cs and 90 Sr are around 1 barn, the spallation reaction will lead to a considerable reduction in the number of LLFP elements. The half lives of 135 Cs and 79 Se are 2.3 × 10 6 and 6.5 × 10 4 years, respectively, which are much longer than those for 137 Cs and 90 Sr. Therefore, after the spallation reactions, the radiotoxicities in 137 Cs and 90 Sr will be reduced.

Summary
In summary, spallation reactions have been studied for the long-lived fission products 137 Cs, 90 Sr and 107 Pd on proton and deuteron in inverse kinematics at RIBF. Cross sections on proton and deuteron were obtained at 185 MeV/nucleon for 137 Cs and 90 Sr. It is found that the difference between σ d and σ p becomes larger towards the neutron-deficient side for the light-mass products. An overall agreement is found between the experimental data and the PHITS calculation including both the intranuclear cascade and evaporation processes. The SPACS parameterization also shows a reasonable agreement with the results of the proton-induced reactions. The total spallation cross sections on both proton and deuteron are found to be larger than those for the neutron-capture reactions, suggesting the spallation reaction is promising for the transmutation of 137 Cs and 90 Sr.