Cross-section measurement in the reactions of 136Xe on proton, deuteron and carbon

The isotopic production cross sections for the reactions of 136Xe induced by proton, deuteron and carbon at 168 MeV/u were obtained by using the inverse kinematics technique at RIKEN Radioactive Isotope Beam Factory. The target dependence of the cross sections was investigated systematically. It was found that for the light-mass products, the cross sections on carbon are larger than those on deuteron and proton. The measured cross sections on proton were compared with the previous data at higher reaction energies to study the energy dependence. The experimental results were compared with the theoretical calculations including both the intranuclear cascade and evaporation processes using PHITS and with the EPAX and SPACS empirical


Introduction
The spallation and fragmentation reaction play important roles in the production of the nuclei far from stability in radioactive beam facilities [1], which allow us to study the properties of both the proton-rich and neutron-rich nuclei. In addition, the spallation reaction has been considered as a promising mechanism for the nuclear waste transmutation. In recent years, the production cross sections of the proton-and deuteron-induced spallation reactions for the long-lived fission products (LLFPs) 137 Cs, 90 Sr [2], 107 Pd [3] and 93 Zr [4] were measured. For both of the two aspects, having a systematic understanding of the reaction mechanisms is of great importance and the cross section data are required .
For the stable nucleus 136 Xe, which is usually used as a primary beam, several experiments have been performed to study the spallation/fragmentation reactions. The production cross sections were measured for the protoninduced reactions at 1 GeV/u [5], 500 MeV/u [6], 200 MeV/u [7], and for the deuteron-induced reactions at 500 MeV/u [8] and beryllium-induced reactions at 1 GeV/u [9]. In order to investigate the energy dependence and target dependence for the cross sections of 136 Xe, we mea- * e-mail: xhsun@pku.edu.cn sured the cross sections for the reactions of 136 Xe + p, 136 Xe + d and 136 Xe + C at 168 MeV/u. These experimental results are fundamental data for the investigation of the reaction mechanism.
The isotopic distributions of the cross sections for 136 Xe induced by proton, deuteron and carbon at 168 MeV/u were obtained in the present work. The inverse kinematics was applied in the experiment by using the Bi-gRIPS separator and the ZeroDegree spectrometer. By using the inverse kinematics technique, the reaction products were identified unambiguously and the target dependence can be investigated at the same reaction energy. The proton-induced cross sections were compared with the ones at 200, 500 and 1000 MeV/u to investigate the energy dependence.

Experiment
The experiment was performed at RIKEN Radioactive Isotope Beam Factory (RIBF), operated by RIKEN Nishina Center and the Center for Nuclear Study, University of Tokyo. The secondary beams were produced by the inflight fission of a 238 U primary beam at 345 MeV/u bombarding on a beryllium target located at the entrance of the BigRIPS separator [10]. The particles in secondary beams were identified in BigRIPS separator event by event using the TOF-Bρ-∆E method [11]. The time of flight (TOF), the magnetic rigidity (Bρ) and the energy loss (∆E) were measured to deduce the atomic number Z and the mass-tocharge ratio A/Q.
The inverse kinematics was adopted in the present experiment. The CH 2 (179.2 mg/cm 2 ), CD 2 (217.8 mg/cm 2 ) [12] and carbon (226.0 mg/cm 2 ) targets were used to induce the secondary reactions. In order to subtract the background contribution, the data by using the target frame without target material (empty target) were taken. The energy of 136 Xe was 168 MeV/u at the center of the secondary target, with the average intensity of 2.6×10 3 particles per second (pps). The reaction products were analyzed by ZeroDegree spectrometer [10] and the particle identification was made in a similar way to BigRIPS separator, by using the TOF-Bρ-∆E method. In order to cover a broad range of the reaction products, 5 different Bρ settings (+3%, 0%, -3%, -6%, -9%) were applied to the Ze-roDegree spectrometer.
A particle identification plot in ZeroDegree spectrometer for the products produced from 136 Xe on CD 2 target with Bρ -9% setting was shown in Fig. 1. The typical A/Q and Z resolutions were 6.1×10 −3 (FWHM) and 0.52 (FWHM), respectively. For the reactions on CD 2 target, after the particles pass through the ZeroDegree spectrometer, the ratio of the fully-stripped ions (Q = Z) was about 66% for the xenon isotopes.

Results and discussion
The isotopic distributions of the cross sections for the products produced by 136 Xe on proton, deuteron and carbon at 168 MeV/u are shown in Fig. 2. The cross sections on carbon (σ C ) were obtained from the data on carbon target after subtracting the background contribution from the empty target. The cross sections on proton (σ p ) and deuteron (σ d ) were obtained from the data on CH 2 and CD 2 targets, respectively, after subtracting the contributions from the carbon target and empty target. The statistical uncertainties were shown in Fig. 2. The systematic uncertainties originate from the contributions in the target thickness (less than 2%), the charge state distribution (less than 5%) and the acceptance in the ZeroDegree spectrometer (less than 10% for low-momentum products). For the cesium isotopes produced by the charge pickup reactions, the σ p is larger than both the σ d and σ C , as shown in Fig. 2(a). The larger cross sections on proton than those on deuteron for charge pickup reactions were also found for 137 Cs at 185 MeV/u [2] and 107 Pd at 118 MeV/u [3]. For the xenon and iodine isotopes in Fig. 2(b) and 2(c), the cross sections keep almost constant over a wide mass range and then the cross sections gradually decrease towards the neutron-deficient side. These products are produced mainly from the peripheral reactions [9], where the evaporation process is dominated by the neutron evaporation. For other elements from tellurium to cadmium, the isotopic distributions show a bell shape. For these products, σ p becomes smaller than σ d and σ C , especially for the isotopes in the neutron-deficient side. These light-mass products are produced by the central collision, where the production cross sections mainly dependend on the excitation energy of the pre-fragments. Since the number of nucleons is larger for carbon and deuteron than that of proton, the relatively higher energy can be deposited in the carbon-and deuteron-induced reactions. Therefore, σ d and σ C become larger than σ p .
The cross sections on carbon measured in the present work were compared with the calculations by EPAX empirical parameterization [16], as shown in Fig. 2. In general, EPAX calculations reproduce the experimental re-sults well, especially for the elements with atomic number Z < 52. Underestimation by EPAX was found in the neutron-deficient side of the xenon, iodine and tellurium isotopic chain. It is noted that the cross sections for cesium isotopes can not be calculated by EPAX. The comparison between the measured cross sections on proton and deuteron with the model calculations using Particle and Heavy Ion Transport system (PHITS) 2.76 [13] are shown in Fig. 3. The intranuclear cascade model of Liège (INCL) [14] and GEM [15] were used in PHITS calculations for the intranuclear cascade and evaporation processes, respectively. The PHITS calculations reproduced the experimental data for both the proton-and deuteron-induced reactions. PHITS underestimated the cross sections on the neutron-deficient side of cesium and xenon isotopic chain, which can be found in Fig. 3(a) and  3(b). The overestimation by PHITS was observed for the neutron-rich side of tellurium, antimony and tin, as shown in Fig. 3(d)-(f). For 135 Xe and 135 I that are produced by one-nucleon removal, PHITS calculations overestimated the cross sections. Similar results were also found for 93 Zr at 105 MeV/nucleon [4]. The calculations by SPACS semi-empirical parameterization [17] were also plotted in Fig. 3 to compared with the cross sections on proton. The SPACS calculations reproduced the trend of the experimental data on proton overall, while it was found that the SPACS calculations underestimate the cross sections for the neutron-deficient side of xenon isotopes in Fig. 3(b) and overestimate the cross sections in the neutron-rich side for iodine, tellurium, antimony and tin isotopes, as shown in Fig. 3(c)-(f).
The energy dependence for the proton-induced cross sections was studied by comparing the measured cross sec-tions in the present work at 168 MeV/u with the results obtained previously at higher reaction energies. As shown in Fig. 4, the production cross sections at 200 MeV/u [7] (diamond) , 500 MeV/u [6] (square), and 1000 MeV/u [5] (circles) were plotted for comparison. For the charge pickup reactions in Fig. 4(a), the shape of the isotopic distribution is similar at different reaction energies, and the value of the cross sections decrease as the reaction energy increase. Such behavior for this reaction channel was also observed in the studies for 107 Pd [3]. The energy dependence for xenon isotopes was found in a similar minor as cesium isotopes, except the production of 135 Xe, for which the difference of the cross sections at different reaction energies is very small. For the elements with atomic number Z < 54 in Fig. 4 (c)-(h), the coverage of the isotopic distribution is wider at higher reaction energy. For the iodine and tellurium isotopes, the cross sections are larger at higher reaction energy in the neutron-deficient side, and the cross sections at 200 and 168 MeV/u decrease rapidly. As discussed above, for the antimony, tin, indium and cadmium elements, which are produced by central collision, the cross sections depend on the energy deposited in the pre-fragment. At higher reaction energy, more energy deposited during the cascade stage, resulting in a large production cross sections for the light-mass products by evaporating more nucleons.

Summary
The isotopic distribution of the cross sections for 136 Xe on proton, deuteron and carbon at 168 MeV/u were ob-tained in inverse kinematics technique at RIKEN Radioactive Isotope Beam Factory. The target dependence of the cross sections was investigated systematically. The cross sections of the light-mass products are found to be larger for the carbon-induced reaction because of the higher deposited energy. The cross sections for the proton-induced reactions obtained in the present work were compared with the previous data at higher reaction energies. It was found that the cross sections for cesium isotopes decrease as the reaction energy increase. The experimental results were compared with several calculations, PHITS, EPAX and SPACS. The overall tendency of the isotopic cross sections was reproduced by all these calculations. The comparison of the experimental data with the model calculations is expected to be helpful for the model benchmarking.