Isotope-production cross sections of residual nuclei in proton- and deuteron-induced reactions on 93Zr at 50 MeV/u

The isotope-production cross sections in pand d-induced reactions on Zr at approximately 50 MeV/nucleon were measured by using the inverse-kinematics method at RIKEN RI Beam Factory. The measured data were compared with the previous experimental Zr + p, d at 105 and 209 MeV/nucleon data. This comparison represents that the isotopic distribution of production cross sections at 51 MeV p-induced reaction is appreciably different from those at 105 and 209 MeV. On the other hand, these three data sets show that the shape of isotopic distribution is similar in the case of the d-induced reaction. Also, the measured production cross sections were compared with the theoretical model calculations with Particle and Heavy Ion Transport code System (PHITS) version 3.10 in order to investigate the reproducibility of the models implemented in PHITS. The calculations well reproduced the experimental data even in such low incident energy, while several discrepancies were still seen as in the pand d-induced reactions at 105 and 209 MeV/nucleon.


Introduction
The treatment of high-level radioactive waste (HLW) is one of the crucial issues concerning nuclear power generation. The geological disposal has been advanced as the first candidate for the option of its disposal, however there is still the risk of long-term radiotoxicity. To resolve this situation, nuclear transmutation has been proposed as a powerful tool to give a new option for the HLW disposal for the last several decades. In recent years, a series of nuclear data measurements for long-lived fission products (LLFPs) has been performed in Japan in order to accumulate the basic data necessary to design nuclear transmutation system for LLFPs [1][2][3][4][5][6]. Isotope-production cross sections in pand d-induced reactions on 93 Zr, which is a typical LLFP with its half-life of 1.5 × 10 6 years, have been measured at the reaction energies of 105 and 209 MeV/nucleon, and theoretical model analyses with the intra-nuclear cascade model and evaporation model have been performed so far [1,2]. As a next step, it is of our in- * e-mail: knakano@aees.kyushu-u.ac.jp terest to investigate the incident energy dependence of isotopic distribution of production cross sections by further measurements in the lower incident energy region where the spallation reaction is no more dominant.
In the present work, isotope-production cross sections for 93 Zr were measured at the reaction energy of approximately 50 MeV/nucleon using the inverse-kinematics method. The measured cross sections are compared with those measured previously at 105 and 209 MeV/nucleon, and the incident energy dependence of isotopic distributions is discussed. In addition, theoretical model calculations are compared with the measured data for benchmarking of the models in the low incident energy region.

Experiment
The experiment was performed at RIKEN RI Beam Factory (RIBF). The BigRIPS RI beam separator was used for separation and identification of the secondary beam, and ZeroDegree Spectrometer (ZDS) was used for identification of the reaction products [7]. First, an accelerated 238 U primary beam up to 345 MeV/nucleon impinged onto a 3-mm-thick 9 Be production target located at the entrance of BigRIPS to produce the secondary cocktail beam via the in-flight fission. Next, the secondary beam was purified and identified via the TOF−Bρ − ∆E method [8] at the first-and secondhalves of BigRIPS, respectively. Figure 1 shows a twodimensional identification plot for the secondary beam by the atomic number Z and the mass-to-charge ratio A/Q, and 93 Zr was clearly identified. The purity and typical count rate of 93 Zr were 57.8% and 980 count per second, respectively.
Then the secondary beam impinged onto the reaction targets. As the reaction targets, cooled H 2 and D 2 gases pressurized to 4 atm were used. The thicknesses of H 2 and D 2 gases were 20.2 and 34.5 mg/cm 2 , respectively. The incident energy of 93 Zr was 51 MeV/nucleon at the center of the H 2 target and was 52 MeV/nucleon at the center of the D 2 target. The reaction products were also identified at ZDS using a method similar to that for the secondary beam. To cover the wide range of produced isotopes, nine different Bρ settings for ZDS were adopted. Figure 2 represents the identification plot for the reaction products from the H 2 reaction target. Since the fragments have lower kinetic energy than those in the previous measurements [1,2], they easily pick up electrons and change their charge states. As a result, reaction products with a few charge states, i.e., fully-stripped, hydrogen-like, and helium-like fragment, were observed in Fig. 2. The isotope-production cross section for each reaction product was derived from the yields of incident 93 Zr beam and each isotope produced with each charge state by subtracting the contribution from beamline materials which can be estimated by the empty target runs.

Results and Discussion
The red circles in Figs. 3 and 4 show the measured isotope-production cross sections for the p-induced re- action at 51 MeV (σ p51 ) and the d-induced reaction at 52 MeV/nucleon (σ d52 ) on 93 Zr, respectively. The error bars indicate the statistical uncertainties. The σ p51 and σ d52 data were obtained for 17 and 20 nuclides, respectively. It should be emphasized that the inverse-kinematics enables us to obtain systematic isotope-production data including not only short-lived nuclei but also stable ones.

Energy dependence
The isotope-production cross sections measured in the present work were compared with the previous experimental data in order to investigate the energy dependence of isotope production. The previously measured data at 105 and 209 MeV/nucleon [1,2] are displayed by the black triangles (σ p105 and σ d105 ) and the blue squares (σ p209 and σ d209 ) in Figs 3 and 4, respectively. Four following differences are observed among the three data sets. To begin with, in Fig. 3 (b) and (c), the lower mass limits of σ p51 distribution end at larger mass number than those of σ p105 and σ p209 , resulting in the narrow distribution. The measured range of the cross section is restricted by the lower limit of measurable cross section and by the acceptance of ZDS. Since incident particle with higher kinetic energy can remove more nucleons than that with lower kinetic energy, the isotopic distribution of σ p51 has such a narrower range than the previous data. Next, σ p51 have much larger production cross sections near the target nucleus 93 Zr. These nuclei are mainly produced via the fusion-evaporation process where incident particle is captured by the target nuclei and subsequently deexcited with emission of several particles. In the lower incident energy case, such process is largely enhanced. As a result, Nb and Zr isotopes with large-mass number have much larger cross sections than those in the higher incident energy cases. Then, in Fig. 3 (c), σ p51 for Y isotopes show a very different trend from σ p105 and σ p209 . In particular, 87 Y has quite large production cross section in σ p51 , and the unique behavior is observed in the Y isotopic chain. This indicates that the production of 87 Y is enhanced in the incident energy of around 50 MeV. Finally, in the previous data, the productions of 90 Zr and 89 Y were enhanced due to closed shell effect at the neutron magic number N = 50, resulting in discontinuous jumps at 90 Zr and 89 Y. Although isotopic distribution of Zr shows a jump between 90 Zr and 91 Zr, no clear jump is seen in Y isotopes regardless of the presence of jumps in σ p105 and σ p209 .
As for the d-induced reaction shown in Fig. 4, the distributions of σ d52 , σ d105 , and σ d209 have similar shape. In terms of their quantities, the Nb and Zr isotope-production cross sections decrease with an increase in incident energy. In contrast, Sr isotope-production cross sections increase with an increase in incident energy. As mentioned above, the Nb and Zr isotopes which are near the target nucleus 93 Zr are largely produced by the fusion-evaporation process which is dominant in nuclear reactions at lower kinetic energies. On the other hand, the production of Sr isotopes, which requires much particle emissions like a spallation reaction, is enhanced in the higher incident energy cases. As a result, the dependence of isotope-production cross sections on incident energy has a different tendency in each isotopic chain. Finally, these three data sets show jumps at the neutron magic number N = 50 in both Zr and Y isotopes.

Comparison with theoretical calculation
The measured isotope-production cross sections were compared with theoretical model calculations with Particle and Heavy Ion Transport code System (PHITS) version 3.10 [9,10] as shown in Fig. 5. In the PHITS calculation, the nuclear reaction is assumed to proceed as a two-step process, that is, the intra-nuclear cascade process modeled as incoherent nucleon-nucleon collisions and the evaporation process where pre-fragments deexcite with  [11] and the Generalized Evaporation Model (GEM) [12] were employed for each process to calculate the isotope-production cross section in PHITS. Although INCL-4.6 model was developed for nuclear reactions having the kinetic energy above several hundred MeV, the calculations well predict the measured isotopic distributions of production cross sections even in the 50 MeV/nucleon data. However, they show some discrepancies seen in the 105 and 209 MeV/nucleon cases. First, the calculations are shifted by one-mass number to the heavy side in the distribution of the Nb isotopeproduction cross sections in both of the pand d-induced reactions. Next, the calculations overestimate the production cross sections near the target nucleus 93 Zr. Also, the exaggerated even-odd staggering is observed in calculated Sr isotopes in the d-induced reaction regardless of weak staggering of the measured data. These discrepancies are also pointed out in the previous studies [1,2], and they still appear over the range of these incident energy. Finally, the calculated isotopic distribution of Y has a sharp rise seen at the mass number of 87, but underestimates the production cross section.

Conclusions
We have measured isotope-production cross sections for pand d-induced reactions on long-lived fission product 93 Zr at approximately 50 MeV/nucleon at RIKEN RIBF. The energy dependence of isotopic distribution of production cross sections were investigated for both of the reactions. In the d-induced reaction, three data sets showed similar tendency but different quantities each other. In the p-induced reaction, in contrast, a narrower distribution was observed in 51 MeV data compared with the higher incident energy cases due to the insufficient energy to knock out and/or emit many nucleons. Also, the measured isotope-production cross sections were compared with the calculations by PHITS version 3.10 employing INCL-4.6 model plus GEM. The comparison represented an overall agreement even in approximately 50 MeV/nucleon case. However, several discrepancies were seen in the present data as in the data measured at 105 and 209 MeV/nucleon. In the future, continuous expansions to wider incident energy ranges will be required especially in lower incident energy such as 30 and/or 20 MeV/nucleon for comprehensive understanding of the reaction process.