Double differential light charged particle emission cross sections for some structural fusion materials

In fusion reactors, neutron induced radioactivity strongly depends on the irradiated material. So, a proper selection of structural materials will have been limited the radioactive inventory in a fusion reactor. First-wall and blanket components have high radioactivity concentration due to being the most fluxexposed structures. The main objective of fusion structural material research is the development and selection of materials for reactor components with good thermo-mechanical and physical properties, coupled with low-activation characteristics. Double differential light charged particle emission cross section, which is a fundamental data to determine nuclear heating and material damages in structural fusion material research, for some elements target nuclei have been calculated by the TALYS 1.8 nuclear reaction code at 14–15 MeV neutron incident energy and compared with available experimental data in EXFOR library. Direct, compound and pre-equilibrium reaction contribution have been theoretically calculated and dominant contribution have been determined for each emission of proton, deuteron and alpha particle.


Introduction
Fusion reactors need proper structural materials to become an efficient source of energy, especially if the promise of a green machine is to be maintained.Reactor components, such as first wall, divertor and blanket, are subjected not only to the high-energy neutron impact, but also to strong mechanical, heat and electromagnetic loadings.Activation characteristics of candidate materials are important in classification as low activation elements (C, Si, Ti, Fe, Cr and V) and as high activation materials (Al, Ni, Ag, Co and Nb) [1][2][3][4].The choice of the materials depends not only on mechanical properties, compatibility with other materials and irradiation performance, but also on their radiological properties [5][6][7].The aim of the fusion structural material research studies is to develop fusion reactor structural materials with good thermo-mechanical and physical properties coupled with low-activation characteristics.
In a fusion reactor neutrons carry most of the energy produced by the D-T fusion reaction.Those neutrons lose their energy by interacting with reactor devices such as the blanket through various nuclear reactions and the heat produced by these nuclear reactions is called "nuclear heating" and is estimated by a simulation calculation in a reactor design.One of the essential data for simulation calculation is the energy and angular distributions of charged particles emitted by a nuclear reaction.These distributions are called "double differential cross section (DDX) data".The DDX of light charged particle emission have been investigated by several researches both experimentally [8][9][10][11][12][13][14][15][16] and theoretically [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32].
In this study, the DDX for the emission of alpha and proton induced by 14.8 MeV neutrons from 50,52 Cr and 58,60 Ni, and by 15.0 MeV neutrons for 46,48 Ti target nuclei have been calculated using TALYS 1.8 code and the results have been compared with the available experimental data in literature.

Calculation methods
TALYS 1.8 code has been used in DDX calculation according to pre-equilibrium exciton model, direct model and compound nucleus formation [33].The TALYS 1.8 code is able to analyze and predict nuclear reactions induced by up to 1 GeV light particles (A ≤ 4) for target nuclei heavier than lithium [34].The two-component exciton model developed by Kalbach [35] was used for calculating the pre-equilibrium contribution while the compound nucleus was calculated by the Hauser-Feshbach model [36].Direct reaction calculation is obtained via the ECIS-97 [37] code which is implemented as a subroutine in TALYS.

Results and conclusions
The DDX (d 2 σ /d .dE)for the emission of p and α particles at emission angles 30  , 75 • and 135 • for 46,48 Ti target nuclei for incident neutron energy of 15.0 MeV have been calculated using TALYS 1.8 nuclear reaction code.The calculated energy distribution of the emitted light charged particles has been compared with available experimental data of Grimes et al. [38] taken form the EXFOR [39] nuclear data library.
There is a good agreement between the DDX results theoretically calculated using TALYS 1.8 and the experimental data of Grimes et al. [38].Further, the   48 Ti with the experimental data of Grimes [38].
variation in the DDX with the emission angle indicates that the emission of alpha and proton shows similar distribution to the isotropic distribution.
The theoretically calculated and experimental DDX of alpha emission for (n,α) reactions on 46 Ti, 48 Ti, 50 Cr, 52 Cr, 58 Ni and 60 Ni target nuclei at incident neutron energy of 14.8 or 15.0 MeV are shown in Figs.1-6 respectively.
Theoretically calculated DDX for the emission of alpha particles from 46 Ti(n,α) and 48 Ti(n,α) reactions at 15.0 MeV (Figs. 1, 2) shows that the alpha particles up to the most probable energies are emitted predominantly through the compound nucleus formation whereas the higher energy alpha particles are emitted through the preequilibrium or the direct reaction.While the compound contribution is dominant up to 8 MeV and the preequilibrium process is in the range of 8-12 MeV at 45 • alpha emission angle, the emission probabilities are very low for energetic alpha particles at 135 • emission angle.
The calculated and experimental DDX of alpha emission for 50 Cr(n,α) and 52 Cr(n,α) reactions at 14.8 MeV are shown in Figs. 3 and 4, respectively.The compound contribution is more dominant in 52 Cr target nucleus than 50 Cr and increases with increasing angle for both target nuclei.The pre-equilibrium contribution is dominant in the range of 8-12 MeV at 30 • and 45 • alpha emission angles for 50 Cr target nucleus.The higher energy alpha particles are emitted through the direct reaction.The DDX of proton emission are compared with experimental data [38] at incident neutron energy 15.0 MeV as shown in Figs.7 and 8.The calculated results of DDX for proton emission are mainly from the   contribution of the compound emission.While the preequilibrium emission contribution is observed after 7 MeV proton emission energy for forward emission angles, it is observed after 9 MeV proton emission energy for 135 • backward emission angle.The direct reaction contribution to the proton emission in 46 Ti target nucleus is not as much as in 48 Ti for the energetic proton emission.
The experimental and calculated DDX of proton emissions are compared at incident neutron energy    contribution of the compound emission.While the direct emission contribution is observed after 12 MeV for proton emission energy for 60 Ni target nucleus, it is not directly observed for 58 Ni target nucleus.

Conclusion
The compound, direct and pre-equilibrium emissions complete the description of the light charged particle emission over the full energy range.TALYS calculations agree quite well with the experimental data of Grimes et al. [38] for proton and alpha emission.The graphs show that for almost all light charged particles emission, compound contribution is dominant.While a strong component from the pre-equilibrium process is present at low emission energy, contribution of direct emission becomes dominant at higher energy for proton emission.In addition, the direct emission contribution arises from the decay of residual nuclei as known.The shapes of the DDX distribution show that nuclear reaction models require a good description of the energy-differential cross sections.

Figure 1 .
Figure 1.The comparison of calculated DDX of (n,α) reaction on 46 Ti with the experimental data of Grimes [38] available in EXFOR [39].

Figure 2 .
Figure 2. The comparison of calculated DDX of (n,α) reaction on48 Ti with the experimental data of Grimes[38].

Figure 3 .
Figure 3.The comparison of calculated DDX of 50 Cr target nucleus with the experimental data taken from EXFOR [39].

Figure 4 .
Figure 4.The comparison of calculated DDX of 52 Cr target nucleus with the experimental data taken from EXFOR [39].

Figure 5 .
Figure 5.The comparison of calculated DDX of (n,α) reaction on58 Ni with the experimental data of Grimes[38].

Figure 6 .
Figure 6.The comparison calculated double differential alpha emission cross section for 60 Ni target nucleus with the experimental data which are taken from EXFOR [39].

Figure 7 .
Figure 7.The comparison of calculated DDX of (n,p) reaction on 46 Ti with the experimental data reported in literature.Experimental values were taken from EXFOR [39].

Figure 8 .
Figure 8.The comparison of DDX of proton emission for 48 Ti target nucleus with the experimental data which are taken from EXFOR [39].

Figure 9 .
Figure 9.The comparison DDX of proton emission for 50 Cr target nucleus with the experimental data which are taken from EXFOR [39].

Figure 10 .
Figure 10.The comparison DDX of proton emission for 52 Cr target nucleus with the experimental data which are taken from EXFOR nuclear library [39].

Figure 11 .
Figure 11.The comparison of DDX of (n,p) reaction on 58 Ni with the experimental data taken from EXFOR [39].

14. 8 Figure 12 .
Figure 12.The comparison DDX of proton emission for 60 Ni target nucleus with the experimental data taken from EXFOR [39].