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Nuclear reaction cross-sections were obtained by means of activation and identification of the radioactive products. Details were described in numerous publications [2–5]. Here only some salient features are presented that are relevant to present measurements.
Natural titanium foils, whose purity and thickness are 99.99% and 2.98–3.0 mm, respectively, were used to make circular samples with a diameter of 20 mm. They each were placed between thin niobium disks of the same diameter of 20 mm, whose purity is 99.99% and thickness is 1 mm.
Irradiation of the samples was carried out at the K-400 Neutron Generator at the Institute of Nuclear Physics and Chemistry, China Academy of Engineering Physics. Samples were irradiated for 3–7.5 h. The neutrons in the 14 MeV region with a yield of 4 × 1010 n/s to 5 × 1010 n/s were produced by the 3H(d,n)4He reaction with a deuteron beam energy of 255 keV and a beam current of 350 µA. The solid tritium–titanium target used in the generator was about 2.19 mg/cm2 thick. During the irradiation, the neutron flux was monitored by the accompanying α-particles, which were measured with a Au–Si surface barrier detector used in the 135° accompanying a-particle tube, so that corrections could be made for the small fluctuations in the neutron flux. Groups of samples were placed at angles of 0°, 45°, 90°, and 135° respectively, which are relative to the direction of the deuteron beam and centered about the T–Ti target at a distance of 3–5 cm. The neutron energies in the measurements were determined in advance by cross-section ratios for the 90Zr(n,2n)89m+gZr and 93Nb(n,2n)92mNb reactions [6]. The measured neutron energies were 13.5 ± 0.2, 14.1 ± 0.2, 14.4 ± 0.2, and 14.8±0.2 MeV at the irradiation positions of 0°, 45°, 90°, and 135° angles relative to the beam direction, respectively.
After irradiation, the samples were cooled for 28 minutes to 87 hours. The activities of 45Ti,46m+gSc,47Sc,48Sc,47Ca, and 92mNb were measured by a well-calibrated GEM-60P coaxial high-purity germanium (HPGe) detector (crystal diameter 70.1 mm, crystal length 72.3 mm) with a relative efficiency of ~68% and an energy resolution of ~1.69 keV FWHM at 1.33 MeV for 60Co. The samples were measured for 1.5–9.5 h. The efficiency of the detector was pre-calibrated using various standard γ sources. Figure 1 and Fig. 2 show part of the γ-ray spectrum acquired from the titanium samples after a cooling time of about 53 min and 78.73 h, respectively.
Figure 1. (color online) Part of γ-ray spectrum of titanium about 53 m after the end of irradiation.
Figure 2. (color online) Part of γ-ray spectrum of titanium about 78.73 h after the end of irradiation.
The associated decay data of all the activation products and the natural abundance of target isotopes under investigation are summarized in Table 1[7]. The abundance of 93Nb comes from Ref. [8], as no abundance of 93Nb is given in Ref. [7].
reaction abundance of target isotope (%) half-life of product Eγ /keV Iγ (%) 46Ti(n,2n)45Ti 8.25 184.8 m 1408.1 0.085 46Ti(n,p)46m+gSc + 47Ti(n,d*)46m+gSc 8.25a 83.79 d 889.277 99.9840 46Ti(n,p)46m+gSc 8.25 83.79 d 889.277 99.9840 47Ti(n,p)47Sc + 48Ti(n,d*)47Sc 7.44a 3.3492 d 159.381 68.3 47Ti(n,p)47Sc 7.44 3.3492 d 159.381 68.3 48Ti(n,p)48Sc + 49Ti(n,d*)48Sc 73.72a 43.67 h 1312.120 100 48Ti(n,p)48Sc 73.72 43.67 h 1312.120 100 50Ti(n,α)47Ca 5.18 4.536 d 1297.09 67 93Nb(n,2n)92mNb 100b 10.15 d 934.44 99.15 aAbundance of target isotope is that of the first mentioned isotope for the 46Ti(n,p)46m+gSc + 47Ti(n,d*)46m+gSc, 47Ti(n,p)47Sc + 48Ti(n,d*)47Sc, and 48Ti(n,p)48Sc + 49Ti(n,d*)48Sc reactions.
bWe used the value given by Ref. [8].Table 1. Reactions and associated decay data of objective activation products.
We calculated the measured cross-sections by means of the equation proposed by Kong et al.[9].
The cross-sections of the 46Ti(n,2n)45Ti, 46Ti(n,p)46m+gSc + 47Ti(n,d*)46m+gSc, 46Ti(n,p)46m+gSc, 47Ti(n,p)47Sc + 48Ti(n,d*)47Sc, 47Ti(n,p)47Sc, 48Ti(n,p)48Sc + 49Ti(n,d*)48Sc, 48Ti(n,p)48Sc, and 50Ti(n,α)47Ca reactions were acquired relative to those of the 93Nb(n,2n)92mNb reaction. The cross-section values of the monitor reaction 93Nb(n,2n) 92mNb were 457.9 ± 6.8, 459.8 ± 6.8, 459.8 ± 6.8 and 459.7 ± 5.0 mb at the neutron energies of 13.5, 14.1, 14.4, and 14.8 MeV, respectively[10]. The results obtained in this work are summarized in Tables 2-6 and plotted in Figs. 3–10. The cross-sections of the 46Ti(n,2n)45Ti, 46Ti(n,p)46m+gSc + 47Ti(n,d*)46m+gSc,46Ti(n,p)46m+gSc,47Ti(n,p)47Sc + 48Ti(n,d*)47Sc,47Ti(n,p)47Sc,48Ti(n,p)48Sc+ 49Ti(n,d*)48Sc,48Ti(n,p)48Sc, and 50Ti(n,α)47Ca reactions around 14 MeV neutron energy have been obtained by about 20, 6, 18, 4, 18, 3, 34, and 14 laboratories, respectively [1]. The previous measurements, whose results were published after 1980, are also summed up in Tables 2–6 and plotted in Figs. 3–10 for comparison. For these reactions mentioned above, their evaluation cross-section curves of JEFF-3.3, CENDL-3.1, ENDF/B-VIII.0 at neutron energies from the threshold to 20 MeV are plotted in Figs. 3-10 for comparison. The theoretical calculation cross-section data at different neutron energies from the threshold to 20 MeV were calculated via the computer code system Talys-1.9 [11–14]. Default values of parameters are adopted in the calculation. The theoretical calculation values at the neutron energies of 13.5, 14.1, 14.4, and 14.8 MeV are also summarized in Tables 2–6 and the theoretical calculation curves plotted in Figs. 3-10 for comparison.
reaction this work literature values En /MeV σ /mb En /MeV σ /mb reference 46Ti(n,2n)45Ti 14.1 ± 0.2 13.3 ± 1.0 (37.8c) 14.7 47 ± 2 [15] 14.4 ± 0.2 37.8 ± 2.8 (54.8c) 14.7 47 ± 2 [16] 14.8 ± 0.2 53.2 ± 3.2 (91.9c) 13.63 0.182 ± 0.029 [17] 13.73 0.894 ± 0.059 [17] 14 8.77 ± 0.48 [17] 14.47 28.9 ± 1.6 [17] 14.72 42 ± 2.3 [17] 15.01 54.9 ± 3 [17] 14.6 51 ± 2 [18] 14.8 33 ± 6.6 [19] 13.5 2.2 ± 0.2 [20] 13.77 7.5 ± 0.6 [20] 14.1 17.7 ± 1.3 [20] 14.39 30.9 ± 2.3 [20] 14.66 42 ± 3.2 [20] 14.78 50.2 ± 3.8 [20] c Theoretical calculation cross-section data obtained from Talys-1.9. Table 2. Summary of the cross section for the 46Ti(n,2n)45Ti reaction around 14 MeV neutron energy.
reaction this work literature values En /MeV σ /mb En /MeV σ /mb reference 46Ti(n,p)46m+gSc + 47Ti(n,d*)46m+gSc 13.5 ± 0.2 289.9 ± 15.1 (212.9 c) 13.447 289.3 ± 10.3 [21] 14.1 ± 0.2 280.6 ± 11.8 (234.3 c) 13.921 296.2 ± 10.7 [21] 14.4 ± 0.2 262.4 ± 11.9 (244.0 c) 14.126 286.8 ± 13.5 [21] 14.8 ± 0.2 251.1 ± 10.6 (255.8 c) 14.347 287.3 ± 11.2 [21] 14.921 292.6 ± 10.9 [21] 14.7 311 ± 7.5 [22] 13.5 306 ± 15 [23] 13.84 286 ± 14 [23] 14.18 299 ± 13 [23] 14.38 305 ± 13 [23] 14.67 294 ± 12 [23] 14.81 305 ± 12 [23] 13.39 305 ± 18 [24] 13.43 312 ± 19 [24] 14.36 299 ± 18 [24] 14.39 294 ± 18 [24] 14.7 304 ± 10 [25] 46Ti(n,p)46m+gSc 13.5 ± 0.2 275.1 ± 14.4 (183.6c) 13.33 274 ± 14 [17] 14.1 ± 0.2 247.8 ± 10.5 (180.9c) 13.56 264 ± 14 [17] 14.4 ± 0.2 218.2 ± 9.9 (163.6c) 13.98 253 ± 13 [17] 14.8 ± 0.2 192.1 ± 8.1 (157.0c) 14.42 240 ± 12 [17] 14.65 234 ± 13 [17] 14.91 210 ± 14 [17] 14.7 261 ± 27 [26] 13.77 302 ± 33 [27] 13.93 291 ± 38 [27] 14.11 302 ± 33 [27] 14.3 298 ± 34 [27] 14.73 298 ± 34 [27] 14.83 267 ± 39 [27] 14.05 267.8 ± 9.3 [28] 13.68 282 ± 13.9 [29] 14.58 284.7 ± 14 [29] 14.8 226.2 ± 22.4 [30] 14.8 266.7 ± 3.2 [31] 13.77 310 ± 33 [32] 13.93 297 ± 38 [32] 14.11 310 ± 33 [32] 14.3 306 ± 37 [32] 14.47 242 ± 33 [32] 14.73 306 ± 34 [32] 14.83 275 ± 39 [32] c Theoretical calculation cross-section data obtained from Talys-1.9. Table 3. Summary of cross sections for 46Ti(n,p)46m+gSc+47Ti(n,d*)46m+gSc and 46Ti(n,p)46m+gSc reactions around 14 MeV neutron energy.
reaction this work literature values En /MeV σ /mb En /MeV σ /mb reference 47Ti(n,p)47Sc + 48Ti(n,d*)47Sc 13.5 ± 0.2 169.3 ± 6.8 (274.2c) 13.447 173.8 ± 4.9 [21] 14.1 ± 0.2 197.6 ± 8.3 (262.3c) 13.921 197.6 ± 5.7 [21] 14.4 ± 0.2 228.0 ± 9.6 (244.3c) 14.126 203.2 ± 5.9 [21] 14.8 ± 0.2 259.6 ± 10.9 (241.2c) 14.347 224.3 ± 6.8 [21] 14.921 267.8 ± 8 [21] 14.7 257 ± 12 [25] 14.1 220 ± 5 [33] + 13.75 164 [34] 13.92 186 [34] 14.11 186 [34] 14.31 192 [34] 14.49 218 [34] 14.76 256 [34] 14.86 271 [34] 47Ti(n,p)47Sc 13.5 ± 0.2 151.0 ± 6.1 (273.0c) 13.33 144.5 ± 9.7 [17] 14.1 ± 0.2 146.9 ± 6.2 (257.5c) 13.56 143.9 ± 9.7 [17] 14.4 ± 0.2 153.3 ± 6.5 (236.5c) 13.98 135.5 ± 9.2 [17] 14.8 ± 0.2 133.6 ± 5.7 (226.0c) 14.42 130.5 ± 8.9 [17] 14.65 127.1 ± 8.7 [17] 14.91 121.5 ± 8.4 [17] 14.7 151 ± 4 [26] 14.73 142 ± 21 [27] 14.83 131 ± 15 [27] 14.6 174.5 ± 13.1 [30] 14.8 169.5 ± 7.0 [31] 14.0 103 ± 10 [35] 14.3 158 ± 9 [36] 14.9 142 ± 12 [36] 14.8 103 ± 10 [37] c Theoretical calculation cross-section data obtained from Talys-1.9. Table 4. Summary of cross-sections for 47Ti(n,p)47Sc+48Ti(n,d*)47Sc and 47Ti(n,p)47Sc reactions around 14 MeV neutron energy.
reaction this work literature values En /MeV σ /mb En /MeV σ /mb reference 48Ti(n,p)48Sc + 49Ti(n,d*)48Sc 13.5 ± 0.2 58.6 ± 2.5 (95.9c) 14.7 68.7 ± 2.1 [25] 14.1 ± 0.2 58.4 ± 2.5 (104.2c) 14.8 73 ± 3.5 [38] 14.4 ± 0.2 60.4 ± 2.6 (108.1c) 14.8 ± 0.2 60.5 ± 2.5 (111.0c) 48Ti(n,p)48Sc 13.5 ± 0.2 58.6 ± 2.5 (95.1c) 13.33 55.3 ± 2.6 [17] 14.1 ± 0.2 58.2 ± 2.5 (102.1c) 13.57 54.7 ± 2.6 [17] 14.4 ± 0.2 60.2 ± 2.6 (104.4c) 13.98 57.8 ± 2.8 [17] 14.8 ± 0.2 60.1 ± 2.5 (104.2c) 14.67 60.4 ± 2.9 [17] 14.93 59.6 ± 2.9 [17] 13.447 63.31 ± 2.23 [21] Table 5. Summary of cross-sections for 48Ti(n,p)48Sc+49Ti(n,d*)48Sc and 48Ti(n,p)48Sc reactions around 14 MeV neutron energy.
Table 5 – continued from previous page reaction this work literature values En /MeV σ /mb En /MeV σ /mb reference 13.921 67.18±2.54 [21] 14.126 63.5±2.42 [21] 14.347 67.75±2.71 [21] 14.921 62.46±2.59 [21] 13.5 61.3±2.8 [23] 13.84 62.4±2.8 [23] 14.18 64.4±2.7 [23] 14.38 65.7±2.7 [23] 14.67 63.5±2.6 [23] 14.81 65.6±2.6 [23] 14.7 76±2 [26] 13.77 51±3 [27] 13.99 53±3 [27] 14.11 55±3 [27] 14.3 55±3 [27] 14.47 55±3 [27] 14.73 60±3 [27] 14.83 58±3 [27] 14.05 58.6±1.8 [28] 13.68 58.7±3.1 [29] 14.36 61.3±3.4 [29] 14.58 62.8±3.2 [29] 14.77 63.4±3.7 [29] 14.8 61.1±6.7 [30] 14.8 71.7±2.7 [31] 13.77 51±3 [32] 13.93 53±3 [32] 14.11 55±3 [32] 14.3 53±3 [32] 14.47 55±3 [32] 14.73 61±3 [32] 14.83 56±3 [32] 14 68±2.6 [33] 14.1 63±2 [33] 14.0 60±4 [35] 14.3 72±3 [36] 14.9 69±6 [36] 14.8 60±4 [37] 14.6 67±4 [39] 14.5 66 [40] 14.66 69.4 [40] 14.8 67.6 [40] 14.85 67.5 [40] 14.9 66.3 [40] 14.8 60±5 [41] c The theoretical calculation cross-section data by using the computer code system Talys-1.9. reaction this work literature values En /MeV σ /mb En /MeV σ /mb reference 50Ti(n,α)47Ca 13.5 ± 0.2 5.75 ± 0.35 (2.01c) 13.35 6.37 ± 0.62 [17] 14.1 ± 0.2 7.94 ± 0.42 (2.51c) 13.58 6.68 ± 0.46 [17] 14.4 ± 0.2 8.46 ± 0.48 (2.97c) 13.99 7.01 ± 0.7 [17] 14.8 ± 0.2 9.47 ± 0.99 (3.53c) 14.68 9.31 ± 0.78 [17] 14.95 10.41 ± 0.88 [17] 13.5 6.6 ± 0.5 [23] 13.84 7.4 ± 0.5 [23] 14.18 8 ± 0.5 [23] 14.38 8.9 ± 0.5 [23] 14.67 9.6 ± 0.5 [23] 14.81 9.5 ± 0.6 [23] 14.7 8.5 ± 0.5 [25] 14.7 11 ± 2 [26] 14.8 9 ± 0.8 [31] 14.6 8.6 ± 0.6 [39] 13.6 6.41 ± 0.68 [42] 13.68 6.54 ± 0.72 [42] 14.1 7.55 ± 0.73 [42] 14.46 8.37 ± 0.75 [42] 14.72 9.22 ± 0.61 [42] 14.86 9.8 ± 0.98 [42] 13.43 6.6 ± 0.5 [43] 14.36 7.9±0.6 [43] c Theoretical calculation cross-section data obtained from Talys-1.9. Table 6. Summary of cross-section for 50Ti(n,α)47Ca reaction around 14 MeV neutron energy.
The complete description of TALYS can be found in the Talys-1.9 manual [11]. TALYS is a computer code system built for the analysis and prediction of nuclear reactions based on physics models and parameterizations [11-13]. It is a versatile tool for the analyses of basic microscopic scientific experiments or for generation of nuclear data for applications. It can simulate nuclear reactions involving neutrons, photons, protons, deuterons, tritons, 3He, and α-particles in the 0.001–200 MeV energy range and for target nuclides of mass of 12 and heavier. To deal with the neutron induced nuclear reactions, we use the optical model. All optical model calculations are performed by ECIS-06 [14], which is implanted as a subroutine in Talys.
The cross-sections of the 46Ti(n,p)46m+gSc + 47Ti(n,d*)46m+gSc reaction were calculated using the equation proposed by Kong et al. [9]. The abundance of the target isotope is equal to that of the first mentioned isotope. The contribution of the 48Ti(n,t)46m+gSc reaction was neglected because of its tiny cross-section (10–7 mb). The cross-sections of the 46Ti(n,p)46m+gSc reaction were computed using the equation proposed by Kong et al. [9], subtracting the contribution of the 47Ti(n,d*)46m+gSc reaction with its evaluated values (16.20, 36.02, 48.40, and 64.61 mb at the neutron energies of 13.5, 14.1,14.4, and 14.8 MeV, respectively) from JEFF-3.3. We ignored the contribution of the 48Ti(n,t)46m+gSc reaction due to its tiny cross-section (10−7 mb).
The cross-sections of the 47Ti(n,p)47Sc + 48Ti(n,d*)47Sc reaction were computed using the same method as above. The contribution from the 50Ti(n,α)47Ca→47Sc decay was subtracted using a formula similar to the one used to reduce the influence of an excited state on the ground state in Ref. [44], and the contribution of the 49Ti(n,t)47Sc reaction was neglected due to its tiny cross-section (on the order of μb). The cross-sections of the 47Ti(n,p)47Sc reaction were computed through the equation proposed by Kong et al. [9] subtracting the contribution from the 50Ti(n,α)47Ca→47Sc decay and the contribution of the 48Ti(n,d*)47Sc reaction with its evaluated values (1.84, 4.77, 7.46, and 12.28 mb at the neutron energies of 13.5, 14.1,14.4, and 14.8 MeV, respectively) from JEFF-3.3. We ignored the contribution of the 49Ti(n,t)47Sc reaction due to its tiny cross-section value (on the order of μb).
The cross-sections of the 48Ti(n,p)48Sc + 49Ti(n,d*)48Sc reaction were also calculated using the same method as above. The contribution of the 50Ti(n,t)48Sc reaction was neglected due to its tiny cross-section (10−9 mb). The cross-sections of the 48Ti(n,p)48Sc reaction were computed by equation proposed by Kong et al. [9], subtracting the contribution of the 49Ti(n,d*)48Sc reaction with its evaluated values (0.60, 1.67, 2.71, and 4.64 mb at the neutron energies of 13.5, 14.1, 14.4, and 14.8 MeV respectively) from JEFF-3.3. We overlooked the contribution of the 50Ti(n,t)48Sc reaction due to its tiny cross-section (10−9 mb).
Activation cross-sections of titanium isotopes at neutron energies of 13.5–14.8 MeV
- Received Date: 2019-03-26
- Available Online: 2019-09-01
Abstract: The cross-sections for 46Ti(n,2n)45Ti, 46Ti(n,p)46m+gSc+47Ti(n,d*)46m+gSc, 46Ti(n,p)46m+gSc, 47Ti(n,p)47Sc+48Ti(n,d*)47Sc, 47Ti(n,p)47Sc, 48Ti(n,p)48Sc+49Ti(n,d*)48Sc,48Ti(n,p)48Sc, and 50Ti(n,α)47Ca reactions were investigated around neutron energies of 13.5–14.8 MeV by means of the activation technique. Fast neutrons were produced by the 3H(d,n)4He reaction. Neutron energies from different directions in the measurements were obtained in advance using the method of cross-section ratios for 90Zr(n,2n)89m+gZr and 93Nb(n,2n)92mNb reactions. The results obtained are analyzed and compared with the experimental data provided by the literature and verified nuclear data in the JEFF-3.3, CENDL-3.1, ENDF/B-VIII.0 libraries, as well as results calculated by Talys-1.9 code.