2.1 Samples and irradiations

Neodymium oxide powder (purity: 99.95%) was pressed at 10 t/cm² into disk samples (diameter: ~12.7 mm, thickness: ~1.6 mm). Two such disks were prepared. The masses of the samples were 1.7 and 1.6 g. Monitor foils of aluminum (Al)(purity: 99.9%, thickness: 50 μm) and standard niobium (Nb) and zirconium (Zr)(purity: 99.99%, thickness: 0.5 mm) with the same size as the Nd sample disk were placed on the front and back surfaces of each sample, which was covered by a polyethylene bag. A cadmium (Cd) foil was covered the sandwiched sample to capture the scattered thermal neutrons during the irradiation.

The bombardment was performed at the 14 MeV neutron generator, OKTAVIAN, in the Division of Sustainable Energy and Environmental Engineering of Osaka University, Japan. In brief, an energetic deuteron beam with 250 μA@265 keV bombarded a T-Ti target to produce 14 MeV energy region neutrons via a T(d,n)⁴He reaction. Since the absolute value of neutron flux can be eliminated by neutron activation analysis, the essential factor is the neutron fluctuation, which was monitored during the entire bombardment process. The intensity of the neutron source can be gauged by its neutron yield, which was estimated to be 1.5×10¹¹ neutrons/s by the monitor reaction ²⁷Al(n,α)²⁴Na.

The two samples were mounted at angles of 45° and 85° relative to the direction of the deuteron beam, at a distance of 3.5 cm from the T-Ti target. The sample positions are shown in Fig.1.

Fig.1Full-screen View

(Color online) The sample assembly and its position with the T-Ti target

2.2 Neutron energy

Neutron energy was calibrated via the method of cross-section ratio, i.e., ⁹⁰Zr(n,2n)⁸⁹Zr to ⁹³Nb(n,2n)^92mNb^[33], and was also estimated by the following formula, which is deduced from the Q-equation of the nuclear reaction:

where E_d is the deuteron energy (in MeV), E_n is the neutron energy (in MeV) at detection angle θ, and the Q value is equal to 17.6 MeV. The uncertainty in the neutron energy, estimated to be 0.2 MeV, arises from the diameter of the beam (~20 mm) and sample (12.7 mm), the cross-section ratio of ⁹⁰Zr(n,2n)⁸⁹Zr to ⁹³Nb(n,2n)^92mNb reactions, and the energy loss of deuterons in the thick T-Ti target.

2.3 Measurement of radioactivity

The samples were irradiated for ~8 hours, and then cooled for ~50 minutes to 10 hours before starting the activity measurement. The gamma activities of ¹⁴⁹Nd, ¹⁴⁷Nd and ¹⁴¹Nd were detected by a low-background HPGe gamma ray spectrometer (ORTEC, GMX30P4) that has a relative efficiency of ~68%. The detection efficiency of the spectrometer was calibrated using the standard sources ⁶⁰Co, ¹³⁷Cs, ¹⁵²Eu, and ²⁴¹Am. The detection efficiency ε satisfied the linear relationship lnε=a+blnE_γ^[34,35] with gamma ray energy E_γ. The abundance of the target isotope and its decay data are shown in Table 1^[36].

2.4 Calculation of cross-sections

The theoretical formula for measuring the cross-section using the relative method is given as ^[27,28,37]

where terms with subscript 0 were set as the parameters of the monitoring reaction, and terms with subscript x were set as the parameters of reactions to be tested.

In this formula, ε is the detection efficiency; I_γ is the branching ratio of the characteristic gamma ray; η is the isotopic abundance of the activated nuclide; S is a growth factor of the product nuclide, i.e., S=1-e^-λT where T is the total irradiation time and λ is the decay constant; M is the sample mass; D =e^-λt1-e^-λt2 represents a collection factor where t₁ is the time interval from the end of irradiation to the beginning of the measurement and t₂ is the time interval to the end of the measurement; A is the atomic weight of the activated nuclide; and C is the net count of the particular gamma ray.

F is a correction factor, expressed as

where the three parts (f_c, f_g, and f_s), correspond to coincidence summing, counting geometry, and self-absorption, respectively ^[38].

K is the so-called neutron flux fluctuation correction factor, which is expressed as

where L is the segment number of the divided radiation time interval; Δt_i is the time interval for each segment; T_i is the interval from the end of the i^th segment to the end of bombardment; and Φ_i and Φ are the averaged neutron fluxes during Δt_i and T, respectively.

The uncertainties in this work originate mainly from isotopic abundance, weight of samples, cross-section of the monitor reaction, branching ratio of gamma ray, half-life of the particular nuclide, detector efficiency, self-absorption correction, counting geometry, and counting statistics, as shown in Table 2.

3.1 Experimental results

To focus clearly on the product nuclide of interest when collecting the gamma spectrum, different time parameters were applied that were based on the half-life of particular product. For example, times of ~1 hour for cooling and ~8 hours for measuring were used for ¹⁴⁹Nd and ¹⁴¹Nd; meanwhile, times of ~16 hours for cooling and ~9 hours for measuring were used for ¹⁴⁷Nd.

Figure 2 illustrates a typical gamma ray spectrum accumulated by the activated Nd₂O₃ sample, which was measured for 8 hours after a cooling time of 1 hour from the end of irradiation. In Fig.2, (a) is a full gamma ray spectrum with the characteristic peaks of interest of ¹⁴¹Nd and ²⁴Na, (b) is a partial gamma ray spectrum at low energy with the peaks of ¹⁴⁷Nd and ¹⁴⁹Nd, and (c) is the background spectrum with the gamma rays of ⁴⁰K, which came from the lead chamber. This background was measured for ~8 hours with the Nd₂O₃ sample before irradiation in the chamber.

Fig.2Full-screen View

(Color online) Gamma ray spectra (The x-axis is the gamma ray energy in keV; the y-axis is the counts per channel.)

Four characteristic gamma peaks were marked for the ¹⁴¹Nd and ¹⁴⁷Nd products, and more than ten characteristic gamma peaks were clearly seen for ¹⁴⁹Nd. We chose the common characteristic peaks with the larger branch to deduce the cross-sections. Following the activation formula in Eq.(2), the cross-sections of the three (n,2n) reactions were deduced. In the calculation, the cross-section of the monitor reaction was obtained by fitting the evaluated data from ENDF/B-VII.1^[39]. The deduced cross-sections are summarized in Table 3.

3.2 Discussion

The evaluated data from databases (of ENDF/B-VII.1^[39], CENDL-3.1^[40] and JENDL-4.0^[41]) were used to show the trend of (n,2n) reaction cross-sections for Nd isotopes in the energy region of E_n<20 MeV. Moreover, the results obtained in this work were compared with literature data and with values calculated by the Talys-1.8 code.

The deduced cross-sections are plotted in Figs.3, 4, 5 together with the previous measurements. To facilitate comparison, the values calculated by the Talys-1.8 program and the evaluated data of the above-mentioned databases^[39,40,41] are plotted in the same figures. Figs.3, 4, 5 show that the cross-sections increase as neutron energy increases from the threshold, i.e., 7.4 MeV for ¹⁴⁸Nd(n,2n)¹⁴⁷Nd, 7.3 MeV for ¹⁴⁸Nd(n,2n)¹⁴⁷Nd, and 9.8 MeV for the ¹⁴²Nd(n,2n)¹⁴¹Nd reaction. The increasing trend gradually reaches a maximum value and then decreases with neutron energy. Most of the experimental data are concentrated in the neutron energy region of 13–15 MeV, while a few experimental results are in a broad neutron energy region, e.g., those of Frehaut 1980 ^[19] in the three reactions, Bormann 1970^[23] in the ¹⁴²Nd(n,2n)¹⁴¹Nd reaction, and Do 1984^[18] in the¹⁵⁰Nd(n,2n)¹⁴⁹Nd reaction.

Fig.3Full-screen View

(Color online) The cross-sections of the ¹⁵⁰Nd(n,2n)¹⁴⁹Nd reaction

Fig.4Full-screen View

(Color online) The cross-sections of the ¹⁴⁸Nd(n,2n)¹⁴⁷Nd reaction

Fig.5Full-screen View

(Color online) The cross-sections of the ¹⁴²Nd(n,2n)¹⁴¹Nd reaction

a) ¹⁵⁰Nd(n,2n)¹⁴⁹Nd reaction

Fig.3 shows the deduced cross-sections, as well as the evaluated data from the databases^[39-41], for the ¹⁵⁰Nd(n,2n)¹⁴⁹Nd reaction. Ten measurements (Wille 1960^[9], Menon 1967^[21], Bari 1972^[14], Das 1977^[20], Kumabe 1977^[24], Gmuca 1983^[17], Kasugai 1997^[22], Pu 2004^[25], and Luo 2015^[26]) were in the neutron energy region of 13–15 MeV, while two groups measured the cross-section in a broad energy region (Frehaut 1980 ^[19] in 9–14 MeV, and Do 1984 ^[18] in 12–18 MeV).

The present results are consistent with literature data within the uncertainty except with those of Wille 1960 ^[9]. In that study, a single value was obtained at 14.8 MeV that is approximately 30% higher than those of other groups. In the 9–18 MeV energy region, the excitation curves of the evaluated data from recent studies^[39-41] are similar to the measured results of Do 1984^[18], Kasugai 1997^[22], Frehaut 1978^[19], Pu 2004^[25], and Luo 2015^[26]. The calculated results from the Talys-1.8 code have the same trend but are lower than others in the 13–15 MeV energy region. The present results are consistent with othersbut have a slightly decreasing trend.

b) ¹⁴⁸Nd(n,2n)¹⁴⁷Nd reaction

A few groups have investigated the cross-section of the ¹⁴⁸Nd(n,2n)¹⁴⁷Nd reaction previously (Wille 1960^[9], Prasad 1969^[13], Bari 1972^[14], Qaim 1974^[15], Kumabe 1977^[24], Frehaut 1980^[19], Pu 2004^[25], and Luo 2015^[26]), and those values are all plotted in Fig.4. Our experimental results are in agreement with the values given by Kumabe 1977^[24] and Frehaut 1980^[19], and also consistent with the results of the databases^[39-41] and the Talys-1.8 code in the 13.8–15.0 MeV energy region. The experimental data reported by Luo 2015^[26] and Prasad 1969 ^[13] are slightly lower than ours, but the results of Qaim 1974 ^[15] are higher. The results of Wille 1960^[9], Bari 1972^[14], and Pu 2004 ^[25] deviate greatly.

c) ¹⁴²Nd(n,2n)¹⁴¹Nd reaction

Figure 5 shows the cross-sections of the ¹⁴²Nd(n,2n)¹⁴¹Nd reaction. In general, the results from the present work are consistent with the reported data from Grissom 1966^[11], Dilg 1968^[12], Qaim 1974^[15], Bormann 1970^[23], and Kumabe 1977^[24] and with the evaluated data of the databases^[39,40]. These values are slightly lower than the results of Pu 2004^[25], Das 1981^[20], Sothras 1978^[16], Kasugai 1997^[22] and the evaluated data from JENDL-4.0^[41], and slightly higher than those reported by Gmuca 1983^[17] and Luo 2015^[26]. The results from Wille 1960^[9], Rayburn 1961^[10], and Prasad 1969^[13] deviate greatly from the evaluated data. Values from Frehaut 1980^[19], Bormann 1970^[23] and Luo 2015^[26] have a trend similar to that of the evaluated cross-section curves^[39-41]. The calculated values are lower than other data in the E_n<20 MeV energy region.