Prompt gamma rays from fast neutron inelastic scattering on aluminum, titanium and copper

Prompt gamma rays induced by inelastic scattering of fast neutrons on aluminum, titanium and copper were measured at an angle of 90o between fast neutron beam and detector of the instrument FaNGaS, operated by Jülich Centre of Neutron Science at Heinz-Maier-Leibnitz Zentrum in Garching. The fast neutron flux was 1.40 108 cm−2 s−1 with the average energy of 2.30 MeV. Intensities and neutron spectrum averaged isotopic partial cross section for production of 214 gamma lines (22 for aluminum, 72 for titanium and 120 for copper) are presented. The results are consistent with the literature data. However, the new sets of gamma lines are recommended to replace the old datasets from fast neutrons reactors with several new lines also recognizing a few false identifications. Additionally, the detection limits of aluminum, titanium, copper, iron and indium were determined as 1.0, 0.4, 0.9, 0.5 and 1.3 mg, respectively, for a counting time of 12 h.


Introduction
FaNGaS (Fast Neutron induced Gamma-ray Spectrometry) is a unique instrument which uses the intense fission neutron beam delivered by the SR10 channel (Strahlrohr 10) of the research reactor FRM II (Forschungs-Neutronenquelle Heinz Maier-Leibnitz) to investigate fast-neutron induced prompt gamma-ray emission [1,2]. FaNGaS offers new possibilities for the chemical analysis of large or small samples as a complementary method to conventional thermal-or coldneutron based PGAA (Prompt Gamma Activation Analysis). Furthermore, it has an ultimate goal to create a modern and comprehensive data catalogue on (n,n´γ)-reactions. Fast neutrons are generated by thermal neutron fission of 235 U in uranium silicide converter plates immersed in the reactor pool. The fast neutron beam is extracted through a beam port and a set of collimators into an irradiation room. The detection of neutron-induced gamma radiation is performed with a well shielded high-purity germanium detector positioned perpendicular to the neutron beam axis. In previous works we reported on the prompt gamma-rays induced by fast neutrons on iron [3] and on the prompt and delayed gamma rays produced by epithermal and fast neutrons on indium [4]. In this work, the results from the measurement of aluminum, titanium and copper are presented and compared to the data provided in the "Atlas of Gamma-rays from the Inelastic Scattering of Reactor Fast Neutrons" published in 1978 by Demidov et al. [5]. Additionally, the detection limits of the elements investigated in this work as well as of iron and indium were determined.

Experimental
Prompt gamma radiation induced by inelastic scattering of fast neutrons on pure aluminum (m = 0.343 g, S = 2.3 × 2.3 cm 2 ), titanium (m = 0.772 g, S = 2.6 × 2.6 cm 2 ) and copper (m = 0.583 g, S = 1.6 × 1.6 cm 2 ) foils of natural composition, 1 3 respectively, was studied with the FaNGaS set-up described in [3]. The foils with a thickness of 0.025 cm were irradiated with their surface perpendicular to the neutron beam of quadratic shape (6 × 6 cm 2 ). The fast neutron flux at sample position was (1.40 ± 0.05) × 10 8 cm −2 s −1 and the average neutron energy 2.30 MeV. The irradiation time was 9.7 h for aluminum, 8.2 h for titanium and 11.8 h for copper. The gamma-ray spectra were collected during neutron irradiation for 8.0, 6.5 and 9.5 h (live times), respectively. The measurement was performed at an angle of 90° between neutron beam axis and spectrometer at a sample-to-detector distance of 67 cm. The spectra were analyzed with the software HYPERMET-PC [6]. Previous beam background analysis [3] was taken into account for gamma lines identification and correction of possible interferences. Part of the spectra and beam background in the energy range 750-3050 keV, are shown in Fig. 1. The scattering of fast neutrons towards the detector leads to an increase of the count rates of background lines by mean factors of 1.10 ± 0.05 for aluminum, 1.27 ± 0.09 for titanium and 1.22 ± 0.08 for copper. These factors were used for correcting possible background interferences. The assignment of the gamma rays to the corresponding isotopes was carried out using the database NutDat 3.0 [7] and nuclear data provided in [8][9][10][11][12][13][14][15].

Method
The net peak area P E of a gamma ray of energy Eγ may be expressed by the following relation: where m (g) is the amount of element, M (g mol −1 ) the molar mass of the element, N A the Avogadro number, h the abundance of the isotope considered, E the full energy peak efficiency, ⟨ E ⟩ (cm 2 ) the fast neutron spectrum averaged isotopic cross section for gamma-ray production, Φ (cm −2 s −1 ) the fast neutron flux, f n a factor for neutron self-shielding and f E a factor for gamma-ray self-absorption. For prompt gamma rays the term g t b , t c , t 1∕2 reduces to t c the counting (live) time. For delayed gamma rays emitted from the decay of activation products it may be expressed by: where t b is the irradiation (real) time, and t 1∕2 the half-life of activation product.
The value of ⟨ E ⟩ is connected to the effective cross section ⟨ ⟩ of the considered reaction through the absolute intensity of the gamma ray I E , including the contribution of internal conversion, as: In the case of (n,n´γ)-reactions ⟨ E ⟩ depends on the measurement angle, i.e. the angle between the neutron beam direction and the detector owing to the anisotropy of the gamma emission.
As the foils are very thin, the corrections for neutron absorption and multiple scattering can be neglected, i.e. f n ≈1. The gamma-ray self-absorption of the foils was determined numerically using the Monte Carlo transport simulation code PHITS (Particle and Heavy Ion Transport code System) Version 3.02 [16] as described in [4]. The dependence of the factor for gamma-ray self-absorption f E on the gamma energy Eγ is shown on Fig. 2 and was approximated with the following semi-empirical function: The parameters a i obtained from the fit of the data with relation (4) are given in Table 1.
The intensity of the gamma rays of aluminum, titanium and copper, respectively, were calculated relative to the element-specific reference gamma line used in [5]. The relationship between the measured intensities ( I R ) and the intensities ( I RD ) determined in [5] was analyzed with the following semi-empirical function: with a and b the coefficients returned by the fit of the data. Additionally, the consistency between the sets of data was derived from the distribution of the residuals in unit of standard deviation [σ], calculated, as: Possible interferences from delayed gamma rays of activation products induced by (n,p) and (n,α) reactions were evaluated by means of Eq. (1) and (2) using the reaction cross sections for a fission spectrum given in [17] and in the case of aluminum and titanium those determined in [3].

Gamma rays of aluminum
Twenty two prompt gamma lines due to inelastic scattering of fast neutrons on aluminum were measured (see Table 2). In comparison with the work of Demidov et al. [5] one additional gamma line at 3395.6 keV was detected. The gamma lines listed at energies 2371.7, 2664.5 and 2940.6 keV in [5] are not observed in our measurement. However, they are reported in the database NuDat 3.0 at Al(n,α) 24 Na reaction were found to interfere significantly with the prompt gamma lines of same energy. Their contributions to the net count rates were estimated to 4.0 ± 0.2%, 39 ± 3% and 54 ± 4%, respectively. The intensities of the corresponding aluminum gamma rays were corrected accordingly. The intensities of the gamma rays were calculated relative to the 1014-keV line (100%), and they are given with the values determined in [5] in Table 2. The relationship between the relative intensities is shown in Fig. 3a and is expressed by Eq. (5) with a =0.94 ± 0.05 and b =1.01 ± 0.03. The histogram of the residuals R calculated from Eq. (6) is given in Fig. 4a. Its fit with a Gaussian shows an agreement between the data at the 0.7σ level, indicating a good consistency. The ⟨ E ⟩-values calculated by means of Eq. (1) are given in column 4 of Table 2.  [5] were not observed. These lines are not mentioned in the database NuDat 3.0 except the 1614-keV line whose placement in the level scheme of 48 Ti is uncertain. It should be mentioned here that the unobserved lines other than the 138.4-keV line were earlier reported as tentative assignments by Demidov and were not placed in any titanium decay scheme. The fact that they are not observed in our measurement helps provide support that they do not belong to titanium. The 138.4-keV gamma was assigned to the 3358.9-keV 3 − level in 48 Ti by Demidov. However, no similar energy gamma from the corresponding level  is reported in NuDat 3.0, even though it is conceivable that a gamma of this energy could be associated with an electric-dipole (E1) transition from this 3 − level to the 3224-keV 3 + level. Such a transition was not observed in our measurement which agrees with NuDat 3.0 but is at odds with Demidov´s findings. Interferences from delayed gamma rays of activation products induced by (n,p) and (n,α) reactions were found to be negligible. The intensities of the gamma rays calculated relative to the 983.5-keV line of 48 Ti (100%) are given with the values determined in [5] in Tables 3, 4, 5 and 6. The relationship between the values is expressed by relation Eq. (5) with a =0.98 ± 0.04 and b =1.06 ± 0.03 as shown in Fig. 3b. The fit of the histogram of the residuals R with a Gaussian shows an agreement between the data at the 0.8σ level, indicating a good consistency (Fig. 4b).

Gamma rays of titanium
The ⟨ E ⟩-values are given in Tables 3, 4, 5 and 6.

Gamma rays of copper
A total of 120 prompt gamma lines induced by inelastic scattering of fast neutrons on copper were identified, 82 associated to 63 Cu and 38 to 65 Cu. (see Tables 7 and 8). Further, the 156-keV prompt gamma line of 63 Ni produced by the 63 Cu(n,p) 63 Ni reaction was also observed. On the other hand, the 525-keV line assigned in [5] to 63 Ni was not observed. This line is also not reported in the database NuDat 3.0. Most likely it was a background line that was observed during the Demidov´s measurement, thus, it is not expected to be observed in the absence of interference. Most of the Eγ is the gamma-ray energy, P Eγ /ε Eγ ·f Eγ the net count in the gamma-ray peak divided by the full-energypeak efficiency and the gamma-ray self-absorption factor,I R the relative intensity of the gamma-ray and ⟨σ Eγ ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at an angle of 90° between neutron beam and detector determined with Eq. (1). R is the residual calculated by means of Eq.   3 Relationship between the relative intensities I R of the prompt gamma rays induced by fast neutron inelastic scattering on a aluminum, b titanium and c copper measured in this work and the relative intensities I RD tabulated in Demidov Atlas [5]. The solide line represents the fit of the data with Eq. (5) Fig. 4 Comparison of the relative intensities of the prompt gamma rays induced by fast neutron inelastic scattering on a aluminum, b titanium and c cooper obtained in this work with the data tabulated in Demidov Atlas [5] in the form of a histogramm of the residuals R in unit of standard deviation [σ] calculated with Eq. (6). The values of R are given in Tables 1, 2, 3, 4, 5, 6 and 7. The solid line represents the fit of the data with a Gaussian Eγ is the gamma-ray energy, P Eγ /ε Eγ ·f Eγ the net count in the gamma-ray peak divided by the full-energypeak efficiency and the gamma-ray self-absorption factor,I R the relative intensity of the gamma-ray and ⟨σ Eγ ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at an angle of 90° between neutron beam and detector determined with Eq. (1). R is the residual calculated by means of Eq. (6) This  Eγ is the gamma-ray energy, P Eγ /ε Eγ ·f Eγ the net count in the gamma-ray peak divided by the full-energypeak efficiency and the gamma-ray self-absorption factor,I R the relative intensity of the gamma-ray and ⟨σ Eγ ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at an angle of 90° between neutron beam and detector determined with Eq.  Eγ is the gamma-ray energy, P Eγ /ε Eγ ·f Eγ the net count in the gamma-ray peak divided by the full-energypeak efficiency and the gamma-ray self-absorption factor,I R the relative intensity of the gamma-ray and ⟨σ Eγ ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at an angle of 90° between neutron beam and detector determined with Eq. (1). R is the residual calculated by means of Eq. (6) This   [5] in Tables 7 and 8. The relationship between the values is expressed by Eq. (5) with a =0.95 ± 0.03 and b =1.02 ± 0.03 as shown in Fig. 3c. The fit of the histogram of the residuals R with a Gaussian shows an agreement between the data at the 0.7σ level, indicating a good consistency (Fig. 4c). The ⟨ E ⟩-values are given in Tables 7 and 8.

Detection limit
Neglecting any neutron and absorption effects, the detection limit (DL) representing here the smallest amount of pure element that can be detected was calculated by means of Eq. (1) from the minimum peak area P E (c) which can be expressed according to [18] by with B E the area of the background below the gamma line of interest and c a predefined value for the relative uncertainty of the peak area. In the case of the presence of an interfering line P E (c) can be given by where P int is the net area of the interfering peak. The detection limits of the elements investigated in this work as well as those of iron and indium were determined from their most intense gamma lines for a counting time of 12 h and for c = 0.5 corresponding to a peak area uncertainty of 50% using the beam background spectrum. The fast neutron flux is 1.40 10 8 cm −2 s −1 and the sample-to-detector distance 67 cm. In this case, the smallest amount of pure element that can be detected is 0.4 mg for titanium ( 48 Ti, Eγ = 982.9 keV, ⟨ E ⟩ = 627 mb), 0.5 mg for iron ( 56 Fe, Eγ = 846.9 keV, ⟨ E ⟩ = 586 mb), 0.

Conclusions
The measurement of prompt gamma rays induced by inelastic scattering of fast neutrons on aluminum, titanium and copper was conducted with the FaNGaS instrument operated at FRM II. The fast neutron flux at sample position was 1.40 10 8 cm −2 s −1 . The detection of gamma rays was performed at an angle of 90° between the neutron beam and the spectrometer. A total of 22, 72 and 120 prompt gamma lines were Eγ is the gamma-ray energy, P Eγ /ε Eγ ·f Eγ the net count in the gamma-ray peak divided by the full-energypeak efficiency and the gamma-ray self-absorption factor,I R the relative intensity of the gamma-ray and ⟨σ Eγ ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at an angle of 90° between neutron beam and detector determined with  Eγ is the gamma-ray energy, P Eγ /ε Eγ ·f Eγ the net count in the gamma-ray peak divided by the full-energypeak efficiency and the gamma-ray self-absorption factor,I R the relative intensity of the gamma-ray and ⟨σ Eγ ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at an angle of 90° between neutron beam and detector determined with Eq. (1). R is the residual calculated by means of Eq.  observed for aluminum, titanium and copper, respectively, and their relative intensities and spectrum-averaged production cross sections were determined. In comparison with the work of Demidov et al. [5], 57 gamma lines were detected additionally (1 for aluminum, 19 for titanium and 37 for copper). We also found that 18 lines (1 for aluminum, 10 for titanium and 4 for copper) were incorrectly assigned in [5]. These lines are not specified in the database NuDat 3.0. The Eγ is the gamma-ray energy, P Eγ /ε Eγ ·f Eγ the net count in the gamma-ray peak divided by the full-energypeak efficiency and the gamma-ray self-absorption factor,I R the relative intensity of the gamma-ray and ⟨σ Eγ ⟩ the fast neutron spectrum averaged isotopic cross section for gamma ray production at an angle of 90° between neutron beam and detector determined with relative intensities of the prompt gamma lines measured in our work are in good agreement (0.7σ level) with the values given [5]. The detection limits of aluminum, titanium, iron, copper and indium are around 1 mg for a counting time of 12 h which is acceptable in view of the chemical analysis of large samples with the FaNGaS instrument.
Funding Open Access funding enabled and organized by Projekt DEAL.

Conflict of interest
The authors have no competing interests to declare that are relevant to the content of this article.
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