Introduction

The FaNGaS (Fast Neutron induced Gamma-ray Spectrometry) instrument [1,2,3] installed at Heinz Maier-Leibnitz Zentrum (MLZ) offers the possibility to perform non-destructive elemental analysis of samples of various sizes origins by means of Prompt Gamma Analysis based on Inelastic Neutron Scattering PGAINS as we are going to call the method from now on. This analytical technique focuses on the measurement of prompt gamma radiation emitted from inelastic scattering of fission neutrons, i.e. (n,n′γ) reactions. In some cases, prompt gamma rays induced by other reactions like (n,pγ), (n,αγ) or (n,γ) as well as delayed gamma rays of activation products formed by the aforementioned reactions can be detected as well. At MLZ, fission neutrons are generated from a uranium converter (93% of 235U) plugged into the heavy water moderator of the research reactor FRM II (Forschungs-Neutronenquelle Heinz Maier-Leibnitz). An intense beam of fission neutrons with an average energy of 2.18 MeV is extracted from the beamtube SR10 (Strahlrohr 10) into the MEDAPP (Medical Application) irradiation room via a set of filters and collimators. A well-shielded electromechanically-cooled n-type HPGe-detector of 50% relative efficiency is used for the detection of the neutron-induced gamma rays. Gamma-ray spectra are recorded at an angle of 90° with respect to the axis of the incident neutron beam.

To perform a precise elemental analysis of samples by means of the PGAINS technique, reliable and accurate information on the fission-neutrons induced (n,n′γ) reactions, i.e. the gamma-ray energies and the gamma-ray production cross sections, is crucial. Such data are also required in other fields of nuclear science and technology [4]. With the aim of developing a comprehensive database on (n,n′γ) reactions, prompt gamma rays induced by fission neutrons on carbon, oxygen, aluminum, chlorine, calcium, titanium, iron, copper, indium, cerium and terbium were measured with the FaNGaS instrument and their associated fission-neutron spectrum-averaged production cross sections were determined [2, 3, 5,6,7,8]. Relative intensities of the gamma rays were found to agree reasonably with the values provided by the only existing database for (n,n′γ) reactions: the “Atlas of Gamma-ray spectra from the Inelastic Scattering of Reactor Fast Neutrons” published by Demidov et al. in 1978 [9]. However, our measurements performed at FRM II show the need for a careful reevaluation of the data compiled in [9].

In the present work, the results from the measurement of gamma rays induced by interaction of fission neutrons with nickel and zirconium are presented and compared to the data given in [9]. Additionally, the elemental detection limits for both elements are given.

Theory

Prompt gamma rays induced by inelastic scattering and radiative capture reactions, i.e. (n,n′γ) and (n,γ) reactions, of fission neutrons on nickel and zirconium isotopes and by fast neutron capture reactions like 58Ni(n,pγ)58Co and 58Ni(n,npγ)57Co were measured. The integral rate \(\left\langle {\varvec{R}} \right\rangle\) (atom−1 s−1) and the effective (spectrum-averaged) cross sections σ (cm2) of the aforementioned reactions were estimated as follows:

$$\left\langle R \right\rangle = \mathop \sum \limits_{i} \sigma \left( {E_{i} } \right) \cdot\Phi \left( {E_{i} } \right){ }$$
(1)

and:

$$\left\langle \sigma \right\rangle = \frac{{\left\langle R \right\rangle }}{{\sum\nolimits_{i} \Phi \left( {E_{i} } \right)}}$$
(2)

where \(\Phi \left( {E_{i} } \right)\) is the neutron flux in the neutron energy bin i and σ(Ei) the reaction cross section averaged over the neutron energy bin i. The neutron-energy spectrum determined at sample position by means of the foil activation technique [2] is shown in Figs. 1 and 2. The neutron flux for each energy bin is given in Table 1 in the supplementary materials. The fission neutrons generated by the converter passed through a series of materials (1.7 mm H2O, 2.5 mm D2O, 2 cm Al–Mg alloy, 3 m air, 5 cm Pb and 1 cm B4C) that down scattered a small fraction of the neutrons making the low-energy side of the spectrum harder compared to a pure 235U fission spectrum [10]. The average neutron energy is calculated to 2.18 ± 0.06 MeV which is significantly higher than the expected value of 2.00 ± 0.01 MeV [11]. This may be due to the coarse energy binning used in the determination of the neutron energy spectrum. The spectrum is split into three regions defined as thermal (10−10 MeV < Ei < 1.42 10−7 MeV), epithermal (1.42 10−7 MeV < Ei < 0.06 MeV) and fast (0.06 MeV < Ei < 20 MeV) with the respective fluxes, (9.4 ± 2.8) × 102 cm−2 s−1, (1.85 ± 0.09) × 106 cm−2 s−1 and (1.40 ± 0.05) × 108 cm−2 s−1. The integral neutron flux is (1.42 ± 0.05) × 108 cm−2 s−1. The limits of the regions were chosen to match the binning of the calculations. The σ(Ei)-values of the investigated reactions were generated from the ENDF/B-VIII.0 [12] nuclear data library using the RECONR, BROADR and GROUPR modules of the NJOY Nuclear Data Processing System (Version 2016) [13, 14]. Their neutron-energy dependence is shown together with the neutron-energy spectrum in Fig. 1. The integral reaction rates R and the effective cross sections σ obtained by means of Eqs. (1) and (2), respectively, for the epithermal and fast region of the neutron spectrum are given in Table 1. The rates of (n,γ) reactions induced by thermal neutrons were neglected because of the low thermal neutron flux. The effective cross sections obtained for the fast neutrons σfast are comparable with the values evaluated for a fission spectrum (kT = 1.35 MeV) given in JANIS (java-based nuclear data information software) Book of neutron-induced cross sections [15]. The differences might be related to the deviation of the fission neutron spectrum from a Watt spectrum. The (n,γ) reaction is mainly induced by the fast neutrons for 58Ni, 60Ni, 64Ni, 90Zr, 92Zr and 94Zr. In the case of 61Ni, 62Ni, 91Zr and 96Zr the rates produced by capture of epithermal and fast neutrons represent roughly 40% and 60% of the total rate, respectively. The rates of the (n,n′)-reactions for nickel and zirconium isotopes are roughly two orders of magnitude higher than the corresponding (n,γ)-reactions rates. The rates of the 58Ni(n,p)58Co and 58Ni(n,np)57Co reactions are 3.5 and 950 times lower than the rate of the 58Ni(n,n′)58Ni reaction.

Fig. 1
figure 1

Neutron-energy spectrum at sample position (right scale of y-axis) and neutron-energy dependence of the grouped microscopic cross section \(\sigma \left( {E_{i} } \right)\) averaged over the neutron-energy bin i for the investigated reactions on nickel

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Fig. 2
figure 2

Neutron-energy spectrum at sample position (right scale of y-axis) and neutron-energy dependence of the grouped microscopic cross section \(\sigma \left( {E_{i} } \right)\) averaged over the neutron-energy bin i for the investigated reactions on zirconium

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Table 1 Reactions rates \(R\) and effective cross sections ‹σ› for the investigated reactions calculated by mean of Eqs. (1) and (2), respectively
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Experimental

Prompt gamma radiation generated by fission neutrons on pure nickel (m = 2.81 g, S = 3.5 × 3.5 cm2) and zirconium (m = 1.11 g, S = 2.6 × 2.6 cm2) foils of natural composition was investigated with the FaNGaS set-up described in [2]. The foils with a thickness of 0.025 cm were irradiated with their surface perpendicular to the neutron beam of quadratic shape (6 × 6 cm2). The fast-neutron flux at sample position was (1.40 ± 0.05) × 108 cm−2 s−1. The irradiation time was 10 h for nickel and 14.5 h for zirconium. The gamma-ray spectra were collected during neutron irradiation for 7 h and 11.4 h (live times), respectively. The measurement was performed at an angle of 90° between neutron beam axis and spectrometer and with a sample-to-detector distance of 67 cm. The spectra were analyzed with the software HYPERMET-PC [18]. Previous beam background analysis [2] was considered for identification and correction of possible interferences. The spectra of the nickel and zirconium foils are shown together with the beam background in Figs. 3, 4 and 5, respectively. Due to the scattering of fission neutrons towards the detector, the count rates of background lines are increased by a mean factor of 1.39 ± 0.19 for nickel and 1.21 ± 0.02 for zirconium. These factors were used to correct possible background interferences. Identification of the gamma rays issued from inelastic scattering as well from capture of fission neutrons was done using the database NutDat 3.0 [19] and nuclear data provided in [20,21,22,23,24,25,26,27,28,29,30]. The PGNAA database [31] was used to check the presence of gamma rays from (n,γ) reactions and possible related interferences.

Fig. 3
figure 3

Gamma-ray spectra in the energy range 30–3000 keV recorded during 25,220 s for nickel (red) and 46,454 s for the beam background (black). Prompt gamma rays issued from (n,γ) reactions are written in bold. (Color figure online)

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Fig. 4
figure 4

Gamma-ray spectra in the energy range 3000–9500 keV recorded during 25,220 s for nickel (red) and 46,454 s for the beam background (black). Prompt gamma rays issued from (n,γ) reactions are written in bold. (Color figure online)

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Fig. 5
figure 5

Gamma-ray spectra in the energy range 0–4500 keV recorded during 41,028 s for zirconium (red) and 46,454 s for the beam background (black). Prompt gamma rays issued from (n,γ) reactions are written in bold. (Color figure online)

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Method

The net peak area PEγ of a prompt gamma ray measured at the energy Eγ can be given by:

$$P_{{E\gamma }} = \frac{m}{M}N_{{\text{A}}} h\varepsilon _{{E\gamma }} \left\langle {\sigma _{{E\gamma }} } \right\rangle \Phi t_{c} f_{n} f_{{E\gamma }}$$
(3)

where m (g) is the amount of element, M (g mol−1) the molar mass of the element, NA the Avogadro number, h the abundance of the isotope considered, \(\varepsilon_{E\gamma }\) the full-energy-peak efficiency, \(\sigma_{E\gamma }\) (cm2) the effective isotopic cross section for gamma-ray production, \({\Phi }\) (cm−2 s−1) the neutron flux, tc the counting live time (s) fn the neutron self-shielding factor and \(f_{{E{\upgamma }}}\) the gamma-ray self-absorption factor. As the foils were very thin, the corrections for neutron absorption and multiple scattering were neglected, i.e. fn≈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 [32] as described in [6]. The dependence of the factor for gamma-ray self-absorption \(f_{{E{\upgamma }}}\) on the gamma energy Eγ is shown in Fig. 6 and was approximated to the following semi-empirical function:

$$f_{{E{\upgamma }}} = a_{0} + a_{1} \cdot \left( {1 - e^{{ - a_{2} \cdot E_{\gamma } }} } \right) + a_{3} \cdot\left( {1 - e^{{ - a_{4} \cdot E_{\gamma } }} } \right)$$
(4)

with a0 =  − 1.1448, a1 = 2.0756, a2 = 0.0343, a3 = 0.0497 and a4 = 2.0917·10−3 for the nickel foil, a0 =  − 1.1170, a1 = 2.0326, a2 = 0.0272, a3 = 0.0698 and a4 = 3.5614·10−3 for the zirconium foil and Eγ in keV.

Fig. 6
figure 6

Dependence of the gamma-ray self-absorption factor \(f_{{E{\upgamma }}}\) on the gamma energy Eγ for the nickel and zirconium foils. The solid lines represent the fit of the data with Eq. (4). (Color figure online)

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Possible interferences from prompt gamma rays induced by (n,γ)-reactions were evaluated by means of Eq. (3) setting the isotopic abundance to one (h = 1) and using, instead of the isotopic cross section \(\sigma_{E\gamma }\), the elemental cross section \(\sigma_{E\gamma }^{Z}\) which is estimated as

$$\left\langle {\sigma _{{E\gamma }}^{Z} } \right\rangle = \sigma _{{E\gamma ,{\text{th}}}}^{Z} \cdot \frac{{\left\langle {\sigma _{0} } \right\rangle }}{{\sigma _{{0,{\text{th}}}} }}$$
(5)

where \(\sigma_{E\gamma ,th}^{Z}\) is the elemental cross section for production of prompt gamma rays by thermal neutron capture [31], \(\sigma_{{0,{\text{th}}}}\) the elemental thermal neutron capture cross section (\(\sigma_{{0,{\text{th}}}}\) = 4.39 ± 0.15 b for nickel, \(\sigma_{{0,{\text{th}}}}\) = 190 ± 30 mb for zirconium [31]) and \(\sigma_{0}\) the effective elemental cross section derived from the isotopic cross sections \(\left\langle {\sigma_{{{\text{int}}}} } \right\rangle\) given in column 6 of Table 1. The resulting values of \(\left\langle {\sigma_{0} } \right\rangle\) are 6 ± 1 mb for nickel and 10 ± 2 mb for zirconium.

The intensity of the gamma rays of nickel and zirconium, respectively, were calculated relative to the element-specific reference gamma line used in [9]. The relationship between the measured intensities (IR) and the intensities (IRD) determined in [9] was analyzed with the following semi-empirical function:

$$I_{R} = a \cdot \left( {I_{RD} } \right)^{b}$$
(6)

with a and b the coefficients obtained by the fit of the data. Additionally, the consistency between the two sets of data was deduced from the distribution of the residuals in unit of standard deviation [σ], calculated, as:

$$r = \frac{{I_{R} - I_{RD} }}{{\sqrt {\left( {s_{{I_{R} }} } \right)^{2} + \left( {s_{{I_{RD} }} } \right)^{2} } }}$$
(7)

with s is the absolute uncertainty of the intensity.

Gamma rays induced in nickel

One hundred sixty-seven prompt gamma lines from the interaction of fission neutrons with nickel were identified, 128 associated to (n,n′γ)-, 32 to 58Ni(n,pγ)58Co-, 5 to (n,γ)- and 2 to 58Ni(n,n + pγ)57Co-reactions. From the 128 (n,n′γ) reactions 41 lines were assigned to 58Ni, 48 to 60Ni, 15 to 61Ni, 18 to 62Ni and 6 to 64Ni. Concerning the 5 (n,γ)-lines, 3 were associated to 58Ni, 2 to 60Ni and 1 to 62Ni. The gamma rays are listed in Tables 2, 3, 4, 5, 6, 7 and 8, respectively. All lines given in [9] were detected except the weak lines of 58Co at 312.9 keV from the 365.7-keV level [21] and of 58Ni at 383.5 keV from the 3420.4-keV level [21] due to the high background at the corresponding energies. These lines are reported in the NuDat 3.0 database and the fact that the strongest gamma from each level (365.6 keV for 58Co, 961.3 keV for 58Ni) were also detected in our measurement makes Demidov’s assignments plausible. Additional lines, which are mentioned in NuDat 3.0, were identified in our spectrum:

  • 1301.3, 1731.4, 1834.6, 1923.4, 2343.8, 2461.0 and 5816 keV for 58Ni,

  • 120.9, 936.5, 1035.3, 1165.1, 1364.9, 1418.9, 1428.9, 1637.7, 1657.4, 1660.0, 1711.7, 1743.3, 1758.4, 1865.2, 2177.1, 2376.5, 2673.1, 2397.3, 2554.2, 2745.0, 4007.2, 4019.6 keV for 60Ni,

  • 947.3, 1131.7, 1184.8, 1541.6, 1633.1, 1666.5, 1918.8, 1958.0, 2581.6, and 3711.9 keV for 61Ni,

  • 755.7, 875.6, 1128.2, 1163.2, 1717.8, 1172.4, 1885.9, 2002.7, 2047.7, 2083.3, 2096.5, 2105.3, 2300.6, 2351.2, 2582.8, 2799.7 and 3368.5 keV for 62Ni,

  • 878.2, 1263.3, 1807.7 and 2971.6 keV for 64Ni,

  • 58.7, 111.8, 727.5, 932.2, 943.2, 987.8, 999.1, 1148.7, 1242.1, 1416.2, 1435.5, 1488.2, 1493.9, 1628.5, 1645.21, 1749.4, 1814.0 and 1867.9 keV for 58Co.

Table 2 Gamma rays of 58Ni induced by inelastic scattering of fission neutrons
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Table 3 Gamma rays of 60Ni induced by inelastic scattering of fission neutrons
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Table 4 Gamma rays of 61Ni induced by inelastic scattering of fission neutrons
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Table 5 Gamma rays of 62Ni induced by inelastic scattering of fission neutrons
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Table 6 Gamma rays of 64Ni induced by inelastic scattering of fission neutrons
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Table 7 Gamma rays of 58Co induced by the 58Ni(n,p)58Co reaction
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Table 8 Counts of radiative capture lines of nickel and zirconium calculated by means of Eq. (3) and measured counts
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The counts of radiative capture lines calculated by means of Eqs. (1) and (2) are compared with the measured values in Table 8. For the lines at 6837.5, 7819.5, 8120, 8533.5 and 8999.4 keV, the calculated and the measured values agree with each other by taking into account their respective uncertainties. This result indicates the reliability of the determined effective cross section of nickel and that the branching ratios of radiative capture lines seem to be independent of the neutron energy as previously observed in our work on indium [6]. The lines at 282.9 and 877.9 keV were found to interfere significantly with the (n,n′γ)-lines of 61Ni and 64Ni at same energy with contributions to the net counts of 9 ± 2 and 25 ± 2%, respectively. In the case of the 339.4- and 464.9-keV lines, radiative capture contributes to 8 ± 1 and 65 ± 12% of the net counts indicating they are also produced by additional reactions, but other than (n,n′γ)- or (n,pγ)- reactions as for the latter no gamma rays at the corresponding energies are reported in NuDat 3.0. Note that an unassigned strong line at 339 keV can also be observed in the nickel spectrum measured by Demidov et al. [9]. In addition, the energy resolution of their detector was not good enough to detect a line at 465 keV close to the 466-keV line of 60Ni. Concerning the 126.8-keV line detected in our spectrum, we exclude the fact that it could correspond to the delayed line at 127.1 keV (IEγ = 16.7% [19]) of 57Ni (T1/2 = 35.60 h) induced by 58Ni(n,2n)57Ni due to the very low value of the fission spectrum averaged cross section of this reaction, 7.0 ± 0.6 μb [15]. Therefore, according to Nudat 3.0, this line as well as the 464.9-keV line could probably be associated to 57Co produced by the 58Ni(n,np)57Co reaction. The energy threshold of this reaction is around 8 MeV [15] and the effective activation flux integrated in the range 8 to 20 MeV is 7.1 ± 0.3 105 cm−2 s−1. However, the 127-keV line is not detected in Demidov’s measurement probably due to a lower neutron flux above 8 MeV in their reactor neutron spectrum.

The intensities of the gamma lines were calculated using the 1454-keV line as reference (100%), and they were compared with the values determined in [9] in Tables 2, 3, 4, 5, 6 and 7. The relationship between the intensities is shown in Fig. 7 and is expressed by Eq. (6) with a = 0.88 ± 0.03 and b = 0.97 ± 0.03. The histogram of the residuals r calculated from Eq. (7) is given in Fig. 7. The fit of the histogram with a Gaussian shows an agreement between the data at the 0.7σ level, indicating a good consistency. The fission-neutron spectrum-averaged isotopic cross sections for gamma-ray production calculated by means of Eq. (3) with a flux of 1.40 × 108 cm−2 s−1 are given in column 4 of Tables 2, 3, 4, 5, 6 and 7.

Fig. 7
figure 7

Comparison of the relative intensities of the prompt gamma rays induced by fast neutrons on nickel obtained in this work with the data tabulated in the Demidov Atlas [9]. Left figure: linear relationship; the solid line represents the fit of the data with Eq. (6). Right figure: histogram of the residuals r in units of standard deviation [σ] calculated with Eq. (7). The values of r are given in column 8 of Tables 2, 3, 4, 5, 6 and 7. The solid line represents the fit of the data with a Gaussian

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Gamma rays of zirconium

A total of 99 prompt gamma lines induced by inelastic scattering of fission neutrons with zirconium were identified, 31 related to 90Zr, 17 to 91Zr, 24 to 92Zr, 19 to 94Zr and 8 to 96Zr (see Tables 9,10,11,12 and 13). Additionally, the delayed gamma lines at 132.7 keV (Iγ = 4.13% [24]) and 2318 9 keV (Iγ = 82.0% [24]) of the activation product 90mZr produced by the 90Zr(n,n′)90mZr were observed. The capture line of 91Zr at 2557 keV was detected, free of any interferences. Most of the gamma lines given in [9] were measured and additional lines that are reported in NuD at 3.0 were detected:

  • 132.3, 828.0, 1255.4, 1584.1, 1755.0, 1913.0, 1937.0, 1952.6, 2013.2, 2050.3, 2054.6, 2239.9, 2280, 2269.5 keV for 90Zr

  • 150.8, 1068.7, 1151.6, 1619.0, 2577.5, 2774.8 keV for 91Zr

  • 257.2, 902.2, 1247.5, 1384.9, 1442.7, 1675.1, 1741.2, 1932.2, 1974.0, 1987.6, 2326.5, 2693.3, 2871.0, 3470.7 keV for 92Zr

  • 1134.9, 1154.7, 1161.1, 1390.6, 1778.6, 1928, 1968.2, 2236.5, 2845.2 keV for 94Zr

  • 474.8, 687.4, 770,4, 779.2, 1184.9 keV for 96Zr

Table 9 Gamma rays of 90Zr induced by inelastic scattering of fission neutrons
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Table 10 Gamma rays of 91Zr induced by inelastic scattering of fission neutrons
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Table 11 Gamma rays of 92Zr induced by inelastic scattering of fission neutrons
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Table 12 Gamma rays of 94Zr induced by inelastic scattering of fission neutrons
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Table 13 Gamma rays of 96Zr induced by inelastic scattering of fission neutrons
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Gamma lines given at energies 213.8, 338.0 and 1065.7 in [9] were not detected in our spectrum. It should be mentioned here that the 213.8- and 1065.7-keV lines were assigned to hafnium in [9] (178Hf, 179Hf, 180Hf for 213.8 keV and 180Hf for 1065.7 keV) due to possible impurities in the zirconium sample. Also, note that an unassigned line at around 325 keV can be observed in Demidov’s spectrum that could correspond to the 325.6 keV line of 178Hf. The 338-keV line was assigned to the 3076-keV 4+ level in 90Zr by Demidov, which is plausible since the 890-, and 331 keV lines deexciting the same level were identified. However, the intensity of the 388-keV line relative to the 890-keV line, 29%, is considerably higher than the reported value in NuDat 3.0, 0.9%. Thus, this line could correspond rather to the 339-keV line of 179Hf. In our measurement, the neutron capture lines at 1205.6, 1880.4, 2042.2 and 2577.3 keV of 90Zr and at 560.9, 934.5 and 1405.1 of 91Zr were found to interfere significantly with the (n,n′γ)-lines of same energies. Their contributions to the net counts were calculated by means of Eqs. (3) and (5) (see Table 8) and were corrected accordingly. The intensities of the lines calculated relative to the 934.5-keV line of 92Zr (100%) are given with the values determined in [9] in Tables 9, 10, 11, 12 and 13. The relationship between the values is expressed by the relation described by Eq. (6) with a = 1.01 ± 0.06 and b = 0.95 ± 0.03 as shown in Fig. 8. The fit of the histogram of the residuals r with a Gaussian shows an agreement between the data at the 1.3σ level, indicating a good consistency (Fig. 8). The fission-neutron spectrum-averaged isotopic cross sections for gamma-ray production calculated by means of Eq. (3) with a flux of 1.40 × 108 cm−2 s−1 are given in column 4 of Tables 9, 10, 11, 12 and 13. From the delayed gamma rays of 90mZr at 132.7 and 2318.9 we derive a fission-neutron spectrum-averaged cross section of 88 ± 8 mb for the 90Zr(n,n′)Zr90m reaction.

Fig. 8
figure 8

Comparison of the relative intensities of the prompt gamma rays induced by fast neutrons on zirconium obtained in this work with the data tabulated in the Demidov Atlas [9]. Left figure: linear relationship; the solid line represents the fit of the data with Eq. (6). Right figure: histogram of the residuals r in units of standard deviation [σ] calculated with Eq. (7). The values of r are given in column 8 of Tables 9, 10, 11, 12 and 13. The solid line represents the fit of the data with a Gaussian

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Detection limit

The detection limit (DL) corresponds here to the smallest amount of pure element that can be detected. It was calculated neglecting gamma self-absorption and neutron self-shielding by means of Eq. (3) using the minimum peak area \(P_{E\gamma } \left( {\text{c}} \right)\) which is defined for the case of an interference-free gamma line by [33]:

$$P_{{E{\upgamma }}} \left( c \right) = \frac{{\sqrt {2 \cdot B_{{E{\upgamma }}} } }}{c}$$
(7)

with \(B_{{E{\upgamma }}}\) the area of the background below the gamma line of interest and c a predefined value for the relative uncertainty of the peak area.

The DL of nickel and zirconium were determined from their most intense gamma lines at 1453.6 keV (58Ni, \(\sigma_{E\gamma } \left( {90^\circ } \right)\) = 338 mb) and 933.8 keV (92Zr, \(\sigma_{E\gamma } \left( {90^\circ } \right)\) = 1068 mb), respectively, for a counting time of 12 h and for c = 0.5 corresponding to a peak area uncertainty of 50%. Here, the value of \(B_{E\gamma }\) was extracted from the beam background spectrum measured with the new version of the FaNGaS instrument [3] which delivers a fast neutron flux at sample position of 1.13 × 108 cm−2 s−1. In this case, the smallest amounts of nickel and zirconium that can be detected are 0.7 mg and 1.4 mg, respectively.

Conclusions

Prompt gamma rays induced by (n,n′γ)-, (n,pγ)-, (n,npγ)- and (n,γ)-reactions on nickel and by (n,n′γ) and (n,γ) on zirconium were measured with the FaNGaS instrument operated at FRM II and their relative intensities and fission-neutron spectrum-averaged partial production cross sections were determined. In total, 167 prompt gamma lines were observed for nickel. From these, 128 were associated to (n,n′γ) reactions (41 from 58Ni, 48 from 60Ni, 15 from 61Ni, 18 from 62Ni and 6 from 64Ni), 32 to 58Ni(n,p)58Co reaction, 2 to 58Ni(n,n + p)57Co reaction and 5 to (n,γ) reactions (3 from 58Ni, 2 from 60Ni, and 1 from 62Ni). In the case of zirconium, 100 prompt gamma lines were detected, 99 assigned to (n,n′γ) reactions (31 from 90Zr, 17 from 91Zr, 24 from 92Zr, 19 from 94Zr and 8 from 96Zr) and 1 to the 90Zr(n,γ)91Zr reaction. Additionally, delayed gamma lines of 90mZr formed by the 90Zr(n,n′)90mZr reaction were observed. Compared to the work of Demidov et al. [9], 126 gamma lines were detected additionally (78 for nickel and 48 for zirconium). The relative intensities of the lines measured in our work agree reasonably (0.7σ level for nickel, 1.3σ level for zirconium) with the corresponding values given in [9]. For the 90Zr(n,n′)90mZr reaction we determine an effective cross section of 88 ± 8 mb. The detection limits of nickel and zirconium are 0.7 and 1.4 mg, respectively, for a counting time of 12 h with the actual version of the FaNGaS instrument.