14.77 MeV neutron-induced nuclear reaction cross sections for zinc, yttrium, and molybdenum targets

Neutron induced cross section data are important for monitors and structural materials in fusion devices. Yttrium (Y), a grayish white metal, is naturally present as a single stable isotope, ⁸⁹Y. The ⁸⁹Y(n, 2n)^88m+gY nuclear reaction is used to monitor the neutron energy in fusion reactors [1]. Zinc (Zn), a silver-gray metal, is found naturally occurring as five stable isotopes, ⁷⁰Zn(0.61%), ⁶⁸Zn(18.45%), ⁶⁷Zn(4.04%), ⁶⁶Zn(27.73%), and ⁶⁴Zn(49.17%). Molybdenum (Mo) is a silvery white metal found occurring naturally as seven stable isotopes, ¹⁰⁰Mo(9.82%), ⁹⁸Mo(24.39%), ⁹⁷Mo(9.6%), ⁹⁶Mo(16.67%), ⁹⁵Mo(15.84%), ⁹⁴Mo(9.15%), and ⁹²Mo(14.53%). Zinc and molybdenum are used as structural materials in fusion reactors [2]. Additionally, ⁶³Zn and ⁹⁹Mo are important radionuclides. ⁹⁹Mo decays to ^99mTc, which along with ⁶³Zn is used in positron emission tomography [3]. Experimental data in the exchange format (EXFOR) database [4], even if reported at the same neutron energies, differ in the nuclear data (half-life of product, γ-ray intensity, and monitor cross section data) and detector used for gamma ray spectrometry. This can lead to disagreement between earlier measurements and recently reported cross sections upon normalization with the updated nuclear databases. In addition, there is a requirement for measured cross sections to be reported with covariances. Therefore, it is important to improve the accuracy by remeasuring cross sections for reactions where discrepancies exist between experimental data and evaluated data.

This paper includes a detailed description of the experimental setup, sample preparation, methodology for induced activity measurements, and uncertainty estimation. Moreover, a brief outline of nuclear model calculations with the TALYS-1.96 [5] and EMPIRE-3.2.3 [6] nuclear codes is provided. The results were compared with the previous measurements and evaluated nuclear data libraries [1, 7, 8].

Samples of pure Zn metal (99.99%) powder, Y₂O₃ (99.99%) powder, and MoO₃ (99.99%) powder of natural isotopic abundance were prepared by packing known weights of sample powder into polythene vials. The samples were sandwiched between two aluminum foils of known weight, and the sample size was 10 mm × 10 mm. Details on the isotopic abundance, weight, thickness, and density of the samples are summarized in Table 1. The samples were irradiated at the 14 MeV Neutron Generator facility [9], Department of Physics, Savitribai Phule Pune University, Pune, India. The 14 MeV neutron beam was produced by bombarding ~150 keV D⁺ ions on an 8 Ci TiT (titanium-tritide) solid target. The temperature of the TiT target with copper backing was controlled by a water-cooling system. The deuterium ion beam current on the target was ~60 μA at an accelerating voltage of 150 ± 1 kV. A sample wrapped in aluminum monitor foil was mounted at 0° with respect to the incident deuterium beam at a distance of 1 cm from the TiT target. Irradiation was carried out separately for each sample. The neutron energy at the sample position corresponds to 14.77 ± 0.17 MeV. The neutron energy of 14.77 MeV was predetermined for the particular sample foil geometry, irradiation position, and D⁺ energy from the ratio of the cross sections of the ⁹⁰Zr(n, 2n)⁸⁹Zr^g reaction to the cross section of the ⁹³Nb(n, 2n)⁹²Nb^m reaction [10]. Here, foils containing ⁹⁰Zr and ⁹³Nb with dimensions of 10 mm × 10 mm were irradiated with neutrons at the same distance from the TiT target. The neutron energy was deduced by comparing the ratio of the saturated activities per unit mass (considering the decay constant, branching ratios, isotopic abundance, irradiation time, and efficiency) of ⁸⁹Zr^g to ⁹²Nb^m with the ratio of the standard ENDF/B-VIII.0 cross section evaluations for the ⁹⁰Zr(n, 2n)⁸⁹Zr^g and ⁹³Nb(n, 2n)⁹²Nb^m reactions. The uncertainty in the neutron energy at the irradiation position was 0.17 MeV, which originated from the sample geometry, sample distance from the TiT target, and the radius of the D⁺ beam [11]. The samples were transferred to the counting room after irradiation.

The gamma-ray activity of the irradiated samples was measured using a pre-calibrated lead-shielded Ortec high-purity germanium (HPGe) detector with 30% relative efficiency and 1.5 keV energy resolution at a gamma energy of 1.33 MeV. The data acquisition was performed with an Ortec-make EASY-MCA-8K Multichannel Analyzer and Maestro software. The dead time during counting was maintained below 2%. The recorded gamma-ray spectra for ^natZn+Al, Y+Al, and ^natMo+Al samples irradiated by 14.77 MeV neutrons are shown in Fig. 1, Fig. 2, and Fig. 3, respectively. In Figs. 1 to 3, $ {t}_{1} $ is the irradiation time, $ {t}_{2} $ is the cooling time, and $ {t}_{3} $ is the counting time. In Fig. 1 (a) and (b), the short half-life gamma-ray spectra are shown for product nuclides ⁶⁸Cu^m, ⁶⁶Cu, and ⁶³Zn along with the monitor reaction product nuclide ²⁷Mg. In Fig. 1 (c), (d), and (e), the long half-life gamma-ray spectra are shown for product nuclides ⁶⁵Ni, ⁶⁷Cu, ⁶⁹Zn^m, and ⁶⁵Zn along with the monitor reaction product nuclide ²⁴Na. In Fig. 2, the gamma-ray spectrum is shown for product nuclides ⁹⁰Y^m and ⁸⁸Y along with the monitor reaction product nuclide ²⁴Na. In Fig. 3 (a), the short half-life gamma-ray spectrum is shown for product nuclides ⁸⁹Zr^m and ⁹⁸Nb^m along with the monitor reaction product nuclide ²⁷Mg. In Fig. 3 (b) and (c), the long half-life gamma-ray spectra are shown for product nuclides ⁹⁷Nb^g, ⁹⁹Mo, ⁹³Mo^m, ⁹⁶Nb, ⁸⁹Zr^g, and ⁹²Nb^m along with the monitor reaction product nuclide ²⁴Na. The nuclear data adopted for the calculation of cross sections are given in Table 2 along with the respective references. The details of the threshold energy, cooling time, counting time, and gamma-ray net peak counts are listed in Table 3.

Figure 1.  Recorded gamma-ray spectra of irradiated ^natZn sample and Al monitor.

Figure 2.  Recorded gamma-ray spectrum of irradiated ^natY sample and Al monitor.

Figure 3.  Recorded gamma-ray spectra of irradiated ^natMo sample and Al monitor.

A standard ¹⁵²Eu (T_1/2 = 13.517 ± 0.009 yr. [29]) source of known activity (A₀ = 4336.98 ± 86.74 Bq as of 1 Oct. 1999) was used to calibrate the HPGe detector. The photo-peaks of six gamma lines of the ¹⁵²Eu source were used to determine the detection efficiency of the HPGe detector. The detection efficiency ε for the point source placed at a distance of 2 mm from the end-cap of the detector is given by

where $ C $ is the number of counts obtained for a counting time ($ \mathrm{\Delta }t $ =3600 seconds) for a particular gamma-line of ¹⁵²Eu with a branching ratio $ {I}_{\gamma } $, $ {K}_{C} $ is the correction factor for the coincidence summing effect calculated using EFFTRAN code [30], $ {A}_{0} $ is the activity of the ¹⁵²Eu source at the time of manufacture, and T is the time between the date of manufacture and the beginning of counting. In addition, the EFFTRAN code was used to transfer efficiencies from point source geometry ($ {\epsilon }_{p} $) to sample geometry ($ {\epsilon }_{f} $). The uncertainty in detection efficiency was calculated by following Ref. [11] and is listed in Table 4. The correlation matrix for the measured detection efficiency is presented in Table 5. The efficiencies of the detector at required energies were generated with a linear parametric function following Ref. [31] by varying m from 1 to 6

$ {\mathit{E}}_{\mathit{\gamma }} $/keV	$ {\mathit{I}}_{\mathit{\gamma }} $(%)	C	$ {\mathit{K}}_{\mathit{C}} $	$ {\mathit{\epsilon }}_{\mathit{p}} $($ {\mathit{E}}_{\mathit{\gamma }}) $	$ {\mathit{\epsilon }}_{\mathit{f}} $	$ {\Delta \mathit{\epsilon }}_{\mathit{f}} $
121.78	28.53 ± 0.016	171345 ± 461	1.2987	15.477	15.107	0.305
344.28	26.59 ± 0.20	98114 ± 338	1.191	8.799	8.516	0.184
778.9	12.93 ± 0.08	21679 ± 182	1.2975	4.364	4.218	0.095
964.08	14.51 ± 0.07	21573 ±176	1.1897	3.542	3.422	0.076
1112.07	13.67 ± 0.08	19538 ± 176	1.099	3.153	3.046	0.069
1408.01	20.87 ± 0.09	24057 ± 167	1.1379	2.632	2.542	0.055

Table 4.  Detection efficiencies (%) for the point source geometry $ {\epsilon }_{p} $, foil geometry $ {\epsilon }_{f} $, and uncertainty.

$ {\mathit{E}}_{\mathit{\gamma }} $/keV	$ {\mathit{\epsilon }}_{\mathit{f}} $ (%)	Correlation matrix
121.78	15.107 ± 0.305	1
344.28	8.516 ± 0.184	0.916	1
778.9	4.218 ± 0.095	0.879	0.82	1
964.08	3.422 ± 0.076	0.895	0.835	0.801	1
1112.07	3.046 ± 0.069	0.873	0.814	0.781	0.796	1
1408.01	2.542 ± 0.055	0.917	0.856	0.821	0.837	0.816	1

Table 5.  Correlation matrix for the measured detection efficiencies.

The best quality of fit was achieved for $ m=4 $, with ${\dfrac{\chi^{2} }{6-4}}=1.073 \approx 1$, where $ {p}_{m} $ is the parameter of the fitting function, m is the order of the fitting function, and $ {E}_{i} $ is the energy of γ-lines in MeV. The efficiencies corresponding to the γ-rays of the reaction products were determined using the following linear parametric model:

The interpolated detection efficiency curve and measured detection efficiencies are plotted in Fig. 4. The interpolated efficiencies, correlation matrix for the sample, and monitor reactions are listed in Table 6.

Figure 4.  (color online) Detector efficiency with gamma energy using a ¹⁵²Eu standard source along with the fitted efficiency curve.

Product Nuclide	$ {\mathit{E}}_{\mathit{\gamma }} $/keV	$ \mathit{\epsilon } $ (%)	Correlation matrix
67Cu	184.577	12.969 ± 0.286	1
69Znm	438.634	6.96 ± 0.147	0.933	1
68Cum	526.44	5.928 ± 0.125	0.886	0.992	1
63Zn	669.62	4.774 ± 0.101	0.826	0.965	0.99	1
27Mg	843.76	3.883 ± 0.082	0.802	0.943	0.975	0.995	1
66Cu	1039.2	3.237 ± 0.067	0.825	0.932	0.958	0.977	0.991	1
65Zn	1115.539	3.050 ± 0.063	0.842	0.926	0.947	0.963	0.979	0.998	1
24Na	1368.626	2.591 ± 0.055	0.887	0.874	0.868	0.864	0.885	0.937	0.959	1
65Ni	1481.84	2.44 ± 0.054	0.889	0.827	0.807	0.791	0.813	0.879	0.909	0.99	1
90Ym	202.53	12.354 ± 0.276	1
88Y	898.042	3.672 ± 0.077	0.795	1
24Na	1368.626	2.591 ± 0.055	0.876	0.898	1
99Mo	181.068	13.095 ± 0.288	1
93Mom	263.049	10.444 ± 0.233	0.994	1
96Nb	568.871	5.53 ± 0.117	0.867	0.886	1
89Zrm	587.8	5.37 ± 0.114	0.858	0.877	1	1
97Nbg	657.23	4.85 ± 0.103	0.832	0.849	0.997	0.998	1
98Nbm	722.626	4.457 ± 0.095	0.816	0.831	0.992	0.995	0.999	1
27Mg	843.76	3.883 ± 0.082	0.805	0.815	0.984	0.987	0.994	0.998	1
89Zrg	909.15	3.633 ± 0.076	0.809	0.815	0.979	0.982	0.99	0.995	0.999	1
92Nbm	934.44	3.547 ± 0.074	0.811	0.816	0.977	0.98	0.988	0.993	0.998	1	1
24Na	1368.626	2.591 ± 0.055	0.89	0.865	0.866	0.865	0.864	0.867	0.885	0.9	0.907	1

Table 6.  Interpolated efficiencies, uncertainties, and correlation matrix for the sample and monitor reactions.

In this study, the cross sections of the ⁷⁰Zn(n, 2n)⁶⁹Zn^m, ⁶⁸Zn(n, α)⁶⁵Ni, ⁶⁷Zn(n, p)⁶⁷Cu, ⁶⁶Zn(n, 2n)⁶⁵Zn, ⁸⁹Y(n, γ)⁹⁰Y^m, ⁸⁹Y(n, 2n)⁸⁸Y, ¹⁰⁰Mo(n, 2n)⁹⁹Mo, ⁹⁷Mo(n, p)⁹⁷Nb^g, ⁹⁶Mo(n, p)⁹⁶Nb, ⁹⁴Mo(n, 2n)⁹³Mo^m, ⁹²Mo(n, p)⁹²Nb^m, and ⁹²Mo(n, α)⁸⁹Zr^g reactions were measured at a neutron energy of 14.77 ± 0.17 MeV with ²⁷Al(n, α)²⁴Na as the monitor reaction. The cross sections of the ⁶⁸Zn(n, p)⁶⁸Cu^m, ⁶⁶Zn(n, p)⁶⁶Cu, ⁶⁴Zn(n, 2n)⁶³Zn, ⁹⁸Mo(n, p)⁹⁸Nb^m, and ⁹²Mo(n, α)⁸⁹Zr^m reactions were measured at a neutron energy of 14.77 ± 0.17 MeV with ²⁷Al(n, p)²⁷Mg as the monitor reaction. The cross sections were determined using the neutron activation equation [32]

Here, the sample and monitor reaction parameters are denoted with the subscripts s and m, respectively. ${\sigma }_{m}= 111.69\pm 2.73~{\rm mb},66.42 \pm 2.02~{\rm mb}$ are the interpolated values taken from the IRDFF-II evaluated data file for the ²⁷Al(n, α)²⁴Na and ²⁷Al(n, p)²⁷Mg reactions at 14.77 ± 0.17 MeV, respectively. ε is the detector efficiency, C is the photo peak counts, a is the isotopic abundance, A is the atomic mass, M is the mass, Iγ is the branching ratio of γ-rays taken from Ref. [33], and f is the timing factor. $ F={f}_{c}\times {f}_{a} $is the correction factor due to the coincidence summing effects ($ {f}_{c} $) and gamma ray self-attenuation $ \left({f}_{a}\right) $. The correction factor due to coincidence summing effects was calculated with the TrueCoinc code [34]. The self-attenuation coefficients $ {f}_{a} $ were calculated with the mass attenuation coefficients taken from the NIST Standard Reference Database [35]. The correction factors $ {f}_{a} $ and $ {f}_{c} $ for sample and monitor reaction product nuclides are listed in Table 7. The timing factor f is given by

Product nuclide	Eγ/keV	Sample	$ {f}_{c} $	$ {f}_{a} $	F
69Znm	438.634	Zn	1	1.032	1.032
68Cum	526.44	Zn	1	1.03	1.03
65Ni	1481.84	Zn	0.99	1.017	1.008
67Cu	184.577	Zn	1	1.065	1.065
66Cu	1039.2	Zn	1.001	1.021	1.022
65Zn	1115.539	Zn	1	1.02	1.02
63Zn	669.62	Zn	1.01	1.026	1.036
90Ym	202.53	Y2O3	1.082	1.049	1.136
88Y	898.042	Y2O3	1.16	1.016	1.178
99Mo	181.068	MoO3	1.053	1.058	1.118
98Nbm	722.626	MoO3	1.102	1.017	1.121
97Nbg	657.23	MoO3	1	1.018	1.018
96Nb	568.871	MoO3	1.099	1.019	1.119
93Mom	263.049	MoO3	1.084	1.036	1.122
92Nbm	934.44	MoO3	1	1.016	1.016
89Zrm	587.8	MoO3	1	1.019	1.019
89Zrg	909.15	MoO3	1.037	1.015	1.053
27Mg	843.76	Al foil	1.002	1.002	1.004
24Na	1368.626	Al foil	1	1.002	1.002

Table 7.  Self-attenuation coefficient $ {f}_{a} $ and coincidence summing correction factor $ {f}_{c} $ for samples and monitor reaction products.

where λ is the decay constant, $ {t}_{1} $ is the irradiation time, $ {t}_{2} $ is the cooling time, and $ {t}_{3} $ is the counting time.

The uncertainty in $ {\sigma }_{s} $ was propagated from the uncertainties in the measured parameters, that is, the monitor cross section$ \left({\sigma }_{m}\right) $, efficiency $\left({\epsilon }_{m},~{\epsilon }_{s}\right)$, counts (${C}_{m},~{C}_{s})$, sample isotopic abundance $ \left({a}_{s}\right) $, mass (${M}_{m},~{M}_{s}$), intensity $\left({I}_{\gamma m},~{I}_{\gamma s}\right)$, and timing factor $\left({f}_{m},~{f}_{s}\right)$. The fractional uncertainties in atomic mass $({A}_{s},~{A}_{m})$ and monitor isotopic abundance ($ {a}_{m}) $ were negligible. The uncertainty in the timing factor $ f $ was calculated following Sec. III.B. of Ref. [36]. The covariances between ($ {\epsilon }_{m},{\epsilon }_{s} $) were obtained by following the methodology described in Sec. III.A. of Ref. [37]. The uncertainty in the detector efficiencies wasreduced by adopting $ {\eta }_{m,s}=\dfrac{{\epsilon }_{m}}{{\epsilon }_{s}} $ [32], where $ {\eta }_{m,s} $ is the detection efficiencyratio of the monitor reaction product ($ {\epsilon }_{m} $) and sample reaction product ($ {\epsilon }_{s} $). The covariances of ($ {\epsilon }_{m},{\epsilon }_{s} $) were further propagated to

The partial uncertainties for each parameter of Eq. (4) and their correlations are given in Table 8, Table 9, and Table 10. In Tables 8 to 10, the correlation coefficients due to different parameters were assigned 0 for uncorrelated and 1 for fully correlated. The value of the correlation coefficient for the parameter $ {\eta }_{m,s} $ lay between $ -1 \le Cor\left({\eta }_{m/s1},{\eta }_{m/s2}\right)\le 1 $ calculated with Eq. (6). The covariance matrix for the measured cross section from the fractional uncertainties given in Tables 8 to 10 was calculated using the following equation:

Nuclide Parameter	69Znm	68Cum	65Ni	67Cu	66Cu	65Zn	63Zn	Correlation
$ {\mathit{C}}_{\mathit{s}} $	2.674	6.082	7.681	10.508	2.345	10.909	1.391	Uncorrelated
$ {\mathit{C}}_{\mathit{m}} $	0.648a	0.362b	0.78c	0.636d	0.348e	0.895f	0.743g	a, c, d, and f are fully correlated; b, e, and g are fully correlated
$ {\mathit{I}}_{\mathit{\gamma }\mathit{s}} $	0.074	2.273	0.593	0.616	0.975	0.2	3.659	Uncorrelated
$ {\mathit{I}}_{\mathit{\gamma }\mathit{m}} $	0.002a	0.028b	0.002c	0.002d	0.028e	0.002f	0.028g	a, c, d, and f are fully correlated; b, e, and g are fully correlated
$ {\mathit{\eta }}_{\mathit{m},\mathit{s}} $	0.276	0.074	0.007	1.194	0.015	0.022	0.074	Partially correlated
$ {\mathit{f}}_{\mathit{\lambda }\mathit{s}} $	0.096	0.932	0.011	0.183	1.184	0.037	0.197	Uncorrelated
$ {\mathit{f}}_{\mathit{\lambda }\mathit{m}} $	0.06a	0.01b	0.074c	0.06d	0.01e	0.018f	0.26g	a, c, d, and f are fully correlated; b, e, and g are fully correlated
$ {\mathit{M}}_{\mathit{s}} $	0.025	0.025b	0.025c	0.025	0.025e	0.025f	0.025	b and c are fully correlated; e and f are fully correlated
$ {\mathit{M}}_{\mathit{m}} $	0.099a	0.099b	0.099c	0.099d	0.099e	0.099f	0.099g	a, c, d, and f are fully correlated; b, e, and g are fully correlated
$ {\mathit{a}}_{\mathit{s}} $	16.393	3.415b	3.415c	3.96	3.534e	3.534f	1.525	b and c are fully correlated; e and f are fully correlated
$ {\mathit{\sigma }}_{\mathit{m}} $	2.444a	3.023b	2.444c	2.444d	3.023e	3.023f	3.023g	a, c, d, and f are fully correlated; b, e, and g are fully correlated
Total (%)	16.805	7.998	8.81	11.59	5.442	11.761	5.240

Table 8.  Partial uncertainties (%) and correlations between the various parameters used to obtain the neutron induced cross sections for the zinc target.

where $ p $ refers to the measured parameter, and $ Cor\left({q}_{pi},{q}_{pj}\right) $ is a square matrix (order is the number of sample product nuclides). The total uncertainty in the measured cross section was calculated with the following equation:

The correlation matrix between the reaction cross sections can be calculated from the covariance matrix $ {V}_{{\sigma }_{ij}} $ and the total uncertainty via the following equation:

Nuclide Parameter	88Y	90Ym	Correlation
$ {\mathit{C}}_{\mathit{s}} $	7.547	8.696	Uncorrelated
$ {\mathit{C}}_{\mathit{m}} $	0.758	0.758	Fully correlated
$ {\mathit{I}}_{\mathit{\gamma }\mathit{s}} $	0.32	0.041	Uncorrelated
$ {\mathit{I}}_{\mathit{\gamma }\mathit{m}} $	0.002	0.002	Fully correlated
$ {\mathit{\eta }}_{\mathit{m},\mathit{s}} $	0.029	0.077	Partially correlated
$ {\mathit{f}}_{\mathit{\lambda }\mathit{s}} $	0.197	0.934	Uncorrelated
$ {\mathit{f}}_{\mathit{\lambda }\mathit{m}} $	0.071	0.071	Fully correlated
$ {\mathit{M}}_{\mathit{s}} $	0.102	0.102	Fully correlated
$ {\mathit{M}}_{\mathit{m}} $	0.167	0.167	Fully correlated
$ {\mathit{a}}_{\mathit{s}} $	-	-	Not available
$ {\mathit{\sigma }}_{\mathit{m}} $	2.444	2.444	Fully correlated
Total (%)	7.981	9.124

Table 9.  Partial uncertainties (%) and correlations between the various parameters used to obtain the neutron induced cross sections for the yttrium target.

Nuclide Parameter	99Mo	98Nbm	97Nbg	96Nb	93Mom	92Nbm	89Zrm	89Zrg	Correlation
$ {\mathit{C}}_{\mathit{s}} $	2.048	8.241	2.622	7.208	8.521	13.095	10.277	12.262	Uncorrelated
$ {\mathit{C}}_{\mathit{m}} $	0.68a	0.436b	0.807c	0.68d	0.68e	0.68f	0.436g	0.68h	a, c, d, e, f, and h are fully correlated; b and g are fully correlated
$ {\mathit{I}}_{\mathit{\gamma }\mathit{s}} $	1.983	2.033	0.081	0.517	1.916	0.04	0.19	0.03	Uncorrelated
$ {\mathit{I}}_{\mathit{\gamma }\mathit{m}} $	0.002a	0.028b	0.002c	0.002d	0.002e	0.002f	0.028g	0.002h	a, c, d, e, f, and h are fully correlated; b and g are fully correlated
$ {\mathit{\eta }}_{\mathit{m},\mathit{s}} $	0.898	0.066	0.081	0.112	0.559	0.034	0.112	0.037	Partially correlated
$ {\mathit{f}}_{\mathit{\lambda }\mathit{s}} $	0.009	0.377	0.012	0.181	0.493	0.194	2.405	0.146	Uncorrelated
$ {\mathit{f}}_{\mathit{\lambda }\mathit{m}} $	0.061a	0.077b	0.199c	0.061d	0.061e	0.061f	0.077g	0.061h	a, c, d, e, f, and h are fully correlated; b and g are fully correlated
$ {\mathit{M}}_{\mathit{s}} $	0.025	0.025	0.025	0.025	0.025	0.025f	0.025g	0.025h	Only f, g, and h are fully correlated
$ {\mathit{M}}_{\mathit{m}} $	0.174a	0.174b	0.174c	0.174d	0.174e	0.174f	0.174g	0.174h	a, c, d, e, f, and h are fully correlated; b and g are fully correlated
$ {\mathit{a}}_{\mathit{s}} $	3.157	1.517	1.458	0.9	0.984	2.065f	2.065g	2.065h	Only f, g, and h are fully correlated
$ {\mathit{\sigma }}_{\mathit{m}} $	2.444a	3.023b	2.444c	2.444d	2.444e	2.444f	2.444g	3.023h	a, c, d, e, f, and h are fully correlated; b and g are fully correlated
Total (%)	5.037	9.164	3.964	7.717	9.18	13.5	11.042	12.821

Table 10.  Partial uncertainties (%) and correlations between the various parameters used to obtain the neutron induced cross sections for the molybdenum target.

The cross sections of the measured nuclear reactions were calculated theoretically using the TALYS-1.96 [5] and EMPIRE-3.2.3 [6] nuclear reaction codes. These codes consider the contributions of compound nucleus theory, direct reactions, and pre-equilibrium processes depending on the incident energy of the projectile. These contributions are incorporated into the code by a set of optical models that determine the transmission coefficients of outgoing particles, nuclear level density models, preequilibrium models, and gamma strength functions that determine the photon transmission coefficients. The theoretical calculations were conducted over neutron incident energies from 13 to 17 MeV and compared with the experimental results from the present study and reported experimental data from the EXFOR database.

The TALYS-1.96 code can be used for nuclear reactions that involve incident projectiles such as gammas, neutrons, protons, deuterons, and α-particles in the incident energy range from 1 keV to 200 MeV. Detailed description of the TALYS-1.96 code and available models can be found in Ref. [5]. $ 384=6\mathrm{ }\times \mathrm{ }2\mathrm{ }\times \mathrm{ }4\times \mathrm{ }8 $ calculations were performed with combinations of six level density models, two nucleon-nucleus optical model potentials, four pre-equilibrium models, and eight γ-ray strength functions available in TALYS-1.96 code. A single set of models was chosen based on chi-square fitting with EXFOR data. The best model combination for neutron induced reactions on ^natZn was i) the level densities based on the generalized superfluid model [38] (ldmodel 3), ii) Koning-Delaroche [39] nucleon-nucleus local optical model (localomp y), iii) exciton model [40] for pre-equilibrium (preeqmode 1), and iv) gamma strength function calculated with the hybrid model of Goriely [41] (strength 5). For neutron induced reactions on ^natY, the chosen model combination was i) level densities based on the generalized superfluid model [38] (ldmodel 3), ii) Koning-Delaroche [39] nucleon-nucleus global optical model (localomp n), iii) exciton model [40] for pre-equilibrium (preeqmode 2), and iv) the gamma strength function calculated with HFB+QRPA [41] (strength 8). The best reproduction of experimental cross sections for neutron induced reactions on ^natMo was obtained with the following model combination: i) Level densities based on the HFB + Skyrme force calculations from Hilaire’s tables [42] (ldmodel 5), ii) the Koning-Delaroche [39] nucleon-nucleus global optical model (localomp n), iii) the exciton model [40] for pre-equilibrium (preeqmode 1), and iv) the gamma strength function calculated with the generalized Lorentzian of Brink and Axel [43, 44] (strength 2). The value of a chosen set of parameters within the models (aadjust, ctable, and avadjust) was randomly varied between ± X % of its central value [45] to account for statistical uncertainties arising from model calculations. The uncertainty in the calculated excitation function due to parameter uncertainties was determined using 1000 calculations. Here, the input parameter values were randomly sampled about the central value, and the energy input file had neutron energies binned at 1 MeV. The uncertainty in the evaluated calculations per neutron energy bin was expressed as the percentage standard deviation per unit calculated cross section at that energy bin.

The EMPIRE-3.2.3 code can be used for nuclear reactions that involve incident projectiles such as photons, neutrons, protons, deuterons, α-particles, and heavy ions in the incident energy range from 1 keV to 200 MeV. Detailed descriptions of the nuclear models in the EMPIRE-3.2.3 code can be found in Ref. [6]. $ 168=4 \times 2 \times 3 \times 7 $ calculations were performed with combinations of four level density models, two nucleon-nucleus optical model potentials, three pre-equilibrium models, and seven γ-ray strength functions available in the EMPIRE-3.2.3 code. A single set of models was chosen based on chi-square fitting with the EXFOR data. The best model combination for neutron induced reactions on ^natZn was i) the level densities based on microscopic HFB level densities [46] (LEVDEN 3), ii) Koning-Delaroche nucleon-nucleus optical model [39] (OMPOT 2405), iii) Monte Carlo pre-equilibrium model for preequilibrium (HMS 1), and iv) gamma strength function calculated with the enhanced generalised Lorentzian from the RIPL database [47] (GSTRFN 4). The chosen model combination for neutron induced reactions on ^natY was i) the EMPIRE-specific level densities [48] (LEVDEN 0), ii) Wilmore-Hodgson optical model [49] (OMPOT 401), iii) multi-step compound model for pre-equilibrium (MSC 1), and iv) gamma strength function given by the modified Lorentzian [50] (GSTRFN 1). For neutron induced reactions on ^natMo, the best fit was obtained with i) the EMPIRE-specific level densities [48] (LEVDEN 0), ii) Koning-Delaroche nucleon-nucleus optical model [39] (OMPOT 2405), iii) Monte Carlo pre-equilibrium model for preequilibrium (HMS 1), and iv) gamma strength function calculated with the modified Lorentzian [50] (GSTRFN 3).

The correlation matrix and measured neutron induced reaction cross sections for zinc, yttrium, and molybdenum are listed in Table 11, Table 12, and Table 13, respectively. Additionally, the present experimental cross sections were compared with the evaluated cross section data from the TENDL-2019 [8], JENDL-5 [7], and ENDF/B-VIII.0 [1] libraries along with nuclear model calculations with the TALYS-1.96 and EMPIRE-3.2.3 nuclear codes in Table 14. In Figs. 5 to 21, the cross sections from the TENDL-2019 evaluation are represented by a green solid line, the JENDL-5 evaluation is represented by a blue solid line, the ENDF/B-VIII.0 evaluation is represented by a pink solid line, the EMPIRE-3.2.3 calculations are represented by a solid purple line, the TALYS-1.96 95% upper confidence level by a red solid line, the TALYS-1.96 95% lower confidence level by a black solid line, and the region between the above two dashed lines is filled. The experimental data plotted in Figs. 5 to 21 were normalized with respect to the evaluated cross section data for monitor reactions from the IRDFF-II library [51] for the experimental data where the monitor cross sections are reported.

Figure 5.  (color online) Measured experimental cross section for the ⁷⁰Zn(n, 2n)⁶⁹Zn^m reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

Figure 5 depicts the measured cross section of the ⁷⁰Zn(n, 2n)⁶⁹Zn^m reaction at a neutron energy of 14.77 ± 0.17 MeV compared with the experimental data from the EXFOR database, evaluated data from the TENDL-2019 and JENDL-5 libraries, and the TALYS-1.96 uncertainty calculations. The authors of Refs. [52–58] adopted the ²⁷Al(n, α)²⁴Na reaction as the monitor reaction. After normalization with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na reaction, the cross sections changed by 6% for Ref. [53], whereas for all the other Refs. [52–58], the change was less than 4 %. The authors of Ref. [59] adopted the ⁹³Nb(n, 2n)⁹²Nb^m reaction as the monitor reaction, and upon normalization with the IRDFF-II evaluation, the cross sections changed by 6%. The authors of Ref. [60] adopted the ⁵⁶Fe(n, p)⁵⁶Mn reaction as the monitor reaction.

The measured cross section of the present study is in good agreement within the experimental uncertainty with the cross sections reported in the Refs. [52, 54–56, 58] as well as the JENDL-5 evaluation and TALYS-1.96 calculations. The TENDL-2019 evaluation and EMPIRE-3.2.3 calculations were lower than the measured cross section of the present study.

The measured cross section of the ⁶⁸Zn(n, p)⁶⁸Cu^m reaction at a neutron energy of 14.77 ± 0.17 MeV was compared with the experimental data from the EXFOR database, evaluated data from the TENDL-2019 and JENDL-5 libraries, and the TALYS-1.96 uncertainty calculations, as shown in Fig. 6. The cross section data reported in Refs. [61–68] were normalized with the IRDFF-II evaluation of the ²⁷Al(n,α)²⁴Na monitor reaction at the respective neutron energies. The change in the reported data due to normalization was 6% for Ref. [65] and less than 1% for all the other Refs. [61–64, 66–68]. The cross section data reported in Refs. [54, 69–71] were normalized with the IRDFF-II evaluation for the ²⁷Al (n, p)²⁷Mg reaction. The reported cross section data of Refs. [63, 66, 67, 69] were normalized for the gamma-yield per decay of the respective lines of ⁶⁸Cu^m, and the change was found as 3%, 8%, 17%, and 5%, respectively.

Figure 6.  (color online) Measured experimental cross section for the ⁶⁸Zn(n, p)⁶⁸Cu^m reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

The present result is in good agreement within the experimental uncertainty with the cross sections reported in Refs. [54, 61, 68–70]. The JENDL-5 and TENDL-2019 evaluations were higher than the measured cross section, whereas the TALYS-1.96 calculations were lower than the measured cross section.

Figure 7 shows the measured cross section of the ⁶⁸Zn(n, α)⁶⁵Ni reaction at a neutron energy of 14.77 ± 0.17 MeV along with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations. The reported data of Refs. [53, 54, 57, 62, 71–75] were normalized with the IRDFF-II evaluation for the ²⁷Al(n,α)²⁴Na reaction. The reported cross section data of Ref. [53] changed by 3% after normalization for the gamma-yield per decay of the 1115.53 keV gamma line of ⁶⁵Ni. The reported data of Refs. [76, 77] after normalization with the IRDFF-II evaluation for the ⁵⁶Fe(n, p)⁵⁶Mn reaction changed by 4%.

Figure 7.  (color online) Measured experimental cross section for the ⁶⁸Zn(n, α)⁶⁵Ni reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

The present result is in good agreement within the experimental uncertainty with the cross sections reported in Refs. [54, 76, 78–80], whose neutron energies overlapped with the present measurement. The measured cross section is in good agreement with the TALYS-1.96 calculations and JENDL-5 and ENDF/B-VIII.0 evaluations. The EMPIRE-3.2.3 calculations and TENDL-2019 evaluations were higher than the measured cross section.

The measured cross section of the ⁶⁷Zn(n, p)⁶⁷Cu reaction at a neutron energy of 14.77 ± 0.17 MeV was compared with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations, as shown in Fig. 8. The reported cross section data of Ref. [81] upon normalization with the IRDFF-II evaluation of the ¹⁹⁷Au(n, 2n)¹⁹⁶Au monitor reaction changed by 2%. For the reported data in Refs. [54, 63, 78, 82], normalization was performed with the IRDFF-II data for the respective monitors, and the change was less than 1%.

Figure 8.  (color online) Measured experimental cross section for the ⁶⁷Zn(n, p)⁶⁷Cu reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

The measured cross section of the present study is in good agreement within the experimental uncertainty only with the cross section reported in Ref. [80], whose neutron energy overlapped with the present measurement and ENDF/B-VIII.0 evaluation.

The measured cross section of the ⁶⁶Zn(n, p)⁶⁶Cu reaction at a neutron energy of 14.77 ± 0.17 MeV was compared with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations, as shown in Fig. 9. The reported experimental data of Refs. [57, 62, 63, 67, 83–88] were normalized with the IRDFF-II evaluations for their respective monitor data. The reported cross section data of Refs. [62, 63, 65, 67, 87, 89, 90] were normalized for the gamma-yield per decay of the 1039 KeV γ-line of ⁶⁶Cu, and the change ranged from 3% to 20%.

Figure 9.  (color online) Measured experimental cross section for the ⁶⁶Zn(n, p)⁶⁶Cu reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

From Fig. 9, the result of the present study is in good agreement within the experimental uncertainty with the cross sections reported in Refs. [54, 65, 67, 70, 80, 90, 91], whose neutron energies overlapped with the present measurement. The measured cross section is in good agreement with the JENDL-5 and TALYS-1.96 calculations within the experimental uncertainty, whereas the ENDF/B-VIII.0 evaluation was lower than the measured cross section.

The measured cross section of the ⁶⁶Zn(n, 2n)⁶⁵Zn reaction at a neutron energy of 14.77 ± 0.17 MeV was compared with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations, as shown in Fig. 10. The experimental data of Refs. [54, 56, 57, 59, 78, 92–94] were normalized with the IRDFF-II evaluations for their respective monitor data. The reported cross section data of Refs. [56, 57, 59, 78, 82, 95] were normalized for the gamma-yield per decay of the 1115.539 KeV γ-line of ⁶⁵Zn, and the change ranged from 1% to 3%.

Figure 10.  (color online) Measured experimental cross section for the ⁶⁶Zn(n, 2n)⁶⁵Zn reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

The present results are in good agreement within the experimental uncertainty with the cross sections reported by Refs. [54, 56, 59, 78, 82, 92, 93, 95–97], whose neutron energies overlapped with the present measurement. The measured cross section is in good agreement with the EMPIRE-3.2.3 calculations and TENDL-2019 evaluation within the experimental uncertainty. The evaluations of ENDF/B-VIII.0 and JENDL-5 were higher than the measured cross section.

Figure 11 shows the measured cross section of the ⁶⁴Zn(n,2n)⁶³Zn reaction at a neutron energy of 14.77 ± 0.17 MeV along with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations. The experimental data of Refs. [54, 61, 62, 78, 81, 91, 98, 99] were normalized with the IRDFF-II evaluations for their respective monitor data. The reported cross section data of Refs. [78, 91] were normalized for the gamma-yield per decay of the 669.62 KeV γ-line of ⁶³Zn, and the change was 3%.

Figure 11.  (color online) Measured experimental cross section for the ⁶⁴Zn(n, 2n)⁶³Zn reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

The present results are in good agreement within the experimental uncertainty with the cross sections reported in Refs. [54, 61, 78], whose neutron energies overlapped with the present measurement. The measured cross section is in good agreement with the TALYS-1.96 calculations and the ENDF/B-VIII.0, JENDL-5, and TENDL-2019 evaluations within the experimental uncertainty.

The measured cross section of the ⁸⁹Y(n, 2n)⁸⁸Y reaction at a neutron energy of 14.77 ± 0.17 MeV was compared with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations, as shown in Fig. 12. The reported data of Ref. [81] upon normalization with the IRDFF-II evaluation of the ¹⁹⁷Au(n, 2n)¹⁹⁶Au monitor reaction changed by 2%. The experimental data reported in Refs. [100–109] were normalized with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na monitor reaction at their respective neutron energies. The data of Refs. [108, 109] after normalization changed by 4% and 7%, respectively, whereas for Refs. [100–107], the changes were less than 2%. Refs. [61, 78, 95, 110–112] adopted the ⁹³Nb(n, 2n)⁹²Nb^m reaction as the monitor reaction, and after normalization with the IRDFF-II evaluation, they varied by less than 1%.

Figure 12.  (color online) Measured experimental cross section for ⁸⁹Y(n,2n)⁸⁸Y reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

As shown in Fig. 12, the present results are in good agreement with the cross sections reported in Refs. [61, 78, 107–109, 112–114, 95, 100–106], whose neutron energies overlapped with the present measurement within the experimental uncertainty. The measured cross section is in good agreement with the TALYS-1.96 calculations and ENDF/B-VIII.0, JENDL-5, and TENDL-2019 evaluations within the experimental uncertainty. The EMPIRE-3.2.3 calculations underestimated the cross section at a neutron energy of 14.77 MeV.

Figure 13 shows the measured cross section for the ⁸⁹Y(n, γ)⁹⁰Y^m reaction at a neutron energy of 14.77 ± 0.17 MeV in comparison with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations. The reported data of Ref. [81] after normalization with the IRDFF-II evaluation of the ¹⁹⁷Au(n, 2n)¹⁹⁶Au monitor reaction decreased by 2%. The reported data of Ref. [110] after normalization with the IRDFF-II evaluation of the ⁹³Nb(n, 2n)⁹²Nb^m monitor reaction changed by less than 1%. The data reported by Refs. [74, 115–117] were normalized with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na monitor reaction at their respective neutron energies. The data of Refs. [74, 115–117] upon normalization changed by less than 2% from the reported value.

Figure 13.  (color online) Measured experimental cross section for the ⁸⁹Y(n, γ)⁹⁰Y^m reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

As shown in Fig. 13, the present result is in good agreement within the experimental uncertainty with the cross sections reported by Refs. [115–117], whose neutron energies overlapped with the present measurement. The measured cross section is in good agreement with the TALYS-1.96 calculations within the experimental uncertainty. The ENDF/B-VIII.0, JENDL-5, and TENDL-2019 evaluations were higher than the measured cross section.

Figure 14 shows the measured cross section of the ¹⁰⁰Mo(n, 2n)⁹⁹Mo reaction at a neutron energy of 14.77 ± 0.17 MeV compared with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations. Refs. [118, 119] adopted the ⁵⁶Fe(n, p)⁵⁶Mn reaction as the monitor reaction. Upon normalization with the IRDFF-II evaluation of the ⁵⁶Fe(n, p)⁵⁶Mn reaction, the cross sections changed by 16% and 9%, respectively. Refrences [56, 94, 120–130] adopted the ²⁷Al(n, α)²⁴Na reaction as the monitor reaction. After normalization with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na reaction, the cross sections changed by 7% for Refs. [56, 130], whereas for all the other Refs. [94, 120, 122–129], the changes were less than 4%. Additionally, after normalization for the gamma-yield per decay of the 1368.626 keV gamma line of ²⁴Na, the reported data of Ref. [122] changed by 12%. Refrences [92, 131] adopted the ⁶³Cu(n, 2n)⁶²Cu reaction as the monitor reaction. Upon normalization with the IRDFF-II evaluation of the ⁶³Cu(n, 2n)⁶²Cu reaction, the cross sections changed by 2%–3 %. The reported cross section of Ref. [132] upon normalization with the IRDFF-II evaluation of the ⁶⁵Cu(n,2n)⁶⁴Cu monitor reaction changed by 2%. Refrences [133, 134] adopted the ⁹³Nb(n, 2n)⁹²Nb^m reaction as the monitor reaction, and upon normalization with the IRDFF-II evaluation, they varied by less than 1%. The reported cross sections of Refs. [135–137] after normalization with the IRDFF-II evaluation of the ¹⁹⁷Au(n, 2n)¹⁹⁶Au monitor reaction changed by 0.5%. The contribution of ⁹⁸Mo(n, γ)⁹⁹Mo was subtracted from the measured cross section following the procedure given in Sec. II. D. of Ref. [69].

Figure 14.  (color online) Measured experimental cross section for the ¹⁰⁰Mo(n, 2n)⁹⁹Mo reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

The cross sections reported in Refs. [94, 118, 124, 125, 128], whose neutron energies overlapped with the present measurement, are in good agreement with the present result within the experimental uncertainty. The measured cross section does not agree with the data reported in Refs. [56, 92, 123, 127, 129, 134]. The measured cross section is in good agreement with the EMPIRE-3.2.3, ENDF/B-VIII.0, and TENDL-2019 evaluations within the experimental uncertainty. However, the TALYS-1.96 calculations and JENDL-5 evaluation underestimated the cross section at the 14.77 MeV neutron energy.

Figure 15 depicts the measured cross section of the ⁹⁸Mo(n, p)⁹⁸Nb^m reaction at a neutron energy of 14.77 ± 0.17 MeV compared with the experimental data from the EXFOR database, evaluated data from the TENDL-2019 and JENDL-5 libraries, and the TALYS-1.96 uncertainty calculations. The reported experimental data of Refs. [86, 119, 138] after normalization with the IRDFF-II evaluation of the ⁵⁶Fe(n, p) ⁵⁶Mn reaction changed by 11%, 16%, and 5%, respectively. Refrences [48, 66, 112, 116, 117, 119–121, 126, 131–133, 139–141] adopted the ²⁷Al(n, α)²⁴Na reaction as the monitor reaction. The above data were normalized with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na reaction. The cross sections changed by 7% for Refs. [56, 139] after normalization, whereas for the other authors, the changes were less than 4%. Refrences [131, 142] adopted the ⁶³Cu(n, 2n)⁶²Cu reaction as the monitor reaction. Upon normalization with the IRDFF-II evaluation of the ⁶³Cu(n, 2n)⁶²Cu reaction, the cross sections changed by 1% and 7%, respectively.

Figure 15.  (color online) Measured experimental cross section for the ⁹⁸Mo(n, p)⁹⁸Nb^m reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

The cross section reported in Ref. [125], whose neutron energy overlapped with the present measurement, is in good agreement with the present result within the experimental uncertainty. The measured cross section was lower than the TALYS-1.96 calculations and JENDL-5 and TENDL-2019 evaluations.

Figure 16 shows the measured cross section of the ⁹⁷Mo(n, p)⁹⁷Nb^g reaction at a neutron energy of 14.77 ± 0.17 MeV compared with the experimental data from the EXFOR database; evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations. The ²⁷Al(n, α)²⁴Na reaction was adopted as the monitor reaction in Refs. [69, 109, 120, 121, 123–125, 127–129, 141, 143, 144]. After normalization with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na reaction, the reported cross sections of Ref. [109] changed by 7%, whereas for Refs. [69, 120, 121, 123–125, 127–129, 141, 143, 144], the change was less than 4%. The reported data of Ref. [131] after normalization with the IRDFF-II evaluation of the ⁶⁵Cu(n, 2n)⁶⁴Cu monitor reaction decreased by 7%. The experimental data of Refs. [119, 138] after normalization with the IRDFF-II evaluation of the ⁵⁶Fe(n, p)⁵⁶Mn reaction changed by 10% and 2%, respectively. The same energy γ line (657.23 keV) and branching ratio used in the present study was reported by the authors of Refs. [69, 119, 121, 124, 125, 127, 129, 140, 144, 145]. However, the authors of Refs. [68, 109, 123, 131, 146, 147] did not state the decay data. Although an isomer, ⁹⁷Nb^m with a half-life of 58.7 s was produced after neutron irradiation; the contribution of the metastable state to ground state was neglected owing to a sufficient cooling time.

Figure 16.  (color online) Measured experimental cross section for the ⁹⁷Mo(n, p)⁹⁷Nb^g reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

As shown in Fig. 16, the cross section reported in Refs. [69, 109], whose neutron energy overlapped with the present measurement, is in good agreement with the result within the experimental uncertainty. The measured cross section was lower than the TALYS-1.96 and EMPIRE.3.2.3 calculations and the evaluations of Refs. [1, 7, 8].

The measured cross section of the ⁹⁶Mo(n, p)⁹⁶Nb reaction at a neutron energy of 14.77 ± 0.17 MeV from the present study was compared with the experimental data from the EXFOR database' evaluated data from the TENDL-2019, JENDL-5, and ENDF/B-VIII.0 libraries; and the TALYS-1.96 uncertainty calculations, as shown in Fig. 17. The experimental data reported in Refs. [74, 109, 120, 123–125, 127–129, 139, 140, 148] were normalized with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na monitor reaction. The reported cross sections of Refs. [109, 139] changed by 7%, whereas for Refs. [74, 120, 123–125, 127–129, 140, 148], the changes were less than 5%. The reported data of Ref. [131] after normalization with the IRDFF-II evaluation of the ⁶³Cu(n, 2n)⁶²Cu monitor reaction changed by 3%. The experimental data reported in Refs.[138, 149] after normalization with the IRDFF-II evaluation of the ⁵⁶Fe(n, p)⁵⁶Mn reaction changed by 10% and 2%, respectively. The reported data of Refs. [133, 137] after normalization with their respective monitor data changed by 1%.

Figure 17.  (color online) Measured experimental cross section for the ⁹⁶Mo(n, p)⁹⁶Nb reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

As shown in Fig. 17, the present measurement is in good agreement with the reported data in Refs. [61, 120, 124, 147, 148] within the experimental uncertainty. The measured cross section is in good agreement with the TALYS-1.96 calculations and ENDF/B-VIII.0, JENDL-5, and TENDL-2019 evaluations within the experimental uncertainty. However, the EMPIRE-3.2.3 calculations overestimated the cross section at the 14.77 MeV neutron energy.

The measured cross section of the ⁹⁴Mo(n, 2n)⁹³Mo^m reaction at a neutron energy of 14.77 ± 0.17 MeV from the present study was compared with the experimental data from the EXFOR database, evaluated data from the TENDL-2019 and JENDL-5 libraries, and the TALYS-1.96 uncertainty calculations, as shown in Fig. 18. The experimental data reported in Refs. [120, 124, 127, 128, 134, 139, 148] were normalized with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na monitor reaction. The reported cross sections changed by 4% for Ref. [124], whereas for Refs. [120, 127, 128, 134, 139, 148], the changes were less than 3%. The experimental data of Ref. [138] after normalization with the IRDFF-II evaluation of the ⁵⁶Fe(n, p)⁵⁶Mn reaction changed by 2%. The reported data of Ref. [150] after normalization with IRDFF-II evaluation of the ⁹³Nb(n, 2n)⁹²Nb^m monitor reaction changed by 2%.

Figure 18.  (color online) Measured experimental cross section for the ⁹⁴Mo(n, 2n)⁹³Mo^m reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

As shown in Fig. 18, the present result is in good agreement with the reported data of Refs. [61, 124, 128, 148, 150] within the experimental uncertainty. The measured cross section is in good agreement only with the TALYS-1.96 calculations within the experimental uncertainty. The JENDL-5 and TENDL-2019 evaluations overestimated the cross section at the 14.77 MeV neutron energy.

The measured cross section of the ⁹²Mo(n, p)⁹²Nb^m reaction at a neutron energy of 14.77 ± 0.17 MeV from the present study was compared with the experimental data from the EXFOR database, evaluated data from the TENDL-2019 and JENDL-5 libraries, and the TALYS-1.96 uncertainty calculations, as shown in Fig. 19. The experimental data reported in Refs. [61, 72, 74, 120, 121, 123, 124, 127–129, 140, 148, 151–153] were normalized with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na monitor reaction. The reported experimental data of Refs. [138, 149] were normalized with the IRDFF-II evaluation of the ⁵⁶Fe(n, p)⁵⁶Mn reaction, and the change after normalization was 10% and 2%, respectively. The reported data of Ref. [125] after normalization with the IRDFF-II evaluation of the ⁷⁵As(n, 2n)⁷⁴As monitor reaction changed by 6%. The experimental data of Refs. [133, 150, 154, 155] after normalization with the IRDFF-II evaluation of the ⁹³Nb(n, 2n)⁹²Nb^m monitor changed by less than 2%. The experimental data of Refs. [156, 157] changed by 1% after normalization with the IRDFF-II evaluation of the ¹⁹⁷Au(n, 2n)¹⁹⁶Au monitor reaction. Refs. [147, 158, 159] did not provide details on the monitor reaction. Hence, the data of Refs. [147, 158, 159] were not plotted.

Figure 19.  (color online) Measured experimental cross section for the ⁹²Mo(n, p)⁹²Nb^m reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

As shown in Fig. 19, the present results are in good agreement with most of the reported data within the experimental uncertainty. The measured cross section is in good agreement with the TALYS-1.96 calculations and JENDL-5 and TENDL-2019 evaluations within the experimental uncertainty.

Figure 20 shows the measured cross section of the ⁹²Mo(n, α)⁸⁹Zr^m reaction at a neutron energy of 14.77 ± 0.17 MeV compared with the experimental data from the EXFOR database, evaluated data from the TENDL-2019 and JENDL-5 libraries, and the TALYS-1.96 uncertainty calculations. The experimental data reported in Refs. [61, 72, 120, 124, 127, 139, 151, 160] were normalized with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na monitor reaction. The experimental data of Ref. [150] after normalization with the IRDFF-II evaluation of the ⁹³Nb(n, 2n)⁹²Nb^m monitor changed by 2%.

Figure 20.  (color online) Measured experimental cross section for the ⁹²Mo(n, α)⁸⁹Zr^m reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

As shown in Fig. 20, the present results are in good agreement with only the data reported in Ref. [150] within the experimental uncertainty. The measured cross section is in good agreement with the TALYS-1.96 calculations within the experimental uncertainty. The JENDL-5 and TENDL-2019 evaluations were higher than the measured cross section and better represent the experimental trend.

The measured cross section of the ⁹²Mo(n, α)⁸⁹Zr^g reaction at a neutron energy of 14.77 ± 0.17 MeV was compared with the experimental data from the EXFOR database, evaluated data from the TENDL-2019 and JENDL-5 libraries, and the TALYS-1.96 uncertainty calculations, as shown in Fig. 21. The experimental data reported in Refs. [72, 74, 121, 124, 127, 128, 140, 144, 148, 161, 162] were normalized with the IRDFF-II evaluation of the ²⁷Al(n, α)²⁴Na monitor reaction. The reported experimental data of Refs. [76, 138, 149] were normalized with the IRDFF-II evaluation of the ⁵⁶Fe(n, p)⁵⁶Mn reaction, and the change after normalization was 2%, 3%, and 10%, respectively.

Figure 21.  (color online) Measured experimental cross section for the ⁹²Mo(n, α)⁸⁹Zr^g reaction compared with EXFOR data, TALYS-1.96 calculations, and evaluated nuclear data.

As shown in Fig. 21, the present results are in good agreement with most of the reported data within the experimental uncertainty. The measured cross section is in good agreement with the TALYS-1.96 calculations and JENDL-5 and TENDL-2019 evaluations within the experimental uncertainty. However, the evaluations underestimated the experimental trend for the ⁹²Mo(n, α)⁸⁹Zr^g reaction.

In this study, the cross sections for the ⁷⁰Zn(n, 2n)⁶⁹Zn^m, ⁶⁸Zn(n, p)⁶⁸Cu^m, ⁶⁸Zn(n, α)⁶⁵Ni, ⁶⁷Zn(n, p)⁶⁷Cu, ⁶⁶Zn(n, p)⁶⁶Cu, ⁶⁶Zn(n, 2n)⁶⁵Zn, ⁶⁴Zn(n, 2n)⁶³Zn, ⁸⁹Y(n, 2n)⁸⁸Y, ⁸⁹Y(n, γ)⁹⁰Y^m, ¹⁰⁰Mo(n, 2n)⁹⁹Mo, ⁹⁸Mo(n, p)⁹⁸Nb^m, ⁹⁷Mo(n, p)⁹⁷Nb^g, ⁹⁶Mo(n, p)⁹⁶Nb, ⁹⁴Mo(n, 2n)⁹³Mo^m, ⁹²Mo(n, p)⁹²Nb^m, ⁹²Mo(n, α)⁸⁹Zr^m, and ⁹²Mo(n, α)⁸⁹Zr^g nuclear reactions at an incident neutron energy of 14.77 ± 0.17 MeV are reported with a detailed description of the uncertainty quantification and correlation matrix. The corrections due to the coincidence summing-effect and self-attenuation have been considered in γ-ray spectrometry analysis. Covariance analysis was performed to determine the uncertainty of the measured cross sections. The total uncertainty in the measured cross sections was found to be 4%–17%. The reported data in the EXFOR database was normalized with the latest IRDFF-II monitor data and ENDSF decay data for meaningful comparison. The present results agree with the experimental EXFOR data and evaluated data libraries.