Activation cross-sections for short-lived reaction products on hafnium isotopes induced by 1 – 20 MeV neutrons

. Results of new activation cross-section measurements for production of 178m1 Hf (T 1/2 = 4.0 s) and 179m1 Hf (T 1/2 = 18.67 s) are presented for the following reactions: 178 Hf(n,n ´ ) 178m1 Hf, 179 Hf(n,2n) 178m1 Hf, 180 Hf(n,3n) 178m1 Hf, 179 Hf(n,n ´ ) 179m1 Hf, and 180 Hf(n,2n) 179m1 Hf. The irradiations were carried out at the 7-MV Van de Graaff accelerator at EC-JRC, Geel. Neutrons in the 1-3 MeV energy range were produced via the 3 H(p,n) 3 He reaction. Deuteron beam and a deuterium gas target were used to produce 5 and 6 MeV neutrons. For the production of quasi-monoenergetic neutrons between 16 and 19.5 MeV the 3 H(d,n) 4 He reactions was employed. Both samples with natural composition and isotopic enrichment were employed to differentiate reactions leading to the same product. An automated pneumatic system was used for the sample irradiation, transport and radioactivity measurements. The radioactivity of the samples was determined by standard gamma-spectrometry using HPGe detector. The results obtained in the present work are compared with the data from other authors and TENDL-2017 evaluation.


Introduction
Neutron-induced reaction cross-sections on hafnium isotopes are important for research and nuclear applications. Hafnium is considered as a constituent of the control elements and structural materials of nuclear reactors due to its high absorption cross-section for slow neutrons, good mechanical properties and extremely high resistance to corrosion. Hafnium is an alloying element of low activation materials. Many of the neutron-induced reactions on hafnium isotopes populate metastable states. Experimental cross-sections provide a database for investigation of the sensitivity of nuclear models to level properties and decay schemes. Activation cross-section data for short-lived reaction products on hafnium isotopes are scarce. The results obtained in the present work are compared with the data from other authors from the EXFOR database [1] and the TENDL-2017 evaluation [2].

Experimental procedure
The neutron-induced reaction cross sections obtained in the present work have been measured by the activation technique.
The irradiations were carried out at the 7 MV Van de Graaff accelerator at EC-JRC Geel. Neutrons in the energy range 1.3-3.0 MeV were produced by a proton beam incident on a solid-state Ti-T target via the 3 H(p, n) 3 He reaction (Q = −0.764 MeV). The energies of the protons were between 2.2 and 3.9 MeV. A deuterium * Corresponding author: vsemkova@inrne.bas.bg gas target was used for production of neutrons with energies of 5 and 6 MeV via the 2 H(d,n) 3 He reaction (Q = 3.269 MeV) at incident deuteron energies of 2 and 3 MeV, respectively. The target cell was 4 cm in length and 4 cm in diameter with a 5 m molybdenum entrance foil. Quasi-monoenergetic neutrons with energies between 16.5 and 19.5 MeV were produced via the 3 H(d,n) 4 He reaction (Q = 17.59 MeV) at incident deuteron energies of 1, 2 and 3 MeV. The time profile of the neutron flux during the irradiations was monitored by a BF3 long counter operating in a multichannel scaling acquisition mode. The samples were irradiated at 0 degree relative to the incident ion beam at 16 mm distance from the back of the target. A pneumatic transport system was used for the sample transport between the irradiation and activity measurement positions. The sample transport was controlled by the DAQ2000 system developed at JRC-Geel. A multichannel scaler is used to register the neutron-flux time-profile, the time for the sample transport between irradiation and measurement positions as well as the counting period with a resolution of 0.1 s. Simultaneously the gamma-ray spectra from the HPGe detector were recorded. The time for the sample transport was 3.5(1) s. Irradiation times of 120 s and measurement time of 30 s were applied in case of 179m1 Hf production cross section measurements. Cycles of 30 s sample irradiations and 6 s activity measurements were carried out in the measurements of the reactions leading to 178m1 Hf in order to enhance the counting statistics. A single irradiation of 120 s and activity measurement of 30 s were performed for the 179m1 Hf production cross section measurements to minimise the interference between the 214.335 keV and 213.434 keV gammalines from the 179m1 Hf and 178m1 Hf decays. The contribution of the 178m1 Hf decay to the 214 keV gamma line intensity was considered as negligible since there were no other gamma-lines from the 178m1 Hf decay in the gamma-ray spectra under those irradiation and measurement conditions.
Hafnium consists of six isotopes. Both isotopically enriched and samples with natural isotopic composition were used due to interference between reactions on different isotopes leading to the same reaction product. The isotopic composition of the sample materials employed in the present work is given in Table 1. The isotopically enriched samples were prepared by canning about 100 mg of HfO2 powder in plexiglass containers with 10 mm inner diameter. Metallic disks of 10 mm diameter and 0.1 mm thickness were prepared from natural material of 97% hafnium and 3% zirconium. High purity metallic aluminium, niobium, iron, indium, and nickel foils of 10 mm diameter were used to determine the neutron flux and flux density distribution at different incident neutron energies.
The cross-sections for the studied reactions were determined relative to the 27 Al(n,) 24 Na reaction cross section above 16 MeV incident neutron energy. In the energy range below 6 MeV the 115 In(n,n´) 115m In reaction was used for the neutron flux determination. Data for both the 27 Al(n,) 24 Na and 115 In(n,n´) 115m In reaction cross sections were taken from the International Reactor Dosimetry and Fusion File (IRDFF-II) [3].
The mean energy and standard spread of the primary neutrons for the target-sample irradiation geometry were calculated by the NeuSDesc software [4] based on the reaction data and the stopping powers.
The neutron spectra from Ti-T target at 2 and 3 MeV incident deuteron energy consist of primary neutrons from the 3 H(d,n) 4 He reaction and a background of low energy neutron distribution due to scattering and secondary reactions with the target environment. The complexity and intensity of the low-energy neutron distributions depend on incident beam energy, emission angle and history of the target. The neutron flux energy distribution for each irradiation was determined by the method of spectral indexing [5] based on the TOF measurements of the laboratory neutron spectra and well-characterized standard activation cross-sections with different thresholds. The parameters of the fewgroup spectral representations were adjusted by the method of generalized least squares using the known response characteristics of the spectral-index reactions. The following reactions were used in the unfolding procedure: 27 Al(n,) 24 Na, 115 In(n,n´) 115m In, 58 Ni(n,p) 58 Co, 56 Fe(n,p) 56 Mn, 27 Al(n,p) 27 Mg, 93 Nb(n,2n) 92m Nb. Evaluated cross sections from the International Reactor Dosimetry and Fusion File (IRDFF-II) [3] for all reactions were used in the analysis.
The flux density distribution at each incident neutron energy was determined by a separate irradiation of a stack of monitor foils. The count rates from the BF3 long counter were used for the normalization of the neutron flux during the short irradiations.
The radioactivity of the reaction products was determined by gamma-ray spectrometry. Two HPGe detectors were used for the radioactivity measurement. One, attached to the pneumatic transport system, for the measurement of the short-lived reaction products and another for the measurements of the monitor reaction products. The decay data for 178m1 Hf [6] and 179m1 Hf [7] are given in Table 2. . Correction for coincidence summing effects was applied in the 178m1 Hf activity analysis, while for the 179m1 Hf analysis the correction factor is negligible. The measured production rate in the sample is determined by: where is decay constant; is the number of measured gamma-ray counts; is the gamma-ray emission probability; is the detector full-energy-peak efficiency; is the time of irradiation; is the time from the end of irradiation to the beginning of gammaray counting; is the gamma-ray counting time; are correction factors applied. The corrections were applied for the neutron beam intensity fluctuation during the irradiation and gamma-ray self-absorption.
There are more than two reactions contributing to the production of 178m1 Hf or 179m1 Hf in a hafnium sample with natural isotopic composition, including (n,) reaction induced by background neutrons. The cross sections for two (respectively more) interfering reactions were deduced by irradiating samples having different composition. The reaction rates PR 1 and PR 2 due to reactions 1 and 2 contributing to production rates PRx and PRy in the sample x and sample y were deduced by the following equations: were Nx1, Nx2, Ny1 and Ny2 are the number of target nuclei for reaction 1 in sample x, reaction 2 in sample x, reaction 1 in sample y, and reaction 2 in sample y. The obtained reaction rates were corrected for the background neutrons and divided by the neutron flux to determine the reaction cross sections.

Results and discussion
Results from the present measurements for the reactions leading to production of 178m1 Hf are shown in Figure 1 and the reactions leading to production of 179m1 Hf are shown in Figure 2. The data from this work are compared with the experimental data from the EXFOR database and the TENDL-2017 evaluation. (n,n´)  Hf(n,3n) 178m1 Hf reaction cross sections (Fig. 1). Measurements with enriched 177 HfO2 sample were performed as well in order to take into account the contribution of the 178m1 Hf activity from (n,) reaction induced by background neutrons on 177 Hf.

178 Hf
The 1147.388 keV isomeric state decays by 100% isomeric transition. Five gamma-lines are emitted in a cascade. The 325.557 keV gamma-line was used in the present measurements.
Our results agree within the standard uncertainties with TENDL-2017 evaluation for the 179 Hf(n,2n) 178m1 Hf and the 180 Hf(n,3n) 178m1 Hf reaction cross sections.
Our results for the 179 Hf(n,n´) 179m1 Hf reaction cross section are in agreement with the data of Shimizu et al. from 2004 [9] (EXFOR subentry 22838.012) and TENDL-2017 evaluation at low incident neutron energies, but higher than the TENDL-2017 evaluation above 16 MeV.