Cross Section Measurements of (n,x) Reactions at 17.9 and 18.9 MeV Using Highly Enriched Ge Isotopes

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Introduction
Neutron induced cross section measurements on Ge isotopes are of major importance regarding both practical applications as well as fundamental research in the Nuclear Physics field. Practical applications include dosimetry, nuclear medicine, astrophysical projects and reactor technology [1][2][3]. Ge is also widely used in detectors for γ-ray spectroscopy. Furthermore, Ge is a very important material in semi-conductor technology, thus the investigation of its behavior in a neutron field is of considerable significance in these practical applications. Concerning fundamental nuclear physics research, some (n,x) reaction channels on Ge isotopes produce residual nuclei in high spin isomeric states, the population of which is governed by the spin distribution of the continuum phase space and the spins of the discrete levels involved [1,4,5]. The experimental determination of cross sections in reaction channels that produce such residual nuclei, can play a very important role in the study of the compound nucleus evaporation. Neutron induced reactions on the five isotopes of Ge yield a plethora of different reaction channels, revealing very interesting systematics, crucial for the optimization of the input parameters of statistical model calculations. These optimized parameters should simultaneously reproduce the population of isomeric and normal states as well as many other competing reaction channels, * Corresponding author: sotirischasapoglou@mail.ntua.gr acting as a very important constraint to statistical model calculations. Furthermore, in the energy region above 15 MeV, pre-equilibrium effects in the de-excitation of the compound nucleus become more significant [1], rendering the provided data in this energy region very important. In the past, (n,x) reactions on Ge isotopes have been studied by the Nuclear Physics Group of the National Technical University of Athens [6,7], by means of the 2 H(d,n) 3 He reaction, producing quasi-monoenergetic neutron beams in the energy range 8-11.4 MeV. Furthermore, the existing experimental data in literature [8] for many reaction channels, cover a wide energy range, but they are discrepant and scarce especially in the region above 15 MeV. The majority of the aforementioned datasets implement nat Ge targets for the cross section measurements. In this case, for many reaction channels, the residual nucleus can be produced not only from the measured reaction, but also from "parasitic" or "interfering" reactions from neighboring isotopes that inevitably exist in the nat Ge target in their natural abundance. To compensate for these parasitic contributions, theoretical corrections accompanied by their own uncertainties should be applied. On the contrary, the use of isotopically enriched targets such as the ones implemented in this work, does not require such corrections, since no parasitic reactions take place, thus the provided data are more accurate and reliable.

Targets
The targets used in the present work for the determination of the neutron induced cross sections, have been provided by the CERN n_TOF collaboration. Five isotopically enriched GeO2 pellets of 70,72,73,74,76 Ge have been implemented with enrichment levels of 97.71, 96.59, 96.07, 95.51 and 88.46% respectively. The mass of each pellet was ~2 g. Each pellet was glued on a thin mylar foil, which in turn was glued on an Al ring. High purity Al metallic reference foils were also used for the determination of the neutron flux in the Ge targets. All Ge targets and Al reference foils had a diameter of 20 mm.

Neutron facility
The irradiations were carried out at the neutron production facility of the 5.5 MV Tandem Van de Graaf accelerator of N.C.S.R. "Demokritos" [9,10] in Athens, Greece. The quasi-monoenergetic neutron beams were produced via the 3 H(d,n) 4 He reaction. Deuteron beams impinged on a solid Ti-tritiated (TiT) target of 373 GBq activity. In front of the solid TiT target a 10 μm Mo foil was placed, where the deuteron beam lost part of its energy. The TiT target consists of a 2.1 mg/cm 2 Titritiated layer on a 1 mm thick Cu backing for good heat conduction. The flange with the tritium target assembly was air cooled during the deuteron irradiation. The monoisotopic Ge pellets and reference foils were placed at a distance of ~ 2.4 cm from the flange with the Ti-T target, thus limiting the angular acceptance to ±19•, where the neutron beam can practically be considered as monoenergetic according to the reaction kinematics.

Irradiations
The duration of the irradiations varied between 5 and 25 hours, depending on the half-life of the measured isotope, while the fluctuations of the neutron beam were continuously monitored with a BF3 detector. This detector was placed at ~3 m distance from the neutron producing target, at an angle with respect to the neutron beam, to minimize the neutron scattering. The corresponding spectra were saved at regular time intervals (~300 s) in a separate ADC during the irradiation in order to use the beam instabilities in the offline analysis to correct for the decay of the product nuclei during the irradiation. In each irradiation, two Al foils were used to obtain the absolute value of the neutron flux using the well-known 27 Al(n,α) 24 Na reference reaction.
After each irradiation, the induced radioactivity of the samples was measured with the use of HPGe detectors properly shielded and calibrated with a 152 Eu source placed at the same position as the irradiated samples. The activity measurements of the Ge and reference samples were carried out at a distance of 10 cm from the detector window, to avoid significant pileup or true coincidence summing-effect corrections. The yield of the characteristic transitions of each reaction was corrected for self-absorption and counting geometry of the emitted γ-rays in the irradiated sample, using Monte Carlo simulations.

Cross section calculation
The cross section calculation for the reactions involved in this work, is based on the following formula: Where the subscripts "ref" and "tar" refer to the reference foils and measured targets, respectively. Concerning the rest of the factors in eq. (1): • σ is the cross section measured in barns. For the 27 Al(n,α) 24 Na reference reaction, the cross section value was obtained from the ENDF/B-VIII.0 library [11] • is the γ-ray peak integral from the spectrum obtained by the HPGe detector. The obtained γ-ray spectra (such as the one shown in Fig. 1 for the irradiation of the 73 Ge sample), were analyzed via the "Tv" software [12] • is the absolute efficiency of the HPGe detector at the characteristic γ-ray energy • is the γ-ray intensity • is a correction factor for the de-excitation of the residual nuclei during the cooling time (t 1 ) between the end of the irradiation and the start of the measurement in the HPGe detector, and during the measurement itself in front of the HPGe detector (t 2 ). This correction factor is given by the expression D = exp(−λt 1 is a correction factor for the decaying nuclei produced during the irradiation time (tb), taking into account the fluctuations of the neutron beam. This correction factor is given by the where the factor f(t) represents the counts obtained from the BF3 detector, stored in dt time intervals.
• is the number of total nuclei of the measured isotope in the target • / is the neutron flux ratio for the reference foil and the measured target respectively. This ratio was calculated via the combined use of NeusSDesc [13, 14] and MCNP5 [15] Monte Carlo codes. Fig. 1 A typical γ-ray spectrum obtained from a HPGe detector. The most intense γ-rays from the 73 Ga residual nucleus following the 73 Ge(n,p) 73 Ga reaction, are displayed in the spectrum. The total number of channels in the spectrum was 4096, with the keV/channel being 0.73.

Monte Carlo simulations
Monte Carlo simulations were performed by means of the NeuSDesc and MCNP5 codes, in order to calculate the propagation of the neutron beam through the consecutive Ge targets and reference foils. Firstly, the neutron source was produced as an SDEF card from the NeuSDesc code, taking into account the physical and geometrical characteristics of the neutron producing target. Then this SDEF card was fed into the MCNP5 code, in which the detailed geometry of the experiment was described, as seen in Fig. 2. Finally, the neutron flux was calculated in every Ge target and reference foil of the experiment. A typical MCNP5 output can be seen in Fig. 3., where the neutron flux was scored in every Al reference foil (Al1 and Al2) as well as in the two Ge targets ( 72 Ge and 74 Ge) that were simultaneously irradiated. The shape of the neutron flux, as seen in Fig. 3, is not purely monoenergetic, having a mean value 17.9 MeV at the nominal neutron energy and energy dispersion of ±0.3MeV. It is also followed by a low enery parasitic neutron tail with intensity lower by 2-3 orders of magnitude. Since the reactions studied in this work have thresholds in the MeV region, this low energy neutron tail does not interfere with the measured yield. The factor Φ ref /Φ tar of eq. 1 is calculated from the ratio of the integrals of the main peaks of the neutron flux for the reference foil and measured target, respectively.

Preliminary results & discussion
In this section, the preliminary results of the 70 Ge(n,2n) 69 Ge, 76 Ge(n,2n) 75 Ge, 73 Ge(n,p) 73 Ga, 72 Ge(n,p) 72 Ga, 73 Ge(n,d/np) 72 Ga, 74 Ge(n,d/np) 73 Ga, 74 Ge(n,α) 71m Zn, 72 Ge(n,α) 69m Zn, 73 Ge(n,nα) 69m Zn reaction cross sections will be presented. For clarity reasons, in all the relevant figures (Fig. 4, Fig. 5, Fig. 6, Fig. 7, Fig. 10, Fig. 11), the experimental points retrieved from the EXFOR database are presented in grey. Only the ones discussed in the manuscript are presented in blue or black. The preliminary cross section results of the 70 Ge(n,2n) 69 Ge reaction can be seen in Fig. 4 for neutron energies of 17.9 and 18.9 MeV. The residual nucleus 69 Ge decays with a half-life of 39.05h to 69 Ga which deexcites to its ground state through the characteristic gamma-rays 1106.7, 574.1 and 871.9 keV with intensities 36%, 13.3% and 11.9%, respectively. The cross section points for both energies were calculated from the weighted average of the cross sections derived from the 574.1 and 871.9 keV lines which produced similar results, while the cross section value derived from the 1106.7 keV γ-ray was lower by ~12% and was neglected from the calculation. For the 17.9 MeV cross section point, the data of the present work seem to be in good agreement with the dataset of Bormann et al. [16] and Prestwood et al. [17] as well as with the EAF 2010 [18] evaluation library. The 18.9 MeV cross section point seems to be in good agreement with the ROSFOND 2010 [19], ENDF/B-VIII.0 [11], JEFF 3.3 [20], JENDL 4.0 [21] and TENDL 2019 [22]. Two general trends of the data appear for neutron energies above 14 MeV. These very large discrepancies could be attributed to the large errors of the γ-ray intensities that are found in literature and reach up to 13%. More experimental points in the energy region between 14 and 20 MeV are needed to solve these discrepancies. The preliminary cross section results of the 76 Ge(n,2n) 75 Ge reaction can be seen in Fig. 5   The preliminary cross section results of the 72 Ge(n,p) 72 Ga reaction can be seen in Fig. 6 for neutron energies of 16.4 and 17.9 MeV. The produced nucleus 72 Ga decays with a half-life of 14.1 h to 72 Ge, whose deexcitation to its ground state proceeds through the 834.1, 629.9 and 894.33 keV gamma-rays of 95.45%, 26.13% and 10.14% intensity, respectively. The cross-section results were calculated from the weighted average of the three aforementioned γ-rays, and seem to be in good agreement with the lower trend of existing data, also followed by Konno et al. [24] (that also used an enriched target) as well as with the ENDF/B-VIII.0 and JENDL 4.0 evaluation libraries. There are no existing experimental data above 15 MeV except the ones from Hoang et al. [25], while the data in lower energies exhibit discrepancies among them. In this reaction, two general trends are followed from the different evaluation libraries. These discrepancies could possibly be attributed to the different methodologies followed for the subtraction of the parasitic reaction contribution in the case of the nat Ge target, used in most of the experiments.  [24] (that also used an enriched target) within their experimental uncertainties. The trend of the JENDL 4.0 and ENDF/B-VIII.0 evaluations follow the data of the present work but seem to be slightly overestimated. There is also lack of experimental data above 14 MeV, while very large discrepancies exist even at lower energies. These discrepancies can be attributed to the fact that the vast majority of the cross section data found in literature were measured with the use of a nat Ge target, so theoretical corrections should be applied for the subtraction of parasitic reactions from neighboring isotopes found in the nat Ge target in their natural abundances, that lead to the formation of the same residual nucleus, acting as a contamination to the measured yield. The accuracy of the methodologies followed for these corrections should be checked, especially at neutron energies above 14 MeV.  [26] and TENDL 2019 [22] libraries. This reaction is very hard to study with the use of nat Ge target due to its low cross section and low natural abundance of the 73 Ge isotope. The preliminary results for the 74 Ge(n,d/np) 73 Ga reaction are presented in Fig. 9 for neutron energies of 16.4, 17.9 and 18.9 MeV. The decay of the residual nucleus 73 Ga is described in detail in section 4.4. This is another challenging reaction to study with a nat Ge target due to the significant contribution of the 73 Ge(n,p) 73 Ga reaction to the measured yield. In the case of isotopically enriched targets, this contribution can be considered negligible The 74 Ge(n,np) and the 74 Ge(n,d) reactions produce the same residual nucleus ( 73 Ga), so the measured cross section via the activation method refers to the sum of both reaction channels. The sum of these cross sections for the evaluation libraries JEFF 3.3 [20], JENDL 3.3 [26] and TENDL 2019 [22] are plotted in Fig. 9  The preliminary results for the 72 Ge(n,α) 69m Zn reaction are presented in Fig. 10

The 74 Ge(n,α) 71m Zn reaction
The preliminary results for the 74 Ge(n,α) 71m Zn reaction can be seen in Fig. 11 Fig. 11 The 74 Ge(n,α) 71m Zn cross section results of the present work (red solid points), alongside with previous EXFOR data and evaluation curves (continuous and dashed lines).

The 73 Ge(n,nα) 69m Zn reaction
The preliminary results for the 73 Ge(n,nα) 69m Zn reaction along with evaluation libraries can be seen in Fig. 12, displaying large uncertainties reaching up to more than 70% in some energies. The residual nucleus 69 Zn is produced both in its 1/2ground state (T1/2 = 56.4 min) and its metastable 9/2 + (T1/2 = 13.76h) state, and its decay is described in section 4.7. There were no other experimental data found in literature since this is a very challenging reaction to study with a nat Ge target (which are the ones most commonly found in literature) due to the low natural abundance of the 73 Ge isotope (7.76 %) and the low cross section of this reaction.  Fig. 12 The 73 Ge(n,nα) 69m Zn reaction results of the present work (red solid points), alongside with previous EXFOR data and evaluation curves (continuous and dashed lines).

Summary & conclusions
The cross sections of the 70 Ge(n,2n) 69 Ge, 76 Ge(n,2n) 75 Ge, 73 Ge(n,p) 73 Ga, 72 Ge(n,p) 72 Ga, 73 Ge(n,d/np) 72 Ga, 74 Ge(n,d/np) 73 Ga, 74 Ge(n,α) 71m Zn, 72 Ge(n,α) 69m Zn and 73 Ge(n,nα) 69m Zn reactions have been measured at neutron energies of 16.4, 17.9 and 18.9 MeV employing highly enriched Ge targets that were provided by the CERN n_TOF collaboration and the preliminary results of these cross sections are presented. The experimental cross sections were measured at neutron energies where only a few and often discrepant data exist in literature. The use of enriched isotopes produce more accurate cross section results in comparison with the ones obtained from nat Ge targets. In the case of nat Ge targets, neutron induced reactions in neighboring isotopes that are found in the nat Ge target in their natural isotopic abundance, could lead to the production of the same residual nucleus, as the one produced from the measured reaction, acting as a contamination. In this scope, theoretical corrections, that bear their own uncertainties, should be applied. The contribution of these parasitic reactions becomes larger for energies above 14 MeV where very few experimental data points exist. Enriched targets on the other hand, do not suffer from such contaminations, enabling accurate measurements even at higher neutron energies above 14 MeV. These accurate cross section results in a plethora of reaction channels on Ge isotopes could act as a very important constraint in statistical model calculations, via the simultaneous reproduction of all of these channels, using the same set of input parameters. These parameters could also be applied in other medium-heavy nuclei in the same mass region. As a consequence, despite their high cost and difficulty to obtain, cross section measurements with isotopically enriched targets in key medium-heavy even-even nuclei (such as Ge with many natural isotopes that could lead to parasitic reactions) and in strategical energies could significantly improve the accuracy of future evaluation curves and statistical model calculations.